tag:blogger.com,1999:blog-72411163040059660822024-02-20T20:45:05.981-08:00MF MatemáticaBlog dedicado a pessoas que possuem dificuldade em matemática, com conteúdo exclusivo e totalmente gratuito.
Assista vídeo-aulas, faça o download de materiais de apoio, exercícios, e tire suas dúvidas.
Obrigado pela visita!Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.comBlogger86125tag:blogger.com,1999:blog-7241116304005966082.post-48549385874515889952014-11-22T14:12:00.001-08:002014-11-22T14:19:44.697-08:00Dúvida da Maria Pinheiro<span style="font-family: Arial, Helvetica, sans-serif;"><span style="background-color: white; color: #222222; font-size: 13px;"><br /></span>
</span><br />
<div style="font-size: 14px;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJs-cyjtaLeed8bH2VtUddVT2mn7DhpJed7ui6bB0uQUyHnJ1F_yq13LiroFVC6N8O_sO5jTqVwGYZSevh8B0R3NNuvqpVfHYEiGnKqdmzlbXuXGf_lW9TjLfd_GbCiUIEr5YfFWkck2A/s1600/duvida2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJs-cyjtaLeed8bH2VtUddVT2mn7DhpJed7ui6bB0uQUyHnJ1F_yq13LiroFVC6N8O_sO5jTqVwGYZSevh8B0R3NNuvqpVfHYEiGnKqdmzlbXuXGf_lW9TjLfd_GbCiUIEr5YfFWkck2A/s1600/duvida2.jpg" /></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;">Olá Marcelo, tudo bem? </span></div>
<div style="font-size: 14px;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="font-size: 14px;">
<span style="font-family: Arial, Helvetica, sans-serif;">Tenho uma dúvida:</span></div>
<div style="font-size: 14px;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="font-size: 14px;">
<div style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;">Uma piscina com capacidade de 8000 litros está com 65% de sua capacidade. Para esvazia-la será usada uma bomba de sucção de 130 litros por minuto. Quanto tempo será necessário para esvaziar a piscina? </span></div>
</div>
<div style="font-size: 14px;">
<div style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
</div>
<div style="font-size: 14px;">
<span style="font-family: Arial, Helvetica, sans-serif;">Abraços.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Maria</span></div>
<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><br /></span>
<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"></span><br />
<a name='more'></a><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;">-----------------------------------------------------------------------------------------------------------------------------------------------------------------</span>
<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 13px;"><br /></span>
<span style="background-color: white; color: #222222; font-family: arial, sans-serif;">Olá Maria, tudo bem?</span><br />
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
<br /></div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
<br /></div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
Primeiro, vamos calcular quantos litros são referentes a 65%. Para isso, basta fazer 8000*65/100 = 5200 litros.</div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
<br /></div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
<br /></div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
Daí fazemos a regra de três:</div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
<br /></div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
1 minuto ------- 130 litros</div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
<br /></div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
x minutos ------ 5200 litros</div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
<br /></div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
<br /></div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
130x = 5200</div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
<br /></div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
x = 5200/130 = 40 minutos</div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
<br /></div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
<br /></div>
<div style="background-color: white; color: #222222; font-family: arial, sans-serif;">
Portanto, serão necessários 40 minutos para esvaziar a piscina.<br />
<br />
Um abraço! Até mais!</div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com1tag:blogger.com,1999:blog-7241116304005966082.post-32341487473183374432014-11-22T13:12:00.000-08:002014-11-22T14:12:34.367-08:00Nova vídeo-aula no ar! Operações com Frações.Pessoal, finalmente consegui fazer uma nova aula! :)<br />
<br />
Qualquer dúvida ou sugestão, comentem aí!<br />
<br />
<div style="text-align: center;">
<iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/bSNvxqIi8x4" width="560"></iframe><br /></div>
<br />
<a href="http://tinyurl.com/ocvzgu3" style="font-size: x-large;" target="_blank">Vejam aqui </a>alguns exercícios resolvidos de simplificação de frações.<br />
<br />
<br />
Valeu gente, até mais!Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com0tag:blogger.com,1999:blog-7241116304005966082.post-5611861981379877732012-02-01T09:01:00.000-08:002013-11-01T16:32:28.865-07:00Dúvida do Eliel<div style="text-align: center;">
<span style="clear: left; float: left; font-family: Arial, Helvetica, sans-serif; margin-bottom: 1em; margin-right: 1em;"><img alt="duvida2" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TO8ot7vYjPI/AAAAAAAAA9c/grUUwekMFDQ/duvida2_thumb.jpg?imgmax=800" />
</span></div>
<div style="text-align: center;">
<div style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif; text-align: left;">Olá Marcelo, ajude-me nesta questão do concurso do INSS de 2005.</span></div>
</div>
<div style="text-align: left;">
<div style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
</div>
<div style="text-align: left;">
<div style="text-align: justify;">
<i><span style="font-family: Arial, Helvetica, sans-serif;">Um prêmio em dinheiro foi dividido entre 3 pessoas: a primeira recebeu 1/4 do valor do prêmio, a segunda recebeu 1/3 e a terceira ganhou R$ 1000,00. Então, o valor desse prêmio, em reais, era de:</span></i></div>
</div>
<div style="text-align: left;">
<div style="text-align: justify;">
<i><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></i></div>
</div>
<div style="text-align: left;">
<div style="text-align: justify;">
<i><span style="font-family: Arial, Helvetica, sans-serif;">a) R$ 2400,00</span></i></div>
</div>
<div style="text-align: left;">
<div style="text-align: justify;">
<i><span style="font-family: Arial, Helvetica, sans-serif;">b) R$ 2200,00</span></i></div>
</div>
<div style="text-align: left;">
<div style="text-align: justify;">
<i><span style="font-family: Arial, Helvetica, sans-serif;">c) R$ 2100,00</span></i></div>
</div>
<div style="text-align: left;">
<div style="text-align: justify;">
<i><span style="font-family: Arial, Helvetica, sans-serif;">d) R$ 1800,00</span></i></div>
</div>
<div style="text-align: left;">
<div style="text-align: justify;">
<i><span style="font-family: Arial, Helvetica, sans-serif;">e) R$ 1400,00</span></i></div>
<div style="text-align: justify;">
<i><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></i>
<i><span style="font-family: Arial, Helvetica, sans-serif;"></span></i></div>
<a name='more'></a><i><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></i></div>
<div style="text-align: left;">
<span style="background-color: white; color: #555555; line-height: 19px; text-align: justify;"><span style="font-family: Arial, Helvetica, sans-serif;">_______________________________________________________________________</span></span></div>
<div style="text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;">Olá Eliel,</span></div>
<div style="text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;">Este problema não é difícil. Basta saber como trabalhar com frações. Vamos lá:</span></div>
<div style="text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="text-align: left;">
</div>
<span style="font-family: Arial, Helvetica, sans-serif;">Primeiramente, temos que montar a igualdade. Sabemos que, somando as partes das três pessoas, encontramos o valor total do prêmio. Sendo este total x, temos:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">1/4x + 1/3x + 1000 = x</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Agora, basta isolar o x para encontrar seu valor. Veja como eu fiz:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">7/12x + 1000 = x (somei 1/4x com 1/3x)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">7/12x - x + 1000 = 0 (passei o x para o outro lado)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">-5/12x = -1000 (subtraí x de 7/12x)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">5/12x = 1000 (multipliquei ambos os lados por -1)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">5x = 12000 ("passei" o 12 do denominador multiplicando)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">x = 12000/5 ("passei" o 5 dividindo)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">x = 2400</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Pronto! Encontramos o resultado. Portanto, a alternativa correta é a letra a).</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Se ainda tiver dúvidas sobre este tipo de problema, pode consultar a seção <a href="http://www.mfmatematica.blogspot.com/search/label/Resolvendo%20Problemas" target="_blank">Resolvendo Problemas</a>.</span><br />
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Um abraço, e boa sorte nos concursos!</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Marcelo Flora</span><br />
<br />
<div align="justify" style="background-color: white; border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #555555; line-height: 19px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
</div>
<div style="color: black; line-height: normal; text-align: left;">
<span style="color: #555555; line-height: 19px; text-align: justify;"><span style="font-family: Arial, Helvetica, sans-serif;">_______________________________________________________________________</span></span></div>
<br />
<div style="background-color: white; border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #555555; font-family: Arial, sans-serif; font-size: 13px; line-height: 19px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">
<span style="font-family: Arial; font-size: small; margin-bottom: 0pt; margin-left: 0pt; margin-right: 0pt; margin-top: 0pt; padding-bottom: 0pt; padding-left: 0pt; padding-right: 0pt; padding-top: 0pt;">Saiba como enviar suas dúvidas. </span><a href="http://mfmatematica.blogspot.com/p/envie-suas-duvidas.html" style="border-bottom-width: 0px; border-color: initial; border-image: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #0066cc; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;" target="_blank"><span style="font-family: Arial; font-size: small; margin-bottom: 0pt; margin-left: 0pt; margin-right: 0pt; margin-top: 0pt; padding-bottom: 0pt; padding-left: 0pt; padding-right: 0pt; padding-top: 0pt;">Clique aqui!</span></a></div>
<br />Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com3tag:blogger.com,1999:blog-7241116304005966082.post-10608068266843433522010-11-25T19:26:00.001-08:002013-11-01T16:52:18.207-07:00Dúvida do Antônio<div align="justify">
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/TO8otLKw-rI/AAAAAAAAA9Y/5SsDlWKYsls/s1600-h/duvida2%5B1%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="duvida2" border="0" height="179" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TO8ot7vYjPI/AAAAAAAAA9c/grUUwekMFDQ/duvida2_thumb.jpg?imgmax=800" style="background-image: none; border: 0px; display: block; float: none; margin-left: auto; margin-right: auto; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left;" title="duvida2" width="172" /></a><a href="http://lh4.ggpht.com/_7wGgh4VGq1A/TO8otLKw-rI/AAAAAAAAA3E/rtKLX1e2k2o/s1600-h/duvida2%5B4%5D.jpg"><span style="font-family: Arial; font-size: small;"></span></a><span style="font-family: Arial; font-size: small;"></span></div>
<div style="text-align: justify;">
<span style="font-family: Arial;">Marcelo bom dia!</span></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="text-align: justify;">
<span style="font-family: Arial; font-size: small;">Meu nome é Antônio e estou tentado resolver este problema, só que de todo jeito que faço só dá 6, e não tem este resultado nas possíveis respostas. </span></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<span style="font-family: Arial; font-size: small;">Desde já agradeço.</span></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="text-align: justify;">
<em><span style="font-family: Arial; font-size: small;">O dono de uma pizzaria pretende colocar um painel na frente de seu estabelecimento, de dimensões 4 m por 5 m, que deve ser pintado em 30% de sua área. Da área pintada, 12% deve ser na cor azul, que será o nome da pizzaria. Sabendo que cada tubo de tinta possibilita pintar 1200 cm<sup>2</sup>, o número de tubos de tinta azul necessários é:</span></em></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<em><span style="font-family: Arial; font-size: small;"></span></em></div>
<div style="text-align: justify;">
<em><span style="font-family: Arial; font-size: small;">A) 8 </span></em><em><span style="font-family: Arial; font-size: small;">B) 7 </span></em><em><span style="font-family: Arial; font-size: small;">C) 5 </span></em><em><span style="font-family: Arial; font-size: small;">D) 4</span></em></div>
<div style="text-align: justify;">
</div>
<a name='more'></a><br />
<br />
<div align="justify">
<span style="font-family: Arial; font-size: small;">_______________________________________________________________________</span></div>
<br />
<div align="justify">
<span style="font-family: Arial; font-size: small;">Olá pessoal, tudo bem com vocês?</span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<br />
<div align="justify">
<span style="font-family: Arial; font-size: small;">Bom, como já faz um tempo que não posto nada no blog (estou estudando pro vestibular, se lembram?), vou aproveitar esta dúvida para dar as caras por aqui e matar a saudade.</span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<br />
<div align="justify">
<span style="font-family: Arial; font-size: small;">Mas pode ficar tranquilo Antônio, o resultado é 6 mesmo. Vou mostrar o porquê.</span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">_______________________________________________________________________</span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<br />
<div align="justify">
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TO8ouVNuLJI/AAAAAAAAA3M/6_5zXZ_AlqY/s1600-h/pizzaria%5B3%5D.jpg"><span style="font-family: Arial; font-size: small;"><img align="left" alt="pizzaria" border="0" height="240" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TO8ou49tYOI/AAAAAAAAA3Q/oNB9k_82oJM/pizzaria_thumb%5B1%5D.jpg?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: inline; float: left; margin: 0px 9px 0px 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="pizzaria" width="235" /></span></a></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">Para descobrirmos quantos tubos de tinta azul foram gastos na pintura do nome da pizzaria, precisamos calcular a área utilizada nesta pintura, e depois dividir pela capacidade de cada tubo. Antes, porém, é necessário encontrar os percentuais apresentados no exercício.</span></div>
<br />
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">Primeiro, vamos calcular a área total do painel. Uma dica é converter as unidades para cm, e utilizar potências de dez. Isto facilita as contas. </span></div>
<br />
<div align="justify">
<span style="font-family: Arial; font-size: small;">Lembre-se que:</span></div>
<br />
<div align="justify">
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/TO8uvWloGJI/AAAAAAAAA9k/D2PFrNHomiE/s1600-h/clip_image00282.gif"><span style="font-family: Arial; font-size: small;"></span></a><a href="http://lh5.ggpht.com/_7wGgh4VGq1A/TO8uvWloGJI/AAAAAAAAA9s/kWpkI7XniGI/s1600-h/clip_image00283.gif"><img alt="clip_image002[8]" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVQVP29KzxscTD4cfG0h9gl77RGjWWosOglze5QHi78kP-O3UvJRboiUkAFMTWHN8TlXOvLvI7V5FFgD8MS3juhRJ8poyT4Q3uL3kkvkYUGUMWnbsafmPv_bFfcjdXtDdCWmfsTAk0gqE/?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="clip_image002[8]" width="273" /></a></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">Portanto, <br /> </span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5DbD33PQpQJgb0VM4nSjwNwPX2Gj7lUxiL4XnE_51qDHpi5NKiKDUKr_VpR9dMNWe-48FsPMW-4vkui89HTV2SX9LDSDi-86JYR4Q450ix9N13QOMEsuEtsrVY3VNnq7QTQgsF7qBUk0/s1600-h/clip_image002%5B18%5D%5B4%5D.gif"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[18]" border="0" height="25" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TO8oxg_-vmI/AAAAAAAAA3o/exjD4HYdSQ0/clip_image002%5B18%5D_thumb%5B2%5D.gif?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="clip_image002[18]" width="390" /></span></a></div>
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<br />
<span style="font-family: Arial; font-size: small;">Agora, encontraremos os 30% da área total que foram pintados (região em amarelo na figura acima), utilizando para isso uma regra de três simples:</span><br />
<br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<div align="center">
<table align="center" border="1" cellpadding="0" cellspacing="0"><tbody>
<tr> <td width="101"><div align="center">
<b><span style="font-family: Arial; font-size: small;">Área</span></b></div>
</td> <td width="101"><b><span style="font-family: Arial; font-size: small;">Percentual</span></b></td> </tr>
<tr> <td width="101"><div align="center">
<span style="font-family: Arial;"><span style="font-size: small;">2.10<sup>5</sup> cm<sup>2</sup></span></span></div>
</td> <td width="101"><div align="center">
<span style="font-family: Arial; font-size: small;">100</span></div>
</td> </tr>
<tr> <td width="101"><div align="center">
<span style="font-family: Arial; font-size: small;">x</span></div>
</td> <td width="101"><div align="center">
<span style="font-family: Arial; font-size: small;">30</span></div>
</td> </tr>
</tbody></table>
</div>
<span style="font-family: Arial; font-size: small;"></span><br />
<br />
<div align="center">
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/TO8ox1uf8VI/AAAAAAAAA3s/G0XLQwdxcWE/s1600-h/clip_image002%5B22%5D%5B2%5D.gif"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[22]" border="0" height="26" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TO8oysruk-I/AAAAAAAAA3w/FF9yV2upT8c/clip_image002%5B22%5D_thumb.gif?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: inline; margin: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="clip_image002[22]" width="196" /></span></a></div>
<br />
<div align="center">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6tBv0vSLSfy5uy0YSn5tRe-TaR9b_9b3UbOkWKkJNiYWFQT5w6cS4SJUNxbiHJRsie93QOWiGUDlIgQIp1HEeV3eyMnpsPT5JXVb59-K4ew7JxOwvNQFPb6pct6t0a_gLWkYQ4z5vPxs/s1600-h/clip_image004%5B4%5D%5B2%5D.gif"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004[4]" border="0" height="25" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TO8ozmS7b3I/AAAAAAAAA34/kjKdM4BVQ-U/clip_image004%5B4%5D_thumb.gif?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: inline; margin: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="clip_image004[4]" width="143" /></span></a></div>
<br />
<div align="center">
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/TO8o06Z7KdI/AAAAAAAAA38/AaWKRyC_Qv4/s1600-h/clip_image006%5B4%5D%5B2%5D.gif"><span style="font-family: Arial; font-size: small;"><img alt="clip_image006[4]" border="0" height="48" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcq4xUjmH93TGgV3UYMzsMdWTPMEG1ip9rgwAHkHBgm971-HJPv_thWkEPE-amGwPV9YA0ppCdT6ftNKVns7XmsN1g6KGKG1A8-PHPsPlrlqKfoi-c2nVKvlQpeyb8DFZVr_2bla8Ou3Q/?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: inline; margin: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="clip_image006[4]" width="122" /></span></a></div>
<br />
<div align="center">
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/TO8o1wcRPzI/AAAAAAAAA4E/0ZEJKmtHPpA/s1600-h/clip_image008%5B4%5D%5B2%5D.gif"><span style="font-family: Arial; font-size: small;"><img alt="clip_image008[4]" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcy92Tge6TMk7VJnQf-qZX45Ux_bU0gvh_gQ80WX8XrwocpUKuYc1QYHk5QpPW8AVkhlRzsBA80PyrgI2j5h5oWyhi4xsWbJcVFTkkt9CwVJkq8jV3hWSi7TUPJYHGSiVJOtKFoQk-uyQ/?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: inline; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="clip_image008[4]" width="118" /></span></a></div>
<br />
<div align="center">
<span style="font-family: Arial; font-size: small;"></span></div>
<span style="font-family: Arial; font-size: small;"></span><br />
<br />
<div align="justify">
<span style="font-family: Arial; font-size: small;">O próximo passo é encontrar a área pintada em azul, que corresponde a 12% da área anteriormente calculada. O procedimento é análogo ao anterior:</span></div>
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<div align="center">
<table align="center" border="1" cellpadding="0" cellspacing="0" style="width: 204px;"><tbody>
<tr> <td width="101"><div align="center">
<b><span style="font-family: Arial; font-size: small;">Área</span></b></div>
</td> <td width="101"><b><span style="font-family: Arial; font-size: small;">Percentual</span></b></td> </tr>
<tr> <td width="101"><div align="center">
<span style="font-family: Arial;"><span style="font-size: small;">6.10<sup></sup><sup></sup><sup>4</sup> cm<sup>2</sup></span></span></div>
</td> <td width="101"><div align="center">
<span style="font-family: Arial; font-size: small;">100</span></div>
</td> </tr>
<tr> <td width="101"><div align="center">
<span style="font-family: Arial; font-size: small;">x</span></div>
</td> <td width="101"><div align="center">
<span style="font-family: Arial; font-size: small;">12</span></div>
</td> </tr>
</tbody></table>
</div>
<div align="center">
<span style="font-family: Arial; font-size: small;"></span></div>
<br />
<div align="center">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZJPFXxcj24jo5TKOTZnapz23Tcd2Mtj3DaCleS-ME9vWjVQvN9lPWRZsFbaSmSR6vXQ6jeKIAmL_99Z8XAE11gG-1M8u9Kel57JHWTQI6ZuYy2aF9ollAgT3wXSsfQb2SswxOtaXOXPA/s1600-h/clip_image002%5B26%5D%5B2%5D.gif"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[26]" border="0" height="25" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TO8o3z_u8LI/AAAAAAAAA4Q/5CFFKpI2Djg/clip_image002%5B26%5D_thumb.gif?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: inline; margin: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="clip_image002[26]" width="178" /></span></a></div>
<br />
<div align="center">
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/TO8o4sg6-EI/AAAAAAAAA4U/6rpdHcT5S-4/s1600-h/clip_image004%5B8%5D%5B2%5D.gif"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004[8]" border="0" height="25" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TO8o5aQYQxI/AAAAAAAAA4Y/IX2wJpG5--s/clip_image004%5B8%5D_thumb.gif?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: inline; margin: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="clip_image004[8]" width="154" /></span></a></div>
<br />
<div align="center">
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/TO8o5gXSuFI/AAAAAAAAA4c/XMSUv-s0FXI/s1600-h/clip_image006%5B8%5D%5B2%5D.gif"><span style="font-family: Arial; font-size: small;"><img alt="clip_image006[8]" border="0" height="48" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgomclg0PXeGpWsVKJsnOByndxlqNqYAP-pOzriY1EE_LGS-f53K4CO3_1smspTwm4PBau82NTltkw5fxMid9GBuMsr5djL6cUsjZQtyY0ARM4SrbG-SMsQ2HIC0d6yY_L8hj43d4k1NPY/?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: inline; margin: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="clip_image006[8]" width="132" /></span></a></div>
<br />
<div align="center">
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/TO8o6lNoajI/AAAAAAAAA4k/QJLf5FnAFF4/s1600-h/clip_image008%5B8%5D%5B2%5D.gif"><span style="font-family: Arial; font-size: small;"><img alt="clip_image008[8]" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkQmVVFW8vvnI8pm8iYaRBUQ7Pmg9sYqTitcPyzq3K2bEiWA74C-ePlUetAApvguHO13oScqNNq-d_oQt-8sZ8DrxM9FCD5yA2Dj9yv0ldkUmlfeMcFAv4csmF6v1BhvjZZikS7jHzq_k/?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: inline; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="clip_image008[8]" width="129" /></span></a></div>
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<div align="justify">
<span style="font-family: Arial; font-size: small;">Pronto! Descobrimos a área pintada em azul. Agora basta dividir pela capacidade de cada tubo (1200 cm<sup>2</sup>):</span></div>
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/TO83EVbPC_I/AAAAAAAAA88/-I27NvRoTVY/s1600-h/clip_image002%5B5%5D.gif"><img alt="clip_image002" border="0" height="49" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TO83ExLplLI/AAAAAAAAA9E/WXtm9UdXGt4/clip_image002_thumb%5B2%5D.gif?imgmax=800" style="background-image: none; border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto; padding-left: 0px; padding-right: 0px; padding-top: 0px;" title="clip_image002" width="332" /></a><br />
<br />
<br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<div align="justify">
<span style="font-family: Arial; font-size: small;">Assim, acredito que algum erro deve ter ocorrido na elaboração da questão.</span></div>
<div align="justify">
<br /></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">É isso. </span><span style="font-family: Arial; font-size: small;">Espero que tenha compreendido a resolução. Qualquer dúvida é só deixar um comentário.</span></div>
<div align="justify">
<br /></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"><span style="font-family: Calibri;"></span></span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">Um abraço pessoal! Até a próxima!</span></div>
<div align="justify">
<br /></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">Marcelo Flora <br /> <br />_______________________________________________________________________</span></div>
<span style="font-family: Arial; font-size: small;">Saiba como enviar suas dúvidas. </span><a href="http://mfmatematica.blogspot.com/p/envie-suas-duvidas.html" target="_blank"><span style="font-family: Arial; font-size: small;">Clique aqui!</span></a>Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com3tag:blogger.com,1999:blog-7241116304005966082.post-74532778775671944602010-08-27T13:06:00.000-07:002013-11-01T16:48:23.713-07:00Desafio N#13<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/THgUm98HQfI/AAAAAAAAA20/8dlLvg5TFSY/s1600-h/banner_desafio_resolvido13%5B3%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="banner_desafio_resolvido13" border="0" height="228" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJzpXJhrI8_u7IEh7-WJyLNvxvyi_yNRF0xBFHlN5SkhCosD328Skq7ErtVdw-hoCl5Jt3bTPH0y6-ZbumDaMNllYeDOJcVnj1v7R-CT9g6z-SdNswboTSVB9i849kaXRh9UYouzH87ic/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="banner_desafio_resolvido13" width="273" /></a> <br />
<br />
E o desafio desta semana foi o seguinte: <br />
<div align="justify">
<br /></div>
<i>“Um comerciante compra uma caixa de vinho estrangeiro por R$1.000,00 e vende pelo mesmo preço, depois de retirar 4 garrafas e aumentar o preço da dúzia em R$100,00. Então, qual é o número original de garrafas de vinho na caixa?”</i><br />
<i></i><br />
<br />
<br />
<div align="justify">
<br />
<a name='more'></a>__________________________________________________________________ </div>
<div align="justify">
Eis a solução do desafio:</div>
<div align="justify">
<br /></div>
Sendo N o número de garrafas e P o preço de cada garrafa, temos:<br />
<div align="center">
<br />
N*P = 1000 => P=1000/N</div>
<div align="center">
<br /></div>
Tira-se 4 garrafas e aumenta-se o preço da dúzia em R$100,00, logo:<br />
<br />
<div align="center">
(N-4)*P+((N-4)/12)*100) = 1000</div>
<br />
Colocando (N-4) em evidência:<br />
<div align="center">
<br />
(N-4) (P + 100/12) = 1000</div>
<div align="center">
<br /></div>
<div align="center">
(N-4) (1000/N + 100/12) = 1000</div>
<div align="center">
<br /></div>
<div align="center">
(1000N-4000)/N + (100N-400)/12 = 1000 </div>
<div align="center">
<br /></div>
Resolvendo esta última equação, chegamos a equação de segundo grau:<br />
<br />
<div align="center">
100N² - 400N - 48000 = 0 </div>
<div align="center">
<br /></div>
<div align="left">
Aplicando Bhaskara encontramos x = 24. </div>
<br />
Portanto, haviam 24 garrafas na caixa.<br />
<br />
É isso aí galera, obrigado a todos que tentaram resolver o desafio!<br />
____________________________________________________________________________________________ <br />
<br />
Como vocês devem ter percebido, a constância das postagens no blog não vem sendo das melhores. Existe um motivo. O vestibular vem chegando e, como qualquer aluno, preciso estudar também. E põe estudar nisso!<br />
<br />
Assim, estou com pouco tempo pra preparar as postagens. Terminada esta fase, as atividades no blog voltarão ao normal.<br />
<br />
Quanto aos emails, continuarei lendo, respondendo, mas vou ficar em dívida com as resoluções. Espero que entendam.<br />
<br />
Um abraço pessoal! E até a próxima!<br />
<br />
Marcelo FloraMarcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com3tag:blogger.com,1999:blog-7241116304005966082.post-91250979792824945432010-08-13T15:51:00.000-07:002013-11-01T16:48:54.662-07:00Desafio N#12<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7CNA_Hu6XcZndXtXs8NSYvtN5HdJQxyIO75XAy0b2EUJAzYTokpoKsXfcXciJBc_fTwEVWyjjxtV_QkobhhC3xF1pEvlCO0awfHuUsQGTPtzxfIr9vC3WFrVVe_VLP3vGKYmO5SJjigk/s1600-h/banner_desafio_resolvido12pequeno%5B4%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="banner_desafio_resolvido12pequeno" border="0" height="224" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TGXLxYUSnqI/AAAAAAAAA2k/CRdhE-xEAFI/banner_desafio_resolvido12pequeno_thumb%5B2%5D.jpg?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="banner_desafio_resolvido12pequeno" width="269" /></a> <br />
E o desafio desta semana foi o seguinte:<br />
<br />
<div align="justify">
<i>“Um velho professor de matemática e um de seus alunos prediletos se encontram depois de 20 anos. Diante de uma pergunta simples, o pupilo resolve desafiar o mestre. Acompanhe o papo e veja se você também consegue descobrir as idades das filhas do aluno aplicado.</i></div>
<div align="justify">
<br /></div>
<div align="justify">
<br />
<br />
<br />
<br />
<a name='more'></a><br /><br />
<br />
<img alt="image" border="0" height="266" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TGBKumLWlLI/AAAAAAAAA2Q/mnTfacDE5To/image_thumb%5B7%5D.png?imgmax=800" style="display: block; float: none; margin-left: auto; margin-right: auto;" title="image" width="197" /></div>
<div align="justify">
<br /></div>
<div align="justify">
<i>Professor: Eduardo, como vai?</i></div>
<div align="justify">
<br /></div>
<div align="justify">
<i>Eduardo: Vou bem. Casei e tenho três filhas.</i></div>
<div align="justify">
<br /></div>
<div align="justify">
<i>Professor: Que ótimo! Que idades elas têm?</i></div>
<div align="justify">
<br /></div>
<div align="justify">
<i>Eduardo: Suas idades, multiplicadas, dão 72. Somadas, o resultado é igual ao número daquele prédio de apartamentos ali adiante.</i></div>
<div align="justify">
<br /></div>
<div align="justify">
<i>Professor: Humm... ainda não consegui descobrir.</i></div>
<div align="justify">
<br /></div>
<div align="justify">
<i>Eduardo: Ah, me desculpe. A mais velha acaba de aprender a tocar piano.</i></div>
<div align="justify">
<br /></div>
<div align="justify">
<i>Professor: Puxa, é a mesma idade do meu filho!”</i><br />
<i></i><br />
<i><br /></i></div>
<div align="justify">
____________________________________________________________________________________________ </div>
<div align="justify">
<br />
E quem resolveu o desafio desta semana foi a nossa parceira <a href="http://professoraju-mat.blogspot.com/" target="_blank">Professora Ju!</a> Parabéns!</div>
<div align="justify">
<br /></div>
<div align="justify">
<a href="http://professoraju-mat.blogspot.com/" target="_blank"><img alt="professora_ju" border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrnTNmG0vKS80rXLf7ddt9XFMW0XD3a19mz3D2huFD5QQ7uZg3eeKVlK2aHM48t1zvWzdrz0hT6v4hU2DJjlKHvXIntLMJPAoZ5xOcZZtEPvOQ4ts7GL5Xc9KkN6QoMyGIiYwr4YHYrIM/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="professora_ju" width="171" /></a> Vamos à resolução.</div>
<div align="justify">
____________________________________________________________________________________________ </div>
<div align="justify">
<br /></div>
<div align="justify">
Olá Marcelo, </div>
<div align="justify">
<br /></div>
<div align="justify">
Eis a solução do desafio desta semana.</div>
<div align="justify">
<br /></div>
<div align="justify">
Se Eduardo teve três filhas em vinte anos a idade da mais velha é <= 20 anos.</div>
<div align="justify">
<br /></div>
<div align="justify">
Se, suas idades multiplicadas dão 72, devemos decompor o número 72 em 3 fatores para encontrar as possíveis combinações:</div>
<div align="justify">
<br /></div>
<div align="justify">
1, 4 e 18 - soma 23 (1+4+18); </div>
<div align="justify">
1, 6 e 12 - soma 19; </div>
<div align="justify">
1, 8 e 9 - soma 18; </div>
<div align="justify">
2, 2 e 18 - soma 22; </div>
<div align="justify">
2, 3 e 12 - soma 17; </div>
<div align="justify">
2, 4 e 9 - soma 15; </div>
<div align="justify">
2, 6 e 6 - soma 14; </div>
<div align="justify">
3, 3 e 8 - soma 14; </div>
<div align="justify">
3, 4 e 6 - soma 13. </div>
<div align="justify">
<br /></div>
<div align="justify">
Agora está a charada:</div>
<div align="justify">
<br /></div>
<div align="justify">
<b>"Eduardo: ... Somadas, o resultado é igual ao número daquele prédio de apartamentos ali adiante.</b></div>
<div align="justify">
<b>Professor: Humm... ainda não consegui descobrir." </b></div>
<div align="justify">
<b><br /></b></div>
<div align="justify">
Se o professor não sabe com certeza quais são as idades, é porque tem mais de uma possibilidade de resposta. E, das possíveis combinações acima, duas causam dúvida:</div>
<div align="justify">
<br /></div>
<div align="justify">
2, 6 e 6 - soma 14; </div>
<div align="justify">
3, 3 e 8 - soma 14;</div>
<div align="justify">
<br /></div>
<div align="justify">
Para finalizar, quando o Eduardo diz que a filha mais velha acaba de aprender a tocar piano, deixa claro que existe somente uma filha mais velha. Apenas na situação das filhas terem idades 3, 3 e 8 anos é que há uma mais velha. Na outra opção há duas filhas mais velhas com 6 anos.</div>
<div align="justify">
<br /></div>
<div align="justify">
<b>Portanto, a idade das filhas são, 3, 3 e 8 anos.</b></div>
____________________________________________________________________________________________ <br />
É isso mesmo!<br />
<br />
Gostaria de agradecer a Professora Ju, e a todos que tentaram resolver o desafio, pela participação.<br />
<br />
E semana que vem tem mais!<br />
<br />
Um abraço gente!<br />
<br />
Marcelo FloraMarcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com1tag:blogger.com,1999:blog-7241116304005966082.post-85136521346216846492010-08-11T18:38:00.000-07:002013-11-01T16:49:50.286-07:00Aprenda Matemática em Casa!<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TGNQNa8GAUI/AAAAAAAAA2U/xZE34-52PZY/s1600-h/vestibulandia_pequeno%5B3%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="vestibulandia_pequeno" border="0" height="185" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsg1_MG5tu-b_LVE8efVxkx3vHLBqFzugOoxs4r2JJMHA3p5Xcqkh5FqD1ggjjqXlyja-IKoH-IiFyPWZA3t6c8-ONTok9IyjgRtomt_dKPJRjbTFwZGvxixE3l5oc-yPrx_bzoDBO-xc/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="vestibulandia_pequeno" width="240" /></a><br />
<span class="Apple-style-span" style="font-family: Times, 'Times New Roman', serif;">Pessoal,</span> venho através deste post apresentar a vocês um conjunto de vídeo-aulas que podem auxiliar no estudo de Matemática em casa. São as aulas do projeto: <i><a href="http://www.vestibulandia.com.br/" target="_blank">Vestibulandia.com – Suporte total ao vestibulando!</a> </i><br />
<br />
<a href="http://www.vestibulandia.com.br/"><img alt="image" border="0" height="79" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TGNQOg01afI/AAAAAAAAA2c/6GwNVnvvayY/image%5B3%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="image" width="223" /></a> <br />
<br />
<a name='more'></a><br />
O <a href="http://www.vestibulandia.com.br/" target="_blank">Vestibulandia</a> é um projeto <u>sem fins lucrativos</u>, que surgiu com os seguintes intuitos:<br />
<br />
<ul>
<li>Disseminar o conhecimento de níveis Fundamental e Médio;</li>
<li>Transformar o vestibular numa ferramenta de seleção mais justa;</li>
<li>Garantir o direito universal aos meios de aprendizado;</li>
<li>Diminuir os abismos sociais.</li>
</ul>
<br />
Devido a estes objetivos, que muito se assemelham aos meus, estou ajudando na divulgação do projeto.<br />
<br />
Seguem abaixo as aulas disponíveis. <br />
<br />
<br />
<br />
<div align="center">
<span style="font-size: large;"><u>Ensino Fundamental</u></span></div>
<b></b><br />
<br />
<b><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"></span></span></b><br />
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 1 - Adição</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=_WOqxrlXXx8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=_WOqxrlXXx8</a><a href="http://www.youtube.com/watch?v=_WOqxrlXXx8" style="color: #135cae; font-weight: normal; text-decoration: none;"></a></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 2- Subtração</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=liYTWpLtOK4" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=liYTWpLtOK4</a><a href="http://www.youtube.com/watch?v=_WOqxrlXXx8" style="color: #135cae; font-weight: normal; text-decoration: none;"></a></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 3 - Multiplicação</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=UnSyPjKvq0o" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=UnSyPjKvq0o</a><a href="http://www.youtube.com/watch?v=_WOqxrlXXx8" style="color: #135cae; font-weight: normal; text-decoration: none;"></a></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 4 - Divisão </strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=SF6r5wVF5kk" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=SF6r5wVF5kk</a> (Primeira Parte)<a href="http://www.youtube.com/watch?v=_WOqxrlXXx8" style="color: #135cae; font-weight: normal; text-decoration: none;"></a></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong><a href="http://www.youtube.com/watch?v=oosmBgX1Oug" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=oosmBgX1Oug</a></strong> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=sYsUyCfK6LM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=sYsUyCfK6LM</a> <strong><span style="color: red;"></span></strong>(Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=kZz2kOgfq2c" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=kZz2kOgfq2c</a><a href="http://www.youtube.com/watch?v=8HOKrjXlcWk" style="color: #135cae; font-weight: normal; text-decoration: none;"> </a>(Quarta parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 5 - Operações com Inteiros</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=fbs8Fo104yY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=fbs8Fo104yY</a></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<h1 style="color: #666666; font-weight: bold; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; vertical-align: bottom; width: 702px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;"><span class="Apple-style-span" style="font-size: small;">Aula 6 - Regras (Critérios) de Divisibilidade</span></span></span></b></h1>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=_oqZyoFPyD4" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=_oqZyoFPyD4</a></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: black;"><strong>Aula 7 - MMC e MDC</strong></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=LQGTRBAed9E" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=LQGTRBAed9E</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=DKolWWjthMw" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=DKolWWjthMw</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=nxgKNkorXWA" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=nxgKNkorXWA</a> (Terceira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 8 - Frações</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=A92n_aaZck4" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=A92n_aaZck4 </a>(Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=UbQ6WpXdH3A" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=UbQ6WpXdH3A</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=Zhfb9BNCeGQ" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Zhfb9BNCeGQ </a>(Terceira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 9 - Potenciação</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=5tV-6W5_TLA" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=5tV-6W5_TLA</a></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 10 - Radiciação </strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=K73GLTmT8Ys" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=K73GLTmT8Ys</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=c-cO01jXT7k" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=c-cO01jXT7k</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=tuz3JHn88wY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=tuz3JHn88wY</a> (Terceira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 11 - Fatoração</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=V7kVdkNTN8A" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=V7kVdkNTN8A</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=6Q2DUDUbkhs" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=6Q2DUDUbkhs</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=AML025Vop3o" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=AML025Vop3o</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=VEKQt2B6vhY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=VEKQt2B6vhY</a> (Quarta Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: black; font-family: 'Times New Roman'; line-height: normal;"><b><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; font-weight: normal; line-height: 14px;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"></span></span></b></span></span></b></div>
<div style="display: inline !important; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong><br /></strong></span></b></span></b></div>
<br />
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: black; font-family: 'Times New Roman'; line-height: normal;"><b><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; font-weight: normal; line-height: 14px;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"></span></span></b></span></span></b></div>
<div style="display: inline !important; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 12 - Racionalização</strong></span></b></span></b></div>
<br />
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=qvVV_6mYVgo" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=qvVV_6mYVgo</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=sL9_2Z4J-dM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=sL9_2Z4J-dM</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=nyNCZrw1snU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=nyNCZrw1snU</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=v_cyVkf-EJc" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=v_cyVkf-EJc</a> (Quarta Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 13 - Equação do Primeiro Grau</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=g6ANadRKiOs" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=g6ANadRKiOs</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=11x8lU9Q5G8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=11x8lU9Q5G8</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=1SMfQWzcA94" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=1SMfQWzcA94</a> (Terceira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 14 - Equação do Segundo Grau</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=3qs463FeXlo" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=3qs463FeXlo</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=pIroABoqhUI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=pIroABoqhUI</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=LJ8bFPA6xAM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=LJ8bFPA6xAM</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 15 - Razões e Proporções</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=eqcB_6iL648" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=eqcB_6iL648</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=c0leQW4njpI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=c0leQW4njpI</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=kSIuqCMbQPM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=kSIuqCMbQPM</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=o_nj3PYDwbE" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=o_nj3PYDwbE</a> (Quarta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=SNDQBSxS9Rw" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=SNDQBSxS9Rw</a> (Quinta Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 16 - Regra de Três</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=7Y5mFHw9sw8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=7Y5mFHw9sw8</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=JOCZiiCP-Q0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=JOCZiiCP-Q0</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=UDJ28KtNn9Y" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=UDJ28KtNn9Y</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=W-gEjd6eC2w" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=W-gEjd6eC2w</a> (Quarta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=pBqhbmZXXW8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=pBqhbmZXXW8</a> (Quinta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=ZFDrzM1IzYU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=ZFDrzM1IzYU</a> (Sexta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=D-ilWL3g_0c" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=D-ilWL3g_0c</a> (Sétima Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 17 - Conversão de Unidades</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=W7imdrh9ekM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=W7imdrh9ekM</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=vFILWusxARI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=vFILWusxARI</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=-ns3P7jdkRw" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=-ns3P7jdkRw</a> (Terceira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 18 - Análise Dimensional</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=t24Gb30e1-U" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=t24Gb30e1-U</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=NguH5ENs7r0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=NguH5ENs7r0</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=_dWZhxl4PaI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=_dWZhxl4PaI </a>(Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=CXR1r7xiyIU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=CXR1r7xiyIU</a> (Quarta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=eEFH8w0cGHc" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=eEFH8w0cGHc</a> (Quinta Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 19 - Conversão de Temperaturas</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=9NH-5A_1q74" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=9NH-5A_1q74</a></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 20 - Notação Científica</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=X79TOUpbPm0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=X79TOUpbPm0</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=rO8k9yBXH7U" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=rO8k9yBXH7U</a> (Segunda Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 21 - Algarismos Significativos</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=-3RHpdGgUzg" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=-3RHpdGgUzg</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=wRTPSVsjdbE" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=wRTPSVsjdbE</a> (Segunda Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 22 - Porcentagem Básica</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=N2w1E1-5_pk" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=N2w1E1-5_pk</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=67FKEfyajWg" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=67FKEfyajWg</a> (Segunda Parte - Final)</span></b></div>
<br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">__________________________________________________________________________</span>__________________<br />
<div align="center">
<br /></div>
<div align="center">
<span style="font-size: large;"><u>Ensino Médio</u></span></div>
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></strong></b>
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 1 - Conjuntos</span></strong></b><br />
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=1zxL3MYdK04" style="color: #135cae; font-weight: normal; text-decoration: none;" title="Primeira Aula de Conjuntos">http://www.youtube.com/watch?v=1zxL3MYdK04</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=bQ42UcLEjoY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=bQ42UcLEjoY</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=XetNn3fNjMo" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=XetNn3fNjMo</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=ERrIYN-TIIo" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=ERrIYN-TIIo</a> (Quarta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=FWs4qBxo_dw" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=FWs4qBxo_dw</a> (Quinta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=Fdw3EMxVGv4" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Fdw3EMxVGv4</a> (Sexta Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong></strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 2 - Conjuntos Numéricos</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=FL6WQG6Z5tQ" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=FL6WQG6Z5tQ</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=19Gx6x5EKIg" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=19Gx6x5EKIg</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=5luhLfmp6ig" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=5luhLfmp6ig</a> (Terceira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong></strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 3 - Funções - Conceitos Básicos</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=DfTXY698rJ0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=DfTXY698rJ0</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=ulq3V7IIcSI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=ulq3V7IIcSI</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=vTJCbbHFMxU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=vTJCbbHFMxU</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=H7CqfB5fqs8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=H7CqfB5fqs8</a> (Quarta Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /><strong>Aula 4 - Função do Primeiro Grau</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=pYqp-57y0D8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=pYqp-57y0D8</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=ktE0uuDMqyw" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=ktE0uuDMqyw</a> (Segunda Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /><strong>Aula 5 - Função do Segundo Grau</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=W7NbQuiNnsc" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=W7NbQuiNnsc</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=b7KqWu1yYWs" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=b7KqWu1yYWs</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=xIZ6v8_yZXE" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=xIZ6v8_yZXE</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=LUFqHcV-mFU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=LUFqHcV-mFU</a> (Quarta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=16E9ewkLBmY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=16E9ewkLBmY</a> (Quinta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=tZepLLeMjuE" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=tZepLLeMjuE</a> (Sexta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=4FTFKqQTfbQ" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=4FTFKqQTfbQ</a></span> (Sétima Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 6 - Função Inversa</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=LQjfnE3Lswg" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=LQjfnE3Lswg</a> (Primeira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 7 - Função Composta</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=avn4eRRAqCA" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=avn4eRRAqCA</a> (Primeira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 8 - Intervalos Reais</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=nYM8ub2fvL0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=nYM8ub2fvL0</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=XfN8T7vIJUY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=XfN8T7vIJUY</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=pZWzefxSZNY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=pZWzefxSZNY</a></span>(Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=b96wtO8tEaI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=b96wtO8tEaI </a>(Quarta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=POsCsyDQbYc" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=POsCsyDQbYc</a> (Quinta Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 9 - Inequações</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=nYM8ub2fvL0" style="color: #135cae; font-weight: normal; text-decoration: none;"></a><a href="http://www.youtube.com/watch?v=G_k7qrbMguE" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=G_k7qrbMguE</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=JVMj1-xPvmI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=JVMj1-xPvmI </a>(Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=D4X3xRLIVUQ" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=D4X3xRLIVUQ</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=mswdWkY2Ys0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=mswdWkY2Ys0</a> (Quarta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=tqYdfVIfok0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=tqYdfVIfok0</a> (Quinta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=4e2SGfvE-bY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=4e2SGfvE-bY</a> (Sexta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=OJlfwpz8bgM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=OJlfwpz8bgM</a> (Sétima Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=F827POnd70E" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=F827POnd70E</a> (Oitava Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=Gb-zx80R7p8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Gb-zx80R7p8</a> (Nona Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=RMktQ1TpV3g" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=RMktQ1TpV3g</a> (Décima Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 10 - Progressão Aritmética</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=Bv8vRXpvp88" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Bv8vRXpvp88</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=DFykbS5Ures" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=DFykbS5Ures</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=1C2-PtD8vLc" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=1C2-PtD8vLc</a> (Terceira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 11 - Progressão Geométrica</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=IpjQ2HZtMXc" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=IpjQ2HZtMXc</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=ysni0wSkRJk" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=ysni0wSkRJk</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=oGQ_TYuQi1A" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=oGQ_TYuQi1A</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=q_AlJ4jX8tg" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=q_AlJ4jX8tg</a> (Quarta Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 12 - Equação Exponencial</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=bKncTaE-gCc" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=bKncTaE-gCc</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=h2ACYTmGLLg" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=h2ACYTmGLLg</a> (Segunda Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 13 - Logaritmo</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=HifrYF7cKsQ" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=HifrYF7cKsQ</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=yC0q4mO9co0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=yC0q4mO9co0</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=2s1qFnkM3ak" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=2s1qFnkM3ak</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=udvX4J5LGA0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=udvX4J5LGA0</a> (Quarta Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 14 - Função Exponencial</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=7_T2JGEqZgg" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=7_T2JGEqZgg</a> (Primeira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 15 - Função Logarítmica</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=B65JnNhQOgU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=B65JnNhQOgU</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=8Z86BqSeUGc" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=8Z86BqSeUGc</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=XxiM5gckjs0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=XxiM5gckjs0</a> (Terceira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 16 - Logaritmo Decimal</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=Ryrh9aMM-18" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Ryrh9aMM-18</a><span style="color: black;"> (Primeira Parte)</span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: black;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><span style="color: black;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=EOf4Lfr_p-Q" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=EOf4Lfr_p-Q</a> </span></span></span>(Segunda Parte)</span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: black;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=CAW-rX5ztRI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=CAW-rX5ztRI</a> <span style="color: black;">(Terceira Parte)</span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: black;"><span style="color: red;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=LYy14VPSwmQ" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=LYy14VPSwmQ</a> <span style="color: black;">(Quarta Parte -Final)</span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 17 - Inequação Exponencial</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=XBf8RanaB-U" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=XBf8RanaB-U</a> (Primeira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=yieSE3A0nJs" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=yieSE3A0nJs</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 18 - Inequação Logarítmica</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=eGDHbkrX2b8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=eGDHbkrX2b8</a> <span style="color: black;"><span style="color: #333333;">(Primeira Parte)</span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=tr5pucDmuRI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=tr5pucDmuRI</a> (Segunda Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: black; line-height: normal;"><b><span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; font-weight: normal; line-height: 14px;"></span></b></span></b></div>
<div style="display: inline !important; margin-bottom: 5px; margin-top: 0px;">
<b><b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 19 - Matrizes - Conceitos Iniciais</span></strong></b></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=sw18GQESKpA" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=sw18GQESKpA</a> <span style="color: #333333;">(Primeira Parte)</span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=AdwyrhQ5GfA" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=AdwyrhQ5GfA</a> <span style="color: #333333;">(Segunda Parte)<span style="color: red;"><span style="color: black;"><span style="color: red;"><span style="color: red;"><span style="color: black;"></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=V2LRnz54-dQ" style="color: #135cae; font-weight: normal; text-decoration: none;"><span style="color: red;"></span>http://www.youtube.com/watch?v=V2LRnz54-dQ</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=nRD2oTiVhx8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=nRD2oTiVhx8</a> <span style="color: #333333;">(Quarta parte)</span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=Z7TLOzjL5Xo" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Z7TLOzjL5Xo</a> <span style="color: #333333;">(Quinta Parte - Final)</span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><br /></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><strong>Aula 20 - Determinantes</strong></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #333333;"></span><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: black;"><span style="color: red;"><span style="color: red;"><span style="color: black;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=SUbr6zypkLA" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=SUbr6zypkLA</a> <span style="color: #333333;">(Primeira Parte)</span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=hjAn3Uiqaa4" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=hjAn3Uiqaa4</a> <span style="color: #333333;">(Segunda Parte)</span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: #333333;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=LEl1Tu8ZimI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=LEl1Tu8ZimI</a></span> (Terceira Parte)</span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: #333333;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=0TiAF4qPe-4" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=0TiAF4qPe-4</a><span style="color: #333333;"> (Quarta Parte)</span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=UMZHreMc7wo" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=UMZHreMc7wo</a> </span>(Quinta Parte)<span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: black;"><span style="color: red;"><span style="color: red;"><span style="color: black;"></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: black;"><span style="color: red;"><span style="color: red;"><span style="color: black;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=HyT-54ScyFM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=HyT-54ScyFM</a> <span style="color: #333333;">(Sexta Parte)</span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=nVxhjL9NjC0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=nVxhjL9NjC0</a> <span style="color: #333333;">(Sétima Parte)</span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=PTvXc41g8qA" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=PTvXc41g8qA</a><span style="color: red;"> <span style="color: #333333;">(Oitava Parte)</span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=oNF7UzTSv7w" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=oNF7UzTSv7w</a> (Nona Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=qTnhWkEsZ6g" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=qTnhWkEsZ6g</a> <span style="color: #333333;">(Décima Parte)</span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=oehKFf89V0g" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=oehKFf89V0g</a> (Décima Primeira Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=pQGx2Zg1fFs" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=pQGx2Zg1fFs</a> (Décima Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=kXsVhmKDc7Q" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=kXsVhmKDc7Q</a> (Décima Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=coDQ_No0984" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=coDQ_No0984</a> (Décima Quarta Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 21 - Matriz Inversa</span></strong></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"></span></span></span><span style="color: red;"><a href="http://www.youtube.com/watch?v=SI8e3T7icX8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=SI8e3T7icX8</a> <span style="color: #333333;">(Primeira Parte)</span><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=EFn8guBXqCk" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=EFn8guBXqCk</a> <span style="color: #333333;">(Segunda Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=QbwoVGijUBY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=QbwoVGijUBY</a><span style="color: #333333;"> (Terceira Parte)</span></span><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=WgDzlkTXXCU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=WgDzlkTXXCU</a><span style="color: #333333;"> (</span><span style="color: #333333;">Quarta Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=owVlYDaUHi4" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=owVlYDaUHi4</a> (Quinta Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=Iot7K8dUZw8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Iot7K8dUZw8</a> (Sexta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=rph-2sngHBE" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=rph-2sngHBE</a> <span style="color: #333333;">(Sétima Parte)</span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=7QgEtJsQo8I" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=7QgEtJsQo8I</a> <span style="color: #333333;">(Oitava Parte - Final)</span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><br /></span></span></span></span><strong>Aula 22 - Introdução aos Sistemas Lineares</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=HRrUF3eBFXs" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=HRrUF3eBFXs</a> (Primeira Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=4M2agJ03RHo" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=4M2agJ03RHo</a> (Segunda Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=pJZXAYo4ORk" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=pJZXAYo4ORk</a> (Terceira Parte - Final)<a class="toolbar" href="http://www.vestibulandia.com.br/index.php/component/content/?sectionid=-1&task=edit&cid[0]=45" style="color: #135cae; font-weight: normal; text-decoration: none;"></a><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><strong>Aula 23 - Sistemas Lineares</strong></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=Etc33cIF78c" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Etc33cIF78c</a> (Primeira Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=A2JsWo_2CP8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=A2JsWo_2CP8</a> (Segunda Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=VejbFBkN-4g" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=VejbFBkN-4g</a> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=TQjInXLOj4g" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=TQjInXLOj4g</a> (Quarta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=CYIZqz0wd3U" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=CYIZqz0wd3U</a> (Quinta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=EdRtsiRNLs0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=EdRtsiRNLs0</a> <span style="color: #333333;">(Sexta Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=JUFWBIq7KeE" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=JUFWBIq7KeE</a><span style="color: #333333;"> (</span><span style="color: #333333;">Sétima Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=kDfwjNj1cEA" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=kDfwjNj1cEA</a> (Oitava Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=SKcsStUST94" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=SKcsStUST94</a> (Nona Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=zKxtq5CQXks" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=zKxtq5CQXks</a> (Décima Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=hSS7znDKr7g" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=hSS7znDKr7g</a> (Décima Primeira Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=gt5w05x_6ro" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=gt5w05x_6ro</a> (Décima Segunda Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=sil_8JcpL20" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=sil_8JcpL20</a> (Décima Terceira Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=A3A9Myr8zNM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=A3A9Myr8zNM</a> (Décima Quarta Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=Lq7iEDhk4XM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Lq7iEDhk4XM</a> (Décima Quinta Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=tOnSHR8CNvo" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=tOnSHR8CNvo</a> (Décima Sexta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=E-GZ0_nGBRU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=E-GZ0_nGBRU</a> <span style="color: #333333;">(Décima Sétima Parte)</span><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=KwQ8quhcnVY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=KwQ8quhcnVY</a> (Décima Oitava Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 24 - Módulo - Conceitos Iniciais</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=kLNdeRy4SHU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=kLNdeRy4SHU</a> <span style="color: #333333;">(Primeira Parte)<span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=IwbPquJgqgg" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=IwbPquJgqgg</a> (Segunda Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 25 - Equações Modulares</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=1-D4-h2eSms" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=1-D4-h2eSms</a><span style="color: #333333;"> (Primeira Parte)</span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=szVXNUoSI0A" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=szVXNUoSI0A</a> (Segunda Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=GhtNT1Yae3s" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=GhtNT1Yae3s</a></span> (Terceira Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=-yhOqB2qHX8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=-yhOqB2qHX8</a> </span>(Quarta Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=S9IOOZsq_E8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=S9IOOZsq_E8</a> </span>(Quinta Parte - Final)</span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #333333;"></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 26 - Função Modular</span></strong></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=68s-LannfSI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=68s-LannfSI</a> </span></span></span></span></span><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;">(Primeira Parte)</span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=jrc5K4vo-EE" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=jrc5K4vo-EE</a> </span></span></span></span></span>(Segunda Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=mgmHDqA6OYo" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=mgmHDqA6OYo</a></span> (Terceira Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=gnpMLEE8tls" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=gnpMLEE8tls</a> (Quarta Parte)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=I5-CWehCarM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=I5-CWehCarM</a> (Quinta Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 27 - Inequação Modular</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=tAHuaep8nek" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=tAHuaep8nek</a></span> (Primeira Parte)<span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span style="color: red;"><span style="color: #333333;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=CeHW1jkEw80" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=CeHW1jkEw80</a> (Segunda Parte)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=zw6lqTBxM5w" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=zw6lqTBxM5w</a> (Terceira Parte - Final)</span></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 28 - Fatorial:</span></strong></b></div>
<div style="font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<b><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=vpv9i2TnErM" style="color: #135cae; font-weight: normal; text-decoration: none;"></a><span class="Apple-style-span" style="border-color: initial;"><img src="file:///C:/Users/Junior/AppData/Local/Temp/moz-screenshot.png" style="border-bottom-style: none; border-bottom-width: 0px; border-color: initial; border-left-style: none; border-left-width: 0px; border-right-style: none; border-right-width: 0px; border-top-style: none; border-top-width: 0px;" /><img src="file:///C:/Users/Junior/AppData/Local/Temp/moz-screenshot-1.png" style="border-bottom-style: none; border-bottom-width: 0px; border-color: initial; border-left-style: none; border-left-width: 0px; border-right-style: none; border-right-width: 0px; border-top-style: none; border-top-width: 0px;" /></span><a href="http://www.youtube.com/watch?v=D0OF22xbs0Q" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=D0OF22xbs0Q</a> (Primeira Parte - Final)</span></b></div>
<div style="font-family: Arial; font-size: 11px; font-weight: normal; margin-bottom: 5px; margin-top: 0px;">
<br /></div>
<b><strong>Aula 29 - Binômio de Newton</strong></b><br />
<div style="margin-bottom: 5px; margin-top: 0px;">
<b><a href="http://www.youtube.com/watch?v=w8tofUVHxNU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=w8tofUVHxNU</a> (Parte 1)</b></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<b><a href="http://www.youtube.com/watch?v=ASK4VZLp4XY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=ASK4VZLp4XY</a> (Parte 2)</b></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<b><a href="http://www.youtube.com/watch?v=gUKnIHVfiv8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=gUKnIHVfiv8</a> (Parte 3)</b></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<b><a href="http://www.youtube.com/watch?v=yNZy4IW4i4E" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=yNZy4IW4i4E</a> (Parte 4)</b></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<b><a href="http://www.youtube.com/watch?v=MHQT3-et1Kk" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=MHQT3-et1Kk</a> (Parte 5)</b></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<b><a href="http://www.youtube.com/watch?v=uqJu7YA7HmM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=uqJu7YA7HmM</a> (Parte 6)</b></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<b><a href="http://www.youtube.com/watch?v=Szy4v175hIo" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Szy4v175hIo</a> (Parte 7 - Final)</b></div>
<br />
<br />
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 30 - Análise Combinatória</span></strong></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=BVn2EoYBQY0" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=BVn2EoYBQY0</a> (Parte 1)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=UE_F9T2SDYg" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=UE_F9T2SDYg</a> (Parte 2)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=iHCS1momU44" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=iHCS1momU44</a> (Parte 3)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=l98Pb74FEhw" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=l98Pb74FEhw</a> (Parte 4)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=QUeXubQlpF4" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=QUeXubQlpF4</a> (Parte 5)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=nXqoEQwpsmk" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=nXqoEQwpsmk</a> (Parte 6)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=EyjVovBcdFM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=EyjVovBcdFM</a> (Parte 7)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span style="color: red; font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=zBjw3Ws45NU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=zBjw3Ws45NU</a> <span style="color: black;">(Parte 8 - Final)</span></span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; font-size: 11px; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 31 - Probabilidade</span></strong></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=SLzIbZ-7SBM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=SLzIbZ-7SBM</a> </span>(Parte 1)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=TL-igSGXbAQ" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=TL-igSGXbAQ</a> </span>(Parte 2)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=q3oaO14Gx78" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=q3oaO14Gx78</a> </span>(Parte 3)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=Grd3Td_Qwrk" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Grd3Td_Qwrk</a> </span>(Parte 4)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=URSSoml8x5A" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=URSSoml8x5A</a></span> (Parte 5)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><a href="http://www.youtube.com/watch?v=T4TxKIh9OGY" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=T4TxKIh9OGY</a> </span>(Parte 6 - Final)</span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; font-size: 11px; line-height: 14px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; font-size: 11px; line-height: 14px; text-align: left;">
</div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; text-align: left;">
<div style="margin-bottom: 5px; margin-top: 0px;">
<strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 32 - Noções de Geometria e Trigonometria</span></strong></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=qPTk1NafnTU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=qPTk1NafnTU</a> (Parte 1)</span></div>
</div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; text-align: left;">
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=Idfz_ZXWaRE" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Idfz_ZXWaRE</a> (Parte 2)</span></div>
</div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; text-align: left;">
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=BCgIn4vfDtw" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=BCgIn4vfDtw</a> (Parte 3)</span></div>
</div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; text-align: left;">
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=xjrSRDH6cDs" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=xjrSRDH6cDs</a> (Parte 4)</span></div>
</div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; text-align: left;">
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=tU_5Y9Zo6Rg" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=tU_5Y9Zo6Rg</a> (Parte 5)</span></div>
</div>
<div style="-webkit-border-horizontal-spacing: 2px; -webkit-border-vertical-spacing: 2px; color: #333333; line-height: 14px; text-align: left;">
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=Cbx5NMFuhs8" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=Cbx5NMFuhs8 </a>(Parte 6)</span></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=AiMicde39lM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=AiMicde39lM</a> (Parte 7)</span></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=g5Utnv3_NVw" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=g5Utnv3_NVw</a> (Parte 8)</span></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=iqxpWQlvrtA" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=iqxpWQlvrtA</a> (Parte 9 - Final)</span></div>
<div style="font-size: 11px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 33 - Geometria Plana - Definições Preliminares</span></strong></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=0DrV_i20J-c" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=0DrV_i20J-c </a>(Parte 1)</span></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=_6LG2y-swhM" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=_6LG2y-swhM</a> (Parte 2)</span></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=A6bKezbpXRI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=A6bKezbpXRI </a>(Parte 3)</span></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=yAgnuJEoS6o" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=yAgnuJEoS6o </a>(Parte 4 - Final)</span></div>
<div style="font-size: 11px; margin-bottom: 5px; margin-top: 0px;">
<strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></strong></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 34 - Geometria Plana - Triângulos - Noções Gerais</span></strong></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=8ULy_qDQKTU" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=8ULy_qDQKTU</a> (Parte 1)</span></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=oV_ZRN62HIs" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=oV_ZRN62HIs</a> (Parte 2 - Final)</span></div>
<div style="font-size: 11px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;"><strong><br /></strong></span></div>
<div style="font-size: 11px; margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;"><strong>Aula 35 - Geometria Plana - Triângulos - Critérios de Congruência</strong></span></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=5cQKA258xD4" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=5cQKA258xD4</a> (Parte 1)</span></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=deXsf1GqBBI" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=deXsf1GqBBI</a> (Parte 2 - Final)</span></div>
<div style="font-size: 11px; margin-bottom: 5px; margin-top: 0px;">
<strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></strong></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Aula 36 - Geometria Plana - Triângulos - Critérios de Semelhança</span></strong></div>
<div style="margin-bottom: 5px; margin-top: 0px;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.youtube.com/watch?v=WMTZc44DcW4" style="color: #135cae; font-weight: normal; text-decoration: none;">http://www.youtube.com/watch?v=WMTZc44DcW4</a> (Parte 1)</span></div>
</div>
____________________________________________________________________________________________<br />
<br />
Bom, é isso aí galera, agora não tem desculpa pra não estudar! rsrsrs<br />
<br />
Um abraço pessoal! Até mais!<br />
<br />
Marcelo FloraMarcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com18tag:blogger.com,1999:blog-7241116304005966082.post-69238653155565885242010-08-06T11:24:00.000-07:002013-11-01T16:55:32.726-07:00Desafio N#11<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl7lkqIfjyz-gY9mWfilfhyphenhyphenmstWK4I1oc7Mjc4n30z6-WIqtC-O0t3poaYKhQu-hf_rH5k5B332zpfQeyglQmEcPAveHu2Kow9Y3VuaXn6orxkkw4gGvqvR5WJgjyMV06qSQfoNvwLVy0/s1600-h/banner_desafio_resolvido11%5B4%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="banner_desafio_resolvido11" border="0" height="227" src="http://lh6.ggpht.com/_7wGgh4VGq1A/TFxRL5zC6NI/AAAAAAAAA14/owI3PyDuwUU/banner_desafio_resolvido11_thumb%5B2%5D.jpg?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="banner_desafio_resolvido11" width="272" /></a> <br />
<div style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;">E o desafio desta semana foi o seguinte: </span></div>
<div style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;">Em um corredor há 100 portas, todas numeradas e fechadas. Sua missão é atravessar o corredor 100 vezes movendo as portas. Mover significa mudar sua situação: se estiver fechada, abra-a; se estiver aberta, feche-a. Mas, há algumas regras: </span></div>
<div style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;">1) Cada travessia sempre começa pela porta número 1;</span></div>
<div style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Arial, Helvetica, sans-serif;">2) Na travessia 1 mova todas as portas. Na travessia 2 pule uma porta e mova a segunda; e assim por diante (ou seja, mova as portas, 2, 4, 6, 8, ...). Na travessia 3 pule duas e mova a terceira (ou seja, mova as portas 3, 6, 9, ...). Siga assim até a travessia 100, quando você só moverá a porta número 100. </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Depois da última travessia, que portas estarão abertas?</span> </div>
<div align="justify">
<br />
<a name='more'></a><img alt="image" border="0" height="199" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPy5k0tQOadgAtFobLoY7csRMOGTmAR_DP7TkGJJrHbRoChI2Ug9SEzr3P15QJSe0CMkhQvut4x_2Y6Htcg3dSH-USvvHK5XQ0xkIpVYLzL3SwaRWXd8mCMi1KAULGrbxAHPs7dM5Cbuw/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="image" width="278" /></div>
<div align="justify">
<br /></div>
<div align="justify">
<br /></div>
____________________________________________________________________________________________ <br />
<div align="justify">
<br /></div>
<div align="justify">
E quem resolveu o desafio desta semana foi o Arthur F. Santos! Parabéns!</div>
<div align="justify">
<br /></div>
<div align="justify">
Ele não quis enviar a foto pra gente, mas merece o destaque! rsrsrs.</div>
<div align="justify">
<br /></div>
<div align="justify">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgO7HW0fMYoBcJNVyvzg7h-boqOn7oX6tiN8RfSa4NwfG4WbG3v0ygJK4wS5fvyPpFJim3iakJgLxuOvFgyfBXDwcitXFIX8u3gmDIiRXtWjbbJSAMg4qxtVbJVgq_rCIR0tgndycSzYz4/s1600-h/arthur_f_santos%5B5%5D.jpg"><img alt="arthur_f_santos" border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8pXvWA_3Yz8VFbCe7HOXWqHhjqHVL-tghwpSyFPRXo-NcuPWolqzPxf1VUNOFFmSMP1gSOwZMv_7M59MZst4HRYVLCuq1Oa8GY9C2MMjLz-TAzk_VMl_8fCZj7YuMd9qM-JQeQzTduIk/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="arthur_f_santos" width="171" /></a> Vamos à resolução.</div>
<div align="justify">
____________________________________________________________________________________________ </div>
<div align="justify">
<br /></div>
<div align="justify">
Permanecerão abertas as portas que contêm números cuja quantidade de divisores é ímpar, ou seja, os quadrados perfeitos. </div>
<div align="justify">
<br />
Assim ficam abertas as portas 1, 4, 9, 16, 25, 36, 49, 64, 81 e 100. Confira na tabela abaixo:</div>
<div align="justify">
<br /></div>
<div align="left">
<br />
<b>Número Divisores Quantidade de Divisores </b><br />
1 1 1 <br />
4 1, 2, 4 3 <br />
9 1, 3, 9 3 <br />
16 1, 2, 4, 8, 16 5 <br />
25 1, 5, 25 3 <br />
36 1, 2, 3, 4, 6, 9, 36 7 <br />
49 1, 7, 49 3 <br />
64 1,2,4,8,16,32,64 7 <br />
81 1, 9, 81 3 <br />
100 1, 2, 5, 10, 20, 50, 100 7 </div>
<div align="left">
<br /></div>
<div align="justify">
Observação: os divisores de um número n vêm aos pares. A exceção são os números quadrados perfeitos cujo número de divisores é ímpar.</div>
<div align="justify">
____________________________________________________________________________________________ </div>
<div align="justify">
É isso aí pessoal, semana que vem tem mais!</div>
<div align="justify">
<br /></div>
<div align="justify">
Um abraço, e um bom final de semana a todos!</div>
<div align="justify">
<br />
Marcelo Flora</div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com0tag:blogger.com,1999:blog-7241116304005966082.post-64634033799285623412010-07-29T12:24:00.000-07:002013-11-01T16:35:39.826-07:00Dúvida da Gislene<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivtJwNEkzSSsNjXe0jwqXrd91seumUEKjrTbgDQ1zZzLnHDRVxRosEZRwuAwvgfw7_KjU0FE-JHRYy88OaBEmBNHsQdyWumKnahzoe0nroe3_eDG0Whp2NDews2EzyA-Z3KDFV72-y6qM/s1600-h/duvida2%5B3%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="duvida2" border="0" height="200" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TFHVRb5o2eI/AAAAAAAAA08/yUcEOwSp_iI/duvida2_thumb%5B1%5D.jpg?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="duvida2" width="192" /></a> <br />
<span style="font-family: Arial, Helvetica, sans-serif;">Bom dia!</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Estou estudando para umconcurso público por causa da idade estou com dificuldades, me auxilie nestes problemas me ensinando a solução. Obrigada</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<div align="justify">
<span style="font-family: Arial, Helvetica, sans-serif;">1- A quantia de R$ 720,00 foi dividida entre três pessoas, de tal forma que a primeira recebeu a metade, a segunda a terça parte e a terceira o restante. Quanto recebeu a terceira pessoa?</span></div>
<div align="justify">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">2- Um número mais sua metade, mais a quarta parte é igual a 63. Esse número é?</span></div>
<div align="justify">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span style="font-family: Arial, Helvetica, sans-serif;">Agradeço desde já.</span></div>
<div align="justify">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span style="font-family: Arial, Helvetica, sans-serif;">Gislene.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"></span><br />
<a name='more'></a></div>
<br />
_____________________________________________________________<br />
<br />
Olá Gislene, segue abaixo a resolução.<br />
<br />
1) Temos que:<br />
<br />
A primeira pessoa recebeu metade, ou seja, ½<br />
<br />
A segunda pessoa recebeu um terço, ou seja, 1/3<br />
<br />
Portanto, a terceira pessoa recebeu x.<br />
<br />
Temos:<br />
<br />
1/2 + 1/3 + x = 1 <br />
<br />
1/2 + 1/3 -1 = -x <br />
<br />
3/6 + 2/6 - 6/6 = -x <br />
<br />
5/6 - 6/6 = -x <br />
<br />
(- 1/6 = -x) (-1) <br />
<br />
x= 1/6<br />
<br />
1/6 de 720 = 120<br />
<br />
2) Um número mais sua metade mais a quarta parte é igual a 63. Esse número é?<br />
<br />
Um número = x<br />
<br />
Mais sua metade = x/2<br />
<br />
Mais sua quarta parte = x/4<br />
<br />
É igual a 63. Portanto, temos:<br />
<br />
x + x/2 + x/4 = 63<br />
<br />
Temos uma equação de grau 1 para resolver:<br />
<br />
(4x + 2x + x)/4 = 63<br />
<br />
7x/4 = 63<br />
<br />
7x = 252<br />
<br />
x = 252/7<br />
<br />
x = 36<br />
<br />
Portanto, o número é 36<br />
<br />
Abraços,<br />
<br />
Matheus Basílio.<br />
<br />
Fazendo Matemática – <a href="http://www.fazendomatematica.com/">http://www.fazendomatematica.com</a><br />
<span style="font-family: Arial; font-size: small;">____________________________________________________________________________________________</span>
<br />
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"><span style="color: black;">Saiba como enviar suas dúvidas.</span> </span><a href="http://mfmatematica.blogspot.com/2010/01/esclareca-suas-duvidas-em-matematica.html"><span style="font-family: Arial; font-size: small;">Clique aqui!</span></a></div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com1tag:blogger.com,1999:blog-7241116304005966082.post-54508295393784136162010-07-23T14:01:00.000-07:002013-11-01T16:56:56.169-07:00Desafio N#10<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TEoCalAC3WI/AAAAAAAAAzw/SGbFs4PyT-s/s1600-h/banner_desafio_resolvido10%5B4%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="banner_desafio_resolvido10" border="0" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipLUwhNK_q7mL4lRJRdi2dEpyHEoRUT92uhaICUI_iR5-T3zcUfoQmgh696z_fatqnWct7aROnx6TB9Df6IHcy_fxlkoL758eP1IBtNZ1G1lNqLgRx0HlqweWNPkDF68rnxyKOKPPjhbU/?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="banner_desafio_resolvido10" width="260" /></a><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Olá pessoal! Tudo bem com vocês?</span><br />
<div align="justify">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span style="font-family: Arial, Helvetica, sans-serif;">Antes de apresentar a solução do desafio desta semana, gostaria de agradecer a todos que tentaram resolvê-lo. Muito obrigado gente!</span></div>
<div align="justify">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span style="font-family: Arial, Helvetica, sans-serif;">Este desafio é de minha criação, por isso ainda preciso aperfeiçoá-lo. Assim que o fizer, postarei a segunda versão.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"></span><br />
<a name='more'></a></div>
<div align="justify">
<span style="font-family: Arial, Helvetica, sans-serif;">E para quem ainda não viu, o desafio foi o seguinte:</span></div>
_________________________________________________________________________________<br />
<br />
<div align="justify">
<i>“Um diplomata, ao chegar na entrada da casa real de um país aliado, se deparou com cinco soldados em frente a três portas. </i></div>
<div align="justify">
<i><a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TDtemXNyivI/AAAAAAAAAzo/gJZGHDsXev4/s1600-h/soldados25.jpg"><img alt="soldados2" border="0" height="278" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TDtenVJw6lI/AAAAAAAAAzs/ghyb81HBqZY/soldados2_thumb3.jpg?imgmax=800" style="display: block; float: none; margin-left: auto; margin-right: auto;" title="soldados2" width="457" /></a></i><i> Ao pedir permissão para entrar, um deles disse:</i></div>
<br />
<i></i> <br />
<div align="justify">
<i>- Para entrar na casa real, o Sr. terá que descobrir qual destas três portas leva ao Presidente. – O soldado fez uma pausa. O outro continuou:</i></div>
<br />
<i></i> <br />
<div align="justify">
<i>- Cada soldado, ou sempre fala a verdade, ou sempre fala mentiras. Porém, existe um de nós que é louco, e ele dirá algo absurdo. Suas afirmações não devem ser consideradas. Iremos lhe dar as pistas necessárias para vencer o desafio. – dito isto, começaram um a um a falar:</i></div>
<br />
<i></i> <br />
<div align="justify">
<i>- Meu nome é Edgar, e afirmo que a porta correta é a da direita. Pode acreditar no Carlos, que ele fala a verdade.</i></div>
<br />
<i></i> <br />
<div align="justify">
<i>- Meu nome é Raul, e a porta certa é a do centro. Não acredite no Augusto, ele é mentiroso.</i></div>
<br />
<i></i> <br />
<div align="justify">
<i>- Sou o Carlos, e digo que escolha a porta da direita. Sobre Edgar, digo que, às vezes, ele mente.</i></div>
<br />
<i></i> <br />
<div align="justify">
<i>- Meu nome é Artur. Escolha a porta do centro. Mas saiba que eu sou mentiroso.</i></div>
<br />
<i></i> <br />
<div align="justify">
<i>- Por fim, eu digo. Escolha a porta da esquerda. Meu nome é Augusto, e sou louco."</i></div>
<br />
<i><b>Descubra qual é a porta que o diplomata deve escolher.</b></i> <br />
____________________________________________________________________________________________ <br />
E hoje tivemos três vencedores! São eles:<br />
<br />
<div align="center">
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TEoCcfTD2-I/AAAAAAAAAz4/7I0gwqDFq9M/s1600-h/Denilson%5B3%5D.jpg"><img alt="Denilson" border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5mGMDsa04jTpmIOIB0hRURspZcvfEE046Km2Bo9WXIBaXGufVkxgcKJuC8OK901IbedmQO5vNn7cCL32AKHk40BIzxvr43TPs3iN2w0z_jD5QPyHS54Nafwwizzp0DMDAffdMqfoYfqs/?imgmax=800" style="border: 0px none; display: inline;" title="Denilson" width="171" /></a> <a href="http://lh4.ggpht.com/_7wGgh4VGq1A/TEoCd4LqJ6I/AAAAAAAAA0A/6Xx-aN7OSL8/s1600-h/thaisa_lima%5B3%5D.jpg"><img alt="thaisa_lima" border="0" height="240" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TEoCei8eyhI/AAAAAAAAA0E/VwMT1WWvp4U/thaisa_lima_thumb%5B1%5D.jpg?imgmax=800" style="border: 0px none; display: inline;" title="thaisa_lima" width="171" /></a> <a href="http://lh5.ggpht.com/_7wGgh4VGq1A/TEoCfuJ4FoI/AAAAAAAAA0I/EzZ-jSqxmC4/s1600-h/Gabriel%5B3%5D.jpg"><img alt="Gabriel" border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUP6iFQaqjk9j840UYKOnJ3c0r6b5h3IiQiS8qDZvArkPNeHF6hdnD_2gamV8mcdffqV7Ec2gcFZBFQTiDN9tK-WZDHm1ndQjavudKWw_YclMNqwG9s7wBjGKMu76KsZFiruTO80B7wtk/?imgmax=800" style="border: 0px none; display: inline;" title="Gabriel" width="171" /></a></div>
<div align="justify">
Parabéns a todos! Muito obrigado pela participação!</div>
<div align="justify">
<br /></div>
<div align="justify">
E vamos à tão esperada resolução.</div>
<div align="justify">
</div>
<div align="justify">
</div>
<div align="justify">
</div>
<div align="justify">
</div>
<div align="justify">
</div>
<div align="justify">
____________________________________________________________________________________________ </div>
<div align="justify">
Primeiro, temos que ficar atentos às condições propostas no problema:</div>
<div align="justify">
<br />
1) Eles só dizem verdades ou mentiras;<br />
2) Um deles é louco, e sua afirmação não deve ser considerada. Ele irá dizer um absurdo. </div>
<div align="justify">
<br />
Feito isso, comecemos a análise. </div>
<div align="justify">
<br /></div>
<div align="justify">
===> Para Edgar:</div>
<div align="justify">
<br /></div>
<div align="justify">
<i>“… afirmo que a porta correta é a da direita. Pode acreditar no Carlos, que ele fala a verdade.”</i></div>
<div align="justify">
<br /></div>
<div align="justify">
Então, segundo ele:<br />
<br />
* Porta certa: Direita;<br />
<br />
* Carlos fala a verdade.
</div>
<ul>
</ul>
<div align="justify">
<br /></div>
<div align="justify">
===> Para Raul:</div>
<div align="justify">
<br /></div>
<div align="justify">
<i>“… <i>a porta certa é a do centro. Não acredite no Augusto, ele é mentiroso.”</i></i></div>
<div align="justify">
<br /></div>
<div align="justify">
Então, segundo ele:</div>
<div align="justify">
<br />
* Porta certa: Centro;<br />
<br />
* Augusto é mentiroso .
</div>
<ul>
</ul>
<div align="justify">
<br /></div>
<div align="justify">
===> Para Carlos:</div>
<div align="justify">
<br /></div>
<div align="justify">
<i>“… digo que escolha a porta da direita. Sobre Edgar, digo que, às vezes, ele mente.”</i></div>
<div align="justify">
<br /></div>
<div align="justify">
Como é possível alguém mentir “às vezes”?! Foi afirmado anteriormente que eles só podem falar a verdade ou a mentira. Portanto, concluímos que <b>Carlos é mentiroso.</b></div>
<div align="justify">
Muitos colocaram Carlos como o louco, mas está errado, pois um mentiroso pode muito bem dizer que um de seus companheiros mente “às vezes”, e não há absurdo nisso.</div>
<div align="justify">
<br /></div>
<div align="justify">
Então, segundo ele:<br />
<br />
* Porta certa: Direita;</div>
<ul>
</ul>
<div align="justify">
Mas como sabemos que ele é mentiroso, <b>esta porta é incorreta</b>.</div>
<div align="justify">
Como <b>Edgar</b> afirmou que Carlos fala a verdade, concluímos que ele <b>também é mentiroso</b>. Portanto, <b>porta da direita está descartada.</b></div>
<div align="justify">
<br /></div>
<div align="justify">
===> Para Artur:</div>
<div align="justify">
<br /></div>
<div align="justify">
<i>“Escolha a porta do centro. Mas saiba que eu sou mentiroso.”</i></div>
<div align="justify">
<br /></div>
<div align="justify">
Esta é a fala chave do problema. Pense comigo, como alguém pode dizer que é mentiroso? Se ele realmente for mentiroso, ele estará sendo verdadeiro! E se ele fala somente a verdade, ele está mentindo, pois afirma que é mentiroso!</div>
<div align="justify">
Portanto, isto é um absurdo. O que mostra que <b>Artur é o louco! </b>Devido a isso, não vamos avaliar nada do que ele disse.</div>
<div align="justify">
<br /></div>
<div align="justify">
===> Por fim, Augusto</div>
<div align="justify">
<br /></div>
<div align="justify">
<i>“… Escolha a porta da esquerda …e sou louco."</i></div>
<div align="justify">
<br /></div>
<div align="justify">
Nós já encontramos o louco, logo Augusto é mentiroso, como Raul havia afirmado.</div>
<div align="justify">
<br /></div>
<div align="justify">
Portanto, <b>Raul diz a verdade</b>, e a porta certa é a que ele afirmou ser a <b>correta: a do centro!</b></div>
<div align="justify">
____________________________________________________________________________________________ </div>
<div align="justify">
Bom, é isso pessoal. Qualquer dúvida é só deixar aí seu comentário.</div>
<div align="justify">
<br /></div>
<div align="justify">
Um abraço, e um ótimo final de semana a todos!</div>
<div align="justify">
<br /></div>
<div align="justify">
Marcelo Flora</div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com1tag:blogger.com,1999:blog-7241116304005966082.post-53280058186370538982010-07-09T12:04:00.000-07:002013-11-01T17:03:51.598-07:00Desafio N#9<span style="font-family: arial,helvetica,sans-serif; font-size: small;"></span> <br />
<div style="font-family: arial,helvetica,sans-serif;">
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/TDdxxrUDjmI/AAAAAAAAAyU/E5ghfdmoAEM/s1600-h/banner_desafio_resolvido9%5B4%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="banner_desafio_resolvido9" border="0" height="219" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TDdxyI8UnrI/AAAAAAAAAyY/gIR1rfaHoxA/banner_desafio_resolvido9_thumb%5B2%5D.jpg?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="banner_desafio_resolvido9" width="263" /></a><span style="font-size: small;"></span> </div>
<div style="font-family: arial,helvetica,sans-serif;">
E o desafio desta seamana foi o seguinte: </div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> </span></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"><i>“Dois amigos bêbados compraram 8 litros de vinho. Eles estavam caminhando, e na metade do caminho, decidem separar-se, repartindo antes o vinho igualmente.</i></span></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"><i>Para realizar as medidas há um barril de 8 litros (onde está o vinho), uma vasilha de 5 e outra de 3 litros. Como eles podem fazer para repartir igualmente o vinho?”</i></span><br />
<a name='more'></a></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"><a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TDdxzLfH59I/AAAAAAAAAyc/Eicx3aCgfDo/s1600-h/image%5B3%5D.png"><img alt="image" border="0" height="210" src="http://lh6.ggpht.com/_7wGgh4VGq1A/TDdx0W0JwyI/AAAAAAAAAyg/Xj1HySg3xfo/image_thumb%5B1%5D.png?imgmax=800" style="border-bottom-width: 0px; border-left-width: 0px; border-right-width: 0px; border-top-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="image" width="223" /></a></span> </div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">____________________________________________________________________________________________ </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Bom pessoal, como nos últimos desafios venho recebendo várias soluções, vou, a partir desta data, fazer um “mural” com a foto e o nome dos visitantes que resolveram. Foram eles:</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div align="center" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> <a href="http://www.fazendomatematica.com/" target="_blank"><img alt="matheus_basilio" border="0" height="240" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TDej7i6_skI/AAAAAAAAAzM/kdHP7KnnFlk/matheus_basilio%5B1%5D.jpg?imgmax=800" style="border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px; display: inline;" title="matheus_basilio" width="171" /></a> <a href="http://professoraju-mat.blogspot.com/" target="_blank"><img alt="professora_ju" border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEid1mQ-z64olUvoMFqLFnEpwfKBp6LWM38DVoQXEwyTq11K5Uw77ZaXUlZ0bJHd9j-3HSRo1NfqUJFtiRfdhnXvF95x89lRphprWvbXGbXh7_3znf5RIrekV9Pct0R754y607udawWSHv4/?imgmax=800" style="border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px; display: inline;" title="professora_ju" width="171" /></a> </span></div>
<div align="left" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div align="left" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">E os nossos vencedores de hoje possuem blogs muito interessantes também. Conheçam clicando nos retratos.</span></div>
<div align="left" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">____________________________________________________________________________________________ </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Eis a solução do desafio desta semana:</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">· Enchemos a vasilha de 3 litros;</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">· Passamos os 3 litros para a vasilha de 5 litros;</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">· Enchemos outra vez a vasilha de 3 litros;</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">· Enchemos a vasilha de 5 litros com a outra, sendo que sobrará 1 na de 3;</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">· Esvaziamos a de 5 no barril;</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">· Enchemos o litro da vasilha pequena na de 5;</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">· Enchemos a de 3 e esvaziamos na de 5, que como já tinha 1, terá 1+3 = 4;</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">· No barril sobra 4 litros para o outro amigo.</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">____________________________________________________________________________________________ </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">E é isso aí pessoal. E como diria nosso amigo Matheus, difícil seria dois bêbados terem pensado nisso! rsrs.</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> <br />E até o próximo desafio.</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Um abraço! </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Marcelo Flora</span></div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com3tag:blogger.com,1999:blog-7241116304005966082.post-1868693190091383582010-07-08T05:27:00.000-07:002013-11-01T17:04:13.011-07:00Dúvida da Natália (2)<div style="color: #666666;">
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TDXDYjMT2wI/AAAAAAAAAyM/JWDmZKP0FqI/s1600-h/image%5B3%5D.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="image" border="0" height="200" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TDXDZdnCmMI/AAAAAAAAAyQ/tyGiIJQE0BA/image_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="image" width="192" /></a> </div>
<div style="color: #666666;">
<span style="font-family: Arial;">Olá Marcelo, segue a dúvida:</span></div>
<div style="color: #666666;">
<br /></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Numa campanha de prevenção contra a dengue x pessoas dividiram igualmente entre si a tarefa de visitar 1000 casas de uma região da cidade. No dia previsto faltaram 5 pessoas e cada uma das outras pessoas teve de visitar 10 casas a mais. Qual é o número x de pessoas?</span></div>
<div align="justify" style="color: #666666;">
<br /></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Obrigada.</span><br />
<a name='more'></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">____________________________________________________________________________________________</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Olá Natália,</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Achei este exercício bem interessante, pois além de exigir do estudante a capacidade de interpretação do problema, envolve conceitos de </span><a href="http://www.brasilescola.com/matematica/sistemas-lineares.htm"><span style="font-family: Arial; font-size: small;">sistemas lineares</span></a><span style="font-family: Arial; font-size: small;"> e </span><a href="http://www.brasilescola.com/matematica/equacao-2-grau.htm"><span style="font-family: Arial; font-size: small;">equações do 2º grau</span></a><span style="font-family: Arial; font-size: small;">. </span></div>
<div align="justify" style="color: #666666;">
<br /></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Vou resolvê-lo passo a passo, para que ninguém fique com dúvidas.</span></div>
<div align="justify" style="color: #666666;">
<br /></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Vamos à resolução.</span></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;">____________________________________________________________________________________________</span></div>
<div align="justify" style="color: #666666;">
<br /></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Primeiramente, vamos esquematizar nosso raciocínio de acordo com o que nos é fornecido no problema. Sendo x número de pessoas, e chamando de n o número de casas que cada pessoa visitou, temos:</span><br />
<br /></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<ul style="color: #666666;">
<li><span style="font-family: Arial; font-size: small;"><i>“... x pessoas dividiram igualmente entre si a tarefa de visitar 1000 casas de uma região da cidade..." </i></span></li>
</ul>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify" style="color: #666666;">
<br />
<span style="font-family: Arial; font-size: small;">Ou seja, o número x de pessoas, vezes o número de casas que cada um visitou, será igual a 1000. Logo:</span><br />
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/TDXC1aji1FI/AAAAAAAAAvs/gv--v0k_FLE/s1600-h/clip_image002%5B5%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyGvDTAzcN1Ug4vhZvTuriYPuf6Pf4vLGmTvu55yRcAVlrI6UinXg1oJkiCoOf98IadeDFdfXv-d6wHmUukXp3k1870uF2Vxm3256zR47zleNr2nwmIFeE6riEzWkeUGFgZAFIrylBLqw/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002" width="118" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<br />
<ul style="color: #666666;">
<li><i><span style="font-family: Arial; font-size: small;">“… faltaram 5 pessoas e cada uma das outras pessoas teve de visitar 10 casas a mais…”</span></i></li>
</ul>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify" style="color: #666666;">
<br />
<span style="font-family: Arial; font-size: small;">Ou seja, o números x de pessoas menos 5, vezes o número de casas que cada um visitou mais 10, deve ser também igual a 1000. Assim:</span></div>
<div align="justify" style="color: #666666;">
<br /></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEga-Lw1Kh7SSzKYTV8_yvO6YqIpys1O8ZHPR7E12WLTTpqgLrywOT5OmD8UT4vP0ATixWcAynXQtr7O6Hr7vm43vgoYTgiZpEz60IwUsk_cQaokZ_JNP00ErkoM3Y4yZmsD3zv7l1SzIPs/s1600-h/clip_image004%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004" border="0" height="25" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TDXC2_30AmI/AAAAAAAAAv4/xqBIdi8Rgdo/clip_image004_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004" width="194" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Vamos agora desenvolver esta última equação.</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Aplicando a propriedade distributiva:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/TDXC3GjebDI/AAAAAAAAAv8/Yf95ltAdZ68/s1600-h/clip_image006%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image006" border="0" height="25" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TDXC322ieuI/AAAAAAAAAwA/OachvAKo2hQ/clip_image006_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image006" width="227" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Colocando n em evidência, e passando –50 para o outro lado:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TDXC4LyNplI/AAAAAAAAAwE/qyeAxetM1FA/s1600-h/clip_image008%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image008" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAi80Dx1og48aviMKxMO4Xy4H2AjVVtH37nM-nRcllvqTvthvPaOoR7v-YHtO_lz2avE8-y6scoP3VNqx1BIesfqF5x97hhh1a7KqyD5IO6kfwp7uk4Yns-SPW7Xp1_G3ChMebbTnUmo0/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image008" width="232" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Somando 1000 com 50, e passando 10x para o outro lado:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyd-8cNIi61iNZsfAqULNAuGsnr2TqTlClpjVeezJ9IlO5ck6TZ9i1TNuV9y4xwBwJh0nAVmmy1TRl2s0eucP63oadz7-YiHIBcHaAhgfF-b8eeYeyCVJyS60P5Y3qz_rMCPo4yLe4vG8/s1600-h/clip_image010%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image010" border="0" height="25" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TDXC5oEU0MI/AAAAAAAAAwQ/eWNgoFuhWic/clip_image010_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image010" width="189" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Passando (x-5) dividindo:</span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/TDXC57NlkFI/AAAAAAAAAwU/lL40UAPQRuE/s1600-h/clip_image012%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image012" border="0" height="50" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TDXC6dso9II/AAAAAAAAAwY/DtM8Y72rm7A/clip_image012_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image012" width="168" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Agora vamos substituir a eq. II na eq. I, assim:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"><img alt="clip_image002" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyGvDTAzcN1Ug4vhZvTuriYPuf6Pf4vLGmTvu55yRcAVlrI6UinXg1oJkiCoOf98IadeDFdfXv-d6wHmUukXp3k1870uF2Vxm3256zR47zleNr2nwmIFeE6riEzWkeUGFgZAFIrylBLqw/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002" width="118" /></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TDXC7FatHBI/AAAAAAAAAwc/AwaZ6s-Lt9Y/s1600-h/clip_image014%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image014" border="0" height="50" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TDXC7SptEuI/AAAAAAAAAwg/hvDGJhpvMHk/clip_image014_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image014" width="192" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Multiplicando x pelo parênteses:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TDXC71bOdRI/AAAAAAAAAwk/Qcm1TEI3X-k/s1600-h/clip_image016%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image016" border="0" height="50" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7jXsdHOonVYl1UmQvzkejgG1JmI6w2PtbIZ-pqdII53ku9sJGB3HiTn4nxG0iiWGR_BnYtcCQ4BZ0XQZwi7Bhk0T-r6na8_q1AaN409-vjJu0jgLDu5ulSWSaf7oBaT_PIInXM6xIceA/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image016" width="186" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Passando (x-5) multiplicando:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/TDXC8ytVKcI/AAAAAAAAAws/Ibx6slGzJM4/s1600-h/clip_image018%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image018" border="0" height="24" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TDXC9UuliTI/AAAAAAAAAww/jfwcaR4ym2Y/clip_image018_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image018" width="240" /></span></a></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Aplicando a propriedade distributiva:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5QbTOM8SYJ6XMy-p8KiuThRi5s4p1vD-xq3FpNNkNRWWGo4-N_0oRFeFClSpV-PHvNQkSSjzAgTONAeV2z6-NvsuJnArFpWop44FE2evUU86HrMMpS8971MUdn5CljTV15pVRshnHO6w/s1600-h/clip_image020%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image020" border="0" height="24" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TDXC-Y6sc8I/AAAAAAAAAw4/kE9xIPJriPI/clip_image020_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image020" width="240" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Fazendo 1050x – 1000x, e passando –5000 para o outro lado:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUtyvgacOZbPDKXZ-DnK1CjlO-yKyweCqO2aUFCsP5uyfgBkdeepf0uVyRmZJCjz39ps1OJlZ1Gh_dxOtp1lTyRUmEr3FucoHg-NeYqpfGzES4JZnX4YchqL2iHLbeTOhyHs1U3lzhxgg/s1600-h/clip_image022%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image022" border="0" height="25" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TDXC_ddYcgI/AAAAAAAAAxA/mLDJ5w3hnOs/clip_image022_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image022" width="206" /></span></a></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Dividindo todos os termos por 10:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0aF3HK28P9QoIpkS4RDfP1VIwPWTSgzksYpOJ21l_v6XltjkZDlM7xVFBdwiTMvns_NqDIPYmYiR86qtHNTnnbvhv9imDBGYPrEAAGjphlf9uiNRIAVw3HXg0qdolAubb-NnPFHejVCg/s1600-h/clip_image024%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image024" border="0" height="25" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TDXDAZgFl9I/AAAAAAAAAxI/uGNK2Tx4rUI/clip_image024_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image024" width="164" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify" style="color: #666666;">
<br /></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Perceba que chegamos em uma </span><a href="http://www.brasilescola.com/matematica/equacao-2-grau.htm"><span style="font-family: Arial; font-size: small;">equação do 2º grau.</span></a><span style="font-family: Arial; font-size: small;"> Para resolvê-la, aplicamos a fórmula de Bhaskara.</span><br />
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjevRJT95iquTdhCOrpktZ5RmniymhgJH9Dgu6whjt507kRqsu_VaIuVMwgjPytSNgfFjcPPCjJ58JNfdBdNiYrN1O6oZBHLO7AqyY-QYDH34sMxoWgYSe7hJmC3GjDz1UiFGDTocXMl2s/s1600-h/clip_image026%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image026" border="0" height="51" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TDXDBYKsX7I/AAAAAAAAAxQ/zG6z9Ym7l68/clip_image026_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image026" width="165" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<br />
<span style="font-family: Arial; font-size: small;">Onde, para o nosso problema, a = –1; b = 5; e c = 500.</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Substituindo a, b e c na equação, fica:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/TDXDB6yIHEI/AAAAAAAAAxU/F2wyrOsG6gg/s1600-h/clip_image002%5B6%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[6]" border="0" height="51" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TDXDCbM2FGI/AAAAAAAAAxY/No9zafAQlkM/clip_image002%5B6%5D_thumb%5B2%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[6]" width="240" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Desenvolvendo:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/TDXDC3BdPEI/AAAAAAAAAxc/Xo7VlMXWNhE/s1600-h/clip_image004%5B5%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004[5]" border="0" height="50" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TDXDDQhGuvI/AAAAAAAAAxg/cg29TNChL3k/clip_image004%5B5%5D_thumb%5B2%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[5]" width="135" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaGNOynFfzfgN87pgNfadlyBr7WyQ_64lX641C7iRV1pqtmakXDcWv8xGzo9rNeQQjALZ-kTguNpPcrOb4ePRzgOlVYohZPh2-1GTY6_70rnhC9mWp5flMgPP3nKaDnSYvgi6hfcj8-I4/s1600-h/clip_image006%5B5%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image006[5]" border="0" height="46" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TDXDEOcvCkI/AAAAAAAAAxo/ec78YhYRLBI/clip_image006%5B5%5D_thumb%5B2%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image006[5]" width="102" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Temos dois resultados possíveis para x. Um somando 45, e outro subtraindo. Chamarei estes resultados de x’ e x’’.</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"> </span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Encontrando x’:</span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgulxVSqS3Uaj6gHwUjpDLodgokgYy6LMrKuV69wz6PZnks82nUALpPp0beRiJSXSioOwomnWRQIInR0owp7Uta07iw3-A2W1KSlSCMlhGeOfqf0BDvqpSd3QtvRNqOzdxUSzX7T36Qcdk/s1600-h/clip_image032%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image032" border="0" height="46" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TDXDFJzKADI/AAAAAAAAAxw/7E0pKK7-C-M/clip_image032_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image032" width="106" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsokBlsqzbckX8enkACRS0vYD-cWRYPMR-uIBC28FG5_aT-t6uoKDG8qXsLfB5b4H_lS4BogQU3j7O9rewx9Kf4-pnX8rvMuJULTiKbP5ocTGM93wqRtMeDy2W2hfQzSYT4dhhL-jL9EM/s1600-h/clip_image034%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image034" border="0" height="25" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TDXDFwP8GFI/AAAAAAAAAx4/ShKJp2bzHz8/clip_image034_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image034" width="75" /></span></a></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Encontrando x’’:</span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TDXDGPy5zvI/AAAAAAAAAx8/lHqCo1yXM2g/s1600-h/clip_image040%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image040" border="0" height="46" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TDXDGgts8KI/AAAAAAAAAyA/f7zvBd-VHk8/clip_image040_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image040" width="111" /></span></a></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/TDXDG1pMnHI/AAAAAAAAAyE/uUIWiboIbx0/s1600-h/clip_image042%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image042" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgk0jIo5B9oIgaPHeAeeqnIPGU5H5g79DAF3SrspeQmk75GjTlM6U0z9i3HNQEWfvXt_QWIQxdyYbYO-o16WdRaWPdAsbNTWm8dvKqhKvWDRibzdDTzFPCJMd-Ljw2dPJz0fxoNBGzIdL8/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image042" width="65" /></span></a></div>
<div style="color: #666666; text-align: justify;">
<br />
<span style="font-family: Arial; font-size: small;">Por fim, basta analisar qual das duas respostas se encaixa no nosso problema. Como o número de pessoas deve ser positivo, o valor que estamos procurando é x’’ = 25.</span></div>
<div align="justify" style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"></span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Portanto, <b>o número x de pessoas é igual a 25.</b></span></div>
<div style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<b><span style="font-family: Arial; font-size: small;"></span></b></div>
<div align="justify" style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Continue praticando, que é só com persistência que conseguimos sucesso não só em matemática, mas em tudo na vida.</span></div>
<div align="justify" style="color: #666666;">
<br /></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Um abraço!</span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;"> <br />Marcelo Flora <br />____________________________________________________________________________________________</span></div>
<div style="color: #666666;">
<span style="font-family: Arial; font-size: small;">Saiba como enviar suas dúvidas. </span><a href="http://mfmatematica.blogspot.com/2010/01/esclareca-suas-duvidas-em-matematica.html"><span style="font-family: Arial; font-size: small;">Clique aqui!</span></a></div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com2tag:blogger.com,1999:blog-7241116304005966082.post-38184837463993325262010-07-02T15:31:00.000-07:002013-11-01T17:05:17.997-07:00Desafio N#8<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TC5nJpgSbdI/AAAAAAAAAvI/SgWoxG2Bnlg/s1600-h/banner_desafio_resolvidoN%238%5B6%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="banner_desafio_resolvidoN#8" border="0" height="233" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikGr8qKLeyWL7dQFCgXA0HzVN622piBkAJonlL9MKA06SXpslEw63AbJuqNRG6l1E70ynC7sIJivqBDXEpte8QAzV_lgvQ3DF_xEZODsZjm1Jak22nZumy4e9slNt9zY6VCwGz7pLA4Zg/?imgmax=800" style="border: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="banner_desafio_resolvidoN#8" width="280" /></a> <br />
<span style="font-family: Arial, Helvetica, sans-serif;">E o desafio desta semana foi o seguinte:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"> </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><i>Observe a sequência abaixo e responda:</i> </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><i></i> </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><i>2+3 = 10</i> </span><br />
<div align="left">
<i><span style="font-family: Arial, Helvetica, sans-serif;">4+8 = 48</span></i></div>
<div align="left">
<i><span style="font-family: Arial, Helvetica, sans-serif;">5+5 = 50</span></i></div>
<div align="left">
<i><span style="font-family: Arial, Helvetica, sans-serif;">7+2 = 63</span></i></div>
<div align="left">
<i><span style="font-family: Arial, Helvetica, sans-serif;">8+1 = 72</span></i></div>
<div align="left">
<i><span style="font-family: Arial, Helvetica, sans-serif;">9+7 = ?</span></i></div>
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TC5nK-np28I/AAAAAAAAAvQ/1xZKelCb7qQ/s1600-h/image%5B4%5D.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img align="right" alt="image" border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyG6O1zTPwHugNqifrpQWTdD3gIuKL6iVlTPZ9djWQ2jgdNrMuz952QROmoWnx1LVQpKH_xEjuBsJ4tM1fqbuHPAjAvKeKJKELruOFga6iqSU7f9ZMowWUtBm8nB8rX4qRChQmWY8kB4Y/?imgmax=800" style="border: 0px; display: inline; margin-left: 0px; margin-right: 0px;" title="image" width="99" /></a><br />
<a name='more'></a><br /><br /><br />
<br />
Antes de apresentar a solução do desafio, gostaria de agradecer àqueles que me enviaram suas soluções. <br /> <br />Muito obrigado pela participação de todos! <br /> <br />E a melhor resolução recebida foi da Jaqueline Danielle Bueno! Parabéns!<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_P68-pSKztifAxEX6l4qzvNNGfJCpwh2o7mzkcMtbrRce1foq3U-RHMwdfqThbri4k7eK0QfMKH0EfOI8_L0ExIzfnV8hhynAdA7TA5SxjdY2TkY3VpuPY2_X0-3BB_Mzim0va8hltlo/s1600-h/jaqueline_bueno%5B4%5D.jpg"><img alt="jaqueline_bueno" border="0" height="291" src="http://lh6.ggpht.com/_7wGgh4VGq1A/TDiuRAjtAvI/AAAAAAAAAzc/akSc0lpcvfg/jaqueline_bueno_thumb%5B2%5D.jpg?imgmax=800" style="border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="jaqueline_bueno" width="207" /></a>Segue abaixo a sua resolução. <br />____________________________________________________________________________________________ <br /> <br />Boa Noite, segue abaixo a solução do Desafio N#8. <br /> <br /><span style="color: red;">2</span>+3 = 10 <br /><span style="color: red;">4</span>+8 = 48 <br /><span style="color: red;">5</span>+5 = 50 <br /><span style="color: red;">7</span>+2 = 63 <br /><span style="color: red;">8</span>+1 = 72 <br /><span style="color: red;">9</span>+7 = ? <br /> <br />Achei a solução somando os números, e multiplicando pelo 1º ( Em vermelho ). <br /> <br />Exemplo : <br /> <br /><span style="color: red;">2</span>+3 = 5 5.<span style="color: red;">2</span>= 10 <br /><span style="color: red;">4</span>+8 =12 12.<span style="color: red;">4</span>= 48 <br />... <br />Portanto, 9 + 7 será igual a: <br /><span style="color: red;"></span> <br /><span style="color: red;">9</span>+7= 16 16.<span style="color: red;">9</span>= 144 <br /> <br />Resposta: 144. <br />____________________________________________________________________________________________ <br /> <br />É isso mesmo Jaqueline. Obrigado por colaborar com o blog! <br /> <br />E não percam o desafio N#9 segunda-feira! <br /> <br />Um ótimo final de semana a todos! <br /> <br />Marcelo FloraMarcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com0tag:blogger.com,1999:blog-7241116304005966082.post-51858913112076553052010-06-14T11:59:00.001-07:002013-11-01T17:06:51.851-07:00Desafio N#7<div style="font-family: Arial,Helvetica,sans-serif;">
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TCklnCuNA5I/AAAAAAAAAvA/hNnarBPI8Qc/s1600-h/banner_desafio_resolvido7%5B4%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="banner_desafio_resolvido7" border="0" height="236" src="http://lh6.ggpht.com/_7wGgh4VGq1A/TCklnwJdxkI/AAAAAAAAAvE/GIc4Y9xYvn8/banner_desafio_resolvido7_thumb%5B2%5D.jpg?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="banner_desafio_resolvido7" width="283" /></a><span style="font-size: small;"> </span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br />
<span style="font-size: small;">O desafio desta semana foi o seguinte: <br /> </span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><i>“Quantos são os possíveis valores inteiros de x para que </i></span><span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-VzwM8KdjiCEiOXTRaa6-v13mjWFoIh7qcIIC9nogChTrqN1U-zVpJRelM3mkbdk1SNGVC8Nr5oEiOxakvzSg0XP6DcvvCuGAmtA2OwquHhyphenhyphenmRjkCvezx5XQZAO9DeZOSzFFD7CsqStk/s1600-h/clip_image002%5B4%5D.png"><span style="color: black;"><i><img alt="clip_image002" border="0" height="43" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TBZ8B8VhYAI/AAAAAAAAAuU/PgH5HvUH7Lg/clip_image002_thumb%5B1%5D.png?imgmax=800" style="border-width: 0px; display: inline;" title="clip_image002" width="45" /></i></span></a></span><span style="font-size: small;"><i> seja um número inteiro?”</i></span><br />
<span style="font-size: small;"><i><br /></i></span>
<span style="font-size: small;"><i></i></span><br />
<a name='more'></a><span style="font-size: small;"><i><br /></i></span><br />
<span style="font-size: small;"><i><br /></i></span>
<span style="font-size: small;"><i><br /></i></span>
<span style="font-size: small;"><i><br /></i></span>
<span style="font-size: small;"><i><br /></i></span>
<span style="font-size: small;"><i><br /></i></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnN-HuYPBIsRZAkHLepzl5fO_MCYtDf2WvHTXk4IvxQ72I4dmKkPpKaqjAUEh8_Gyj-wowqG2E1Zg6LOVeOQuYWk3c-Wn-8TVzmLIgkQ_M6-M1i02NDPtey1nex91eWDD1Rzw7ir2y0jY/s1600-h/image%5B11%5D.png"><span style="color: black;"><img alt="image" border="0" height="193" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TBZ8DO4IQhI/AAAAAAAAAuc/SEufMTiicE4/image_thumb%5B7%5D.png?imgmax=800" style="border-width: 0px; display: inline; margin-left: 0px; margin-right: 0px;" title="image" width="183" /></span></a></span><span style="font-size: small;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYnkvDmdrDe6ms2nQEPPecSuPqX6QEiT04VES-reaJI-C1_oOWXiVGkWqOlIYNpFv_We9lpMQmz82bdAVaz2dq4e_GA_L6v0sT2x0dtXWQ5lRuDldtfT8JHtyz6p3C7UanxnxWynAJ4us/s1600-h/image%5B13%5D.png"><span style="color: black;"><img alt="image" border="0" height="117" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTPucUbRHDNwD9qSOrwCue1j0GYxd4hW3VrfPSAX5xu2mInTMQTCFvWQVkE6sLlMxbawnREjbETbQAz3DoAuZpU6gWf35BOlu2JvGnDFg33N8Lx53pdQ2kwz8lTaMOmxJmDY15CjJlr70/?imgmax=800" style="border-width: 0px; display: inline; margin-left: 0px; margin-right: 0px;" title="image" width="117" /></span></a></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<div>
<span style="font-size: small;">____________________________________________________________________________________________
</span></div>
<div>
<br />
<span style="font-size: small;">Segue abaixo a resolução do nosso amigo Hever.</span></div>
<span style="font-size: small;"><i>Resolução:</i></span><br />
<span style="font-size: small;"><i> <br />Sendo x+99/x+19 = 1+ 80/x+19, logo, para que x+99/x+19 seja um número inteiro, 80/x+19 deve ser um inteiro. Para que isso aconteça, o denominador da fração (x+19) deve assumir valores divisores de 80. Como os divisores são:</i></span><br />
<span style="font-size: small;"><br /><i>D(80)= {-+1,-+2,-+4,-+5,-+8,-+10,-+16,-+20,-+40,-+80}</i></span><br />
<span style="font-size: small;"><br /><i>Concluímos que x pode assumir 20 valores inteiros.</i></span><br />
<span style="font-size: small;"><br /><i>Hever.</i></span><br />
<span style="font-size: small;">____________________________________________________________________________________________
</span><br />
<br />
<span style="font-size: small;">É isso mesmo Hever, e obrigado por participar!</span><br />
<br />
<span style="font-size: small;">Um abraço pessoal! E até o próximo desafio!</span><br />
<br />
<span style="font-size: small;">Marcelo Flora</span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com0tag:blogger.com,1999:blog-7241116304005966082.post-67384178768071305452010-06-11T13:16:00.000-07:002013-11-01T17:07:37.276-07:00Desafio N#6<span style="font-family: arial,helvetica,sans-serif; font-size: small;"></span> <br />
<div style="font-family: arial,helvetica,sans-serif;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuohYKplq9CJUz4y2SZDwMG7kvg-qKDsKbTqL49YG4dUFY_iCRW7V99aK_sdVk4VtB90q8wpVlF7P865BHVzC40zTle57plLn2FJukQJVGOWNHNPhkDmJFbi7H1DwsjSfwR0chk6y0fcs/s1600-h/banner_desafio_resolvido6%5B5%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="banner_desafio_resolvido6" border="0" height="238" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TBKY_osjQ5I/AAAAAAAAAtw/Q50yTtxGPaw/banner_desafio_resolvido6_thumb%5B3%5D.jpg?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="banner_desafio_resolvido6" width="285" /></a><span style="font-size: small;"></span> </div>
<div style="font-family: arial,helvetica,sans-serif;">
O desafio desta semana foi o seguinte:</div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"><i>Determine o menor número natural cuja:</i></span><br />
<i><br /></i>
<i>a) Divisão por 2 tem resto 1;</i><br />
<i>b) Divisão por 3 tem resto 2;</i><br />
<i>c) Divisão por 4 tem resto 3;</i><br />
<i>d) Divisão por 5 tem resto 4;</i><br />
<i>d) Divisão por 6 tem resto 5;</i><br />
<i>e) Divisão por 7 tem resto 0;</i><br />
<i></i><br />
<a name='more'></a><i><br /></i><br />
<i><br /></i>
<i><br /></i>
<i><br /></i>
<i><br /></i></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"><i><a href="http://lh6.ggpht.com/_7wGgh4VGq1A/TAyH8RhA9jI/AAAAAAAAAtk/EYDXseZ0CyM/s1600-h/image%5B42%5D.png"><img alt="image" border="0" height="172" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TAyH8wfNk5I/AAAAAAAAAto/cC8nFauB7uc/image_thumb%5B28%5D.png?imgmax=800" title="image" width="240" /></a></i></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">E quem resolveu o desafio desta semana foi a Profª Ju, do blog <a href="http://professoraju-mat.blogspot.com/" title="http://professoraju-mat.blogspot.com/">http://professoraju-mat.blogspot.com/</a></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixgTDkU65YpwdKJ3ymDkVFC_AN49zOjaMzlH7Q8Jv6DltpyW19ySxfRa-kO_Vxl5j08GyaIbilLBWN2KCiBoGZ9ouVNylh8EO99yvEgrse-2L1EwTLZkmRQJYLET-xTBlBr1RyLGERvi0/s1600-h/professora_ju%5B4%5D.jpg"><img alt="professora_ju" border="0" height="264" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TDjLd5LvboI/AAAAAAAAAzk/CpwDPKp0SuQ/professora_ju_thumb%5B2%5D.jpg?imgmax=800" style="border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="professora_ju" width="188" /></a> </div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Vamos à sua resolução.</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">____________________________________________________________________________________________ </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Olá Marcelo,</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Eis a solução do desafio desta semana:</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Vamos começar debaixo para cima, a partir da informação da letra e)</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif; text-align: left;">
<span style="font-size: small;">Como ela fala "divisão por 7 tem resto 0", sabemos então, que o número procurado é um multiplo de 7, ou seja, pode ser:</span></div>
<div align="center" style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div align="center" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">7,14,21,28,35,42,49,56,63,70,77,84,91,… 133,140... </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Depois, analisamos as demais letras:</span></div>
<div align="left" style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div align="left" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Dividido por 2 tem resto 1... </span></div>
<div align="center" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">7,21,35,49,63,77,91,105,119,133...</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Dividido por 3 tem resto 2... </span></div>
<div align="center" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> <br />35,77,119...</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Dividio por 4 tem resto 3... </span></div>
<div align="center" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> <br />35,119...</span></div>
<div align="left" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Dividido por 5 tem resto 4... </span></div>
<div align="center" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> <br />119...</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Dividido por 6 tem resto 5... </span></div>
<div align="center" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> <br />119.</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Logo, o número procurado é o 119.</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Abraços</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Juliana </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">____________________________________________________________________________________________ </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Muito obrigado por participar Juliana!</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">E não se esqueçam, semana que vêm tem mais!</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Um abraço!</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Marcelo Flora</span></div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com3tag:blogger.com,1999:blog-7241116304005966082.post-68727357832845496722010-06-04T19:15:00.000-07:002013-11-01T17:08:07.237-07:00Desafio N#5<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><span style="font-size: small;"><span style="font-size: small;"></span></span></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><span style="font-size: small;"><span style="font-size: small;"></span></span></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0tS-gSxx6ZeswUEF77sERYRon4Z-vL3IpkcvZKm8f99aKP59VKDPcMNyselQoGvOVP2KysavKr_qdUUM2-asS_Cke1X1cA6O2TLyNvhNn36x-qur7TlXHukkMQVgKExuTWpNWCPKzFqM/s1600-h/banner_desafio_resolvido5%5B7%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="banner_desafio_resolvido5" border="0" height="246" src="http://lh6.ggpht.com/_7wGgh4VGq1A/TAm0KB54tFI/AAAAAAAAAtg/djeQnFgdizk/banner_desafio_resolvido5_thumb%5B3%5D.jpg?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="banner_desafio_resolvido5" width="295" /></a><span style="font-size: small;"><span style="font-size: small;"><span style="font-size: small;"><span style="font-size: small;"> </span></span></span></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;">O desafio desta semana foi o seguinte:</span><br />
<span style="font-size: small;"><span style="font-size: small;"><span style="font-size: small;"> </span> </span></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"> </span></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><i>“O casal Aguiar tem vários filhos. Cada filha tem o mesmo número de irmãos e irmãs, e cada filho tem duas vezes mais irmãs do que irmãos. Quantos filhos e filhas existem na família?”</i></span></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"> </span><br />
<a name='more'></a><span style="font-size: small;"><br /><span style="color: black; font-size: small;"><br /></span></span><br />
<span style="font-size: small;"><br /></span>
<span style="font-size: small;"><br /></span>
<span style="font-size: small;"><br /></span>
<span style="font-size: small;"><br /></span>
<span style="font-size: small;"><br /></span>
<span style="font-size: small;"><br /></span>
<span style="font-size: small;"><span style="color: black; font-size: small;"><a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TANNQPR3f2I/AAAAAAAAAsM/nZsI_eqgxFo/s1600-h/image%5B10%5D.png"><img alt="image" border="0" height="314" src="http://lh5.ggpht.com/_7wGgh4VGq1A/TANNRIMJsKI/AAAAAAAAAsQ/VqDI3IVlpZE/image_thumb%5B6%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="image" width="314" /></a></span><span style="font-size: small;"> </span></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><span style="font-size: small;">____________________________________________________________________________________________</span> <br /> </span> </div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;">Para resolver este desafio, vamos chamar cada filha de "M" e cada filho de "H".</span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><br /></span></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;">Para facilitar a nossa compreensão do problema, vamos esboçar alguns desenhos. Primeiro, analisemos a afirmação: “<i>Cada filha tem o mesmo número de irmãos e irmãs”.</i> Assim, vamos adotar dois casos:</span></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><br /></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3n8JoM_-mtqbcEsT8f8nXur2VaWTWp7q8ShGw8Sz5y_qocMW6q3TcAaDrb-0iXussHFY_1wArd8CwbuceQlYEN8g7GXSNNM5K1q2tmR4ipVsFaEon-v1zeoCkUqj-U1kxFKm_6Da5evA/s1600-h/desafio%205%5B11%5D.jpg"><span style="color: black;"><img alt="desafio 5" border="0" height="348" src="http://lh4.ggpht.com/_7wGgh4VGq1A/TAmzKSPNIhI/AAAAAAAAAsY/Mr9J2enW7D8/desafio%205_thumb%5B7%5D.jpg?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="desafio 5" width="609" /></span></a></span><span style="font-size: small;"> </span></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<br />
<span style="font-size: small;">Perceba que o número de mulheres é sempre igual ao número de homens mais 1. Desta forma, sendo M o número de mulheres, e H o número de homens, temos:</span></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><br /></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><a href="http://lh3.ggpht.com/_7wGgh4VGq1A/TAmzKrczQ6I/AAAAAAAAAsc/ququShV8aGw/s1600-h/clip_image002%5B9%5D%5B3%5D.png"><span style="color: black;"><img alt="clip_image002[9]" border="0" height="29" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TAmzLNyVgHI/AAAAAAAAAsg/x64oxLsdfWc/clip_image002%5B9%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[9]" width="140" /></span></a></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><br /></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;">Da mesma forma, para a afirmação: <i>“Cada filho tem duas vezes mais irmãs do que irmãos”,</i> temos:</span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><br /></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><a href="http://lh4.ggpht.com/_7wGgh4VGq1A/TAmzLm1QGoI/AAAAAAAAAsk/1CGTm6AQrXw/s1600-h/desafio%205b%5B6%5D.jpg"><span style="color: black;"><img alt="desafio 5b" border="0" height="273" src="http://lh6.ggpht.com/_7wGgh4VGq1A/TAmzMaUX5QI/AAAAAAAAAso/pfyneI__1pA/desafio%205b_thumb%5B4%5D.jpg?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="desafio 5b" width="637" /></span></a></span><span style="font-size: small;"> </span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><br /></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;">Perceba que o número de mulheres é sempre igual a duas vezes o número de homens menos 1. Assim:</span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><br /></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><a href="http://lh4.ggpht.com/_7wGgh4VGq1A/TAmzMn0sCkI/AAAAAAAAAss/qthS1himoM4/s1600-h/clip_image002%5B11%5D%5B4%5D.png"><span style="color: black;"><img alt="clip_image002[11]" border="0" height="29" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLFo3LDivKT_sMOanpCq3-Zl77V52yQ1s5EJ76v1ugnE7f7mzKNEdovYGeu467RHBhStMnLgf6gbbpK4x3Iyeh94SJW5EOnJVhLjD6VhX4zs3FRLfEoLfbfYnECHBmexsErM_9moByf_I/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[11]" width="178" /></span></a></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><br /></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;">Agora é só resolver o sistema. Substituindo I em II:</span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><br /></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8ekUVfZIDUA1YkyBeWah09kuY7QonjWzijl3GMBDzwkimjEx0gwhCAwAVzs2OwIpAcKO92YVDPI8xfeVSxvCkdnC00_CKM0e4eKhgiu_3fvskLHUEzZDu-SNnzTWdZx267hnZ15qBnWg/s1600-h/clip_image002%5B13%5D%5B4%5D.png"><span style="color: black;"><img alt="clip_image002[13]" border="0" height="29" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVlRCHNpXxD6NzJrdLnul7I9ZEx8ik9NL_B5BCSsHYDV0bM3bgJVFeoFNLb9uT_-740xyExOqzp3HF6W9XWe2Gcq_dqJ2zuJBTrYhfwJdtLwJJbRwvEYkoSKiP-Maf3HkpoXDnasTCO6k/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[13]" width="182" /></span></a></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><a href="http://lh6.ggpht.com/_7wGgh4VGq1A/TAmzObH77QI/AAAAAAAAAs8/5DAlewyUEOQ/s1600-h/clip_image002%5B17%5D%5B4%5D.png"><span style="color: black;"><img alt="clip_image002[17]" border="0" height="29" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwFIkc58Dz700_bUKXPLnLbv_JCYC7khvRaYosDj-4PcaJvOhxc1QQtpRkazLJwfEjgkZeM-8zWXbKJLYcwbNMOwQEaadc8HLJwaOc4VXAQYWOcR0OBhvRMl92k1Rc3GGuEbW4Wh-hd_4/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[17]" width="146" /></span></a></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbgoRG3iyXnQjeDQixI7LhvnCUl-SYFU8qGQLZQyQrOHsIDd_b4iOHgfyqhwzdkVEKR2FLFxwVByG9glOOT8rME3vyZHziKM9OTG2sCSizHHL2ayv1TPjslyR8bj1cTySHRgA-GFyxgsg/s1600-h/clip_image002%5B15%5D%5B3%5D.png"><span style="color: black;"><img alt="clip_image002[15]" border="0" height="29" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TAmzQDn9wwI/AAAAAAAAAtI/xIQ43by1xkU/clip_image002%5B15%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[15]" width="56" /></span></a></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;">Substituindo H em I:</span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"> <img alt="clip_image002[9]" border="0" height="29" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TAmzLNyVgHI/AAAAAAAAAsg/x64oxLsdfWc/clip_image002%5B9%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[9]" width="140" /></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic6omAkdHYMK1KBkbhKJEaHdGChfL1rom6XKDp-LEi3830r7zojbSisZgMd0f3l8zryq9I2DBmn4z4oIgrGToP9ySYP1XcMMvV9hdwgJFNHehrkWqY-Stifzo4oQxi_AvkiQaDH-K4HIc/s1600-h/clip_image002%5B19%5D%5B3%5D.png"><span style="color: black;"><img alt="clip_image002[19]" border="0" height="29" src="http://lh6.ggpht.com/_7wGgh4VGq1A/TAmzQ22diSI/AAAAAAAAAtQ/X73DPKHFSwE/clip_image002%5B19%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[19]" width="100" /></span></a></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwQ4QTQfc-uhP6gWYxT8UFof5tQjtIEiKnWmIkPd4mUMIVrdwtV7AAcI10CVsmjj-3awo67140Jg14ll8L7A6yHl2cSZMbKVSeAcCflICDuwT4siotL2VzkKjO7wT2yiA2FUXHjto1DB0/s1600-h/clip_image004%5B5%5D.png"><span style="color: black;"><img alt="clip_image004" border="0" height="29" src="http://lh3.ggpht.com/_7wGgh4VGq1A/TAmzRjr_TCI/AAAAAAAAAtY/1GO5NMmYUhY/clip_image004_thumb%5B2%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004" width="58" /></span></a></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;">Portanto, o casal tem 3 filhos e 4 filhas.</span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;">____________________________________________________________________________________________</span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;">Um abraço! E bom final de semana a todos!</span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;"><br /></span></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<span style="font-size: small;">Marcelo Flora</span></div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com0tag:blogger.com,1999:blog-7241116304005966082.post-5915131091892696252010-05-28T07:07:00.001-07:002013-11-01T17:09:24.468-07:00Provas de Matemática - FUVEST<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisJNfZ5ILVj3uZa1Ae59oJeG7NWyQpctAIxdAzQnlc7X1x68GNcNeErZxYCWOq-M84HgQPEUQYAMiu5icLmD8Z3SpMSiMBDkt1myEjxh4x-xW6g2W8FUfFmTRamLU7sjt3Iud8a7QpeVE/s1600/usp.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisJNfZ5ILVj3uZa1Ae59oJeG7NWyQpctAIxdAzQnlc7X1x68GNcNeErZxYCWOq-M84HgQPEUQYAMiu5icLmD8Z3SpMSiMBDkt1myEjxh4x-xW6g2W8FUfFmTRamLU7sjt3Iud8a7QpeVE/s320/usp.jpg" /></a></div>
<br />
<br />
<br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border: 1pt solid windowtext; width: 616px;">
<tbody>
<tr>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 110.25pt;" valign="top" width="147"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><span id="goog_954942019"></span><span id="goog_954942020"></span>Vestibular
1999</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 118.5pt;" valign="top" width="158"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Vestibular
2000</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 114pt;" valign="top" width="152"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Vestibular
2001</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 116.25pt;" valign="top" width="155"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Vestibular
2002</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 110.25pt;" valign="top" width="147"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/download/vest1999/Prv1f99t.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest1999/provas/1fase/dia2/prv1f99t.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest1999/provas/gab1f2.stm"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest1999/provas/2fase/mat992f.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest1999/provas/2fase/mat992f.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 118.5pt;" valign="top" width="158"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/download/vest2000/p1f2000t.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2000/provas/1fase/dia2/p1f2000t.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2000/provas/gab1f2.stm"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2000/provas/2fase/mat/mat2f.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2000/provas/2fase/mat/mat2f.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 114pt;" valign="top" width="152"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/download/vest2001/p1f2001t.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2001/provas/p1f2001t.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2001/provas/gab1ft.stm"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2001/provas/mat2f.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/download/vest2001/mat2f.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 116.25pt;" valign="top" width="155"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2002/provas/1fase/dia2/p1f2002t.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2002/provas/1fase/dia2/p1f2002t.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2002/provas/1fase/dia2/gab2.stm"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2002/provas/2fase/mat/mat2f.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2002/provas/2fase/mat/mat2f.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 110.25pt;" valign="top" width="147"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Vestibular
2003</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 118.5pt;" valign="top" width="158"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Vestibular
2004</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 114pt;" valign="top" width="152"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Vestibular
2005</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 116.25pt;" valign="top" width="155"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Vestibular
2006</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 110.25pt;" valign="top" width="147"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2003/provas/p1f2003v.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2003/provas/p1f2003v.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2003/provas/gabpro.stm"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2003/provas/2fase/mat/mat2f.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2003/provas/2fase/mat/mat2f.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 118.5pt;" valign="top" width="158"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2004/provas/p1f2004v.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2004/provas/p1f2004v.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2004/provas/gabpro.stm"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2004/provas/2fase/mat/mat2f.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2004/provas/2fase/mat/mat2f.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 114pt;" valign="top" width="152"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2005/provas/p1f2005v.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2005/provas/p1f2005v.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2005/provas/gabpro.stm"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2005/provas/2fase/mat/mat2f.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2005/provas/2fase/mat/mat2f.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 116.25pt;" valign="top" width="155"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2006/provas/p1f2006v.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2006/provas/p1f2006v.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2006/provas/gabpro.stm"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2006/provas/2fase/mat/mat2f.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2006/provas/2fase/mat/mat2f.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 110.25pt;" valign="top" width="147"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Vestibular
2007</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 118.5pt;" valign="top" width="158"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Vestibular
2008</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 114pt;" valign="top" width="152"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Vestibular
2009</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 116.25pt;" valign="top" width="155"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center;">
<b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Vestibular
2010</span></b><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 110.25pt;" valign="top" width="147"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2007/provas/p1f2007v.html.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2007/provas/p1f2007v.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2007/provas/gabpro.stm"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2007/provas/2fase/mat/mat2f.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2007/provas/2fase/mat/mat2f.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 118.5pt;" valign="top" width="158"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2008/provas/p1f2008v.html.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2008/provas/p1f2008v.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2008/provas/gabpro.stm"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2008/provas/2fase/mat/mat2f2008.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2008/provas/2fase/mat/mat2f.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 114pt;" valign="top" width="152"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2009/provas/p1f2009v.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2009/provas/gabpro.stm"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2009/provas/gab1f2009.pdf"><span style="color: #669966;">Gabaritos em PDF</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2009/provas/2fase/mat/mat2f2009.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2009/provas/2fase/mat/mat2f.zip"><span style="color: #669966;">Prova para download</span></a><o:p></o:p></span></div>
</td>
<td style="border: 1pt solid windowtext; padding: 1.5pt; width: 117pt;" valign="top" width="156"><ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Primeira Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2010/1fase/p1f2010v.pdf"><span style="color: #669966;">Prova em PDF</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2010/1fase/p1f2010gab.html"><span style="color: #669966;">Gabarito</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2010/1fase/p1f2010gab.pdf"><span style="color: #669966;">Gabarito em PDF</span></a><o:p></o:p></span></div>
<ul>
<li><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"></span><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;">Segunda Fase<o:p></o:p></span></li>
</ul>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2010/provas/fuv2010_2fase_prova2.pdf"><span style="color: #669966;">Segundo Dia (PDF)</span></a><o:p></o:p></span></div>
<div align="center" class="MsoNormal" style="line-height: normal; margin: 7.5pt 0cm; text-align: center;">
<span style="font-family: "Trebuchet MS","sans-serif"; font-size: 10.5pt;"><a href="http://www.fuvest.br/vest2010/provas/fuv2010_2fase_prova3.pdf"><span style="color: #669966;">Terceiro Dia (PDF)</span></a><o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com0tag:blogger.com,1999:blog-7241116304005966082.post-61139377697816713782010-05-28T06:33:00.000-07:002013-11-01T17:09:51.730-07:00Desafio N#4<span style="clear: left; float: left; font-family: Arial; font-size: small; margin-bottom: 1em; margin-right: 1em;"><img alt="banner_desafio_resolvidoN4" border="0" height="239" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S__FCq7A7hI/AAAAAAAAAmw/nG83uUbrzVM/banner_desafio_resolvidoN4_thumb%5B2%5D.jpg?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="banner_desafio_resolvidoN4" width="287" /></span><span style="font-family: Arial; font-size: small;"> </span><br />
<span style="font-family: Arial;">O desafio desta semana foi o seguinte: </span><br />
<br />
<div align="justify">
<i><span style="font-family: Arial; font-size: small;">“Minha mãe me contou que, em 1938, conversava com sua avó e observaram que a idade de cada uma era expressa pelo número formado pelos dois últimos algarismos dos anos em que haviam nascido. Assim, quando minha mãe nasceu, qual era a idade da minha bisavó?”</span></i><br />
<i><span style="font-family: Arial; font-size: small;"><br /></span></i>
<i><span style="font-family: Arial; font-size: small;"></span></i><br />
<a name='more'></a><i><span style="font-family: Arial; font-size: small;"><br /></span></i><br />
<i><span style="font-family: Arial; font-size: small;"><br /></span></i>
<i><span style="font-family: Arial; font-size: small;"><br /></span></i>
<i><span style="font-family: Arial; font-size: small;"><br /></span></i>
<i><span style="font-family: Arial; font-size: small;"><br /></span></i>
<i><span style="font-family: Arial; font-size: small;"><br /></span></i></div>
<div align="justify">
<br /></div>
<div align="justify">
<br /></div>
<div align="justify">
<i><span style="font-family: Arial; font-size: small;"></span></i></div>
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/S_oBy6CCZJI/AAAAAAAAAl0/ovVB-my1174/s1600-h/image%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="image" border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG-vX-72YBeXdEiYSK2ks8wLxs5W6zAEYYc5MrLsDkIUNHMNU81hIgud3zb-shudoVoZ8O1p_Y2zhLd_qrLisJNFb0j-i2nWUdFDtkZO5r3tndtPLI8at_pLUec3xTArakzLRZD6B7qKs/?imgmax=800" style="display: block; float: none; margin-left: auto; margin-right: auto;" title="image" width="240" /></span></a><br />
<span style="font-family: Arial; font-size: small;">____________________________________________________________________________________________</span><br />
<div align="justify">
<br /></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">Considerando que a neta nasceu no século XX, e que a avó nasceu no século XIX, podemos escrever as seguintes equações:</span></div>
<div align="justify">
<br /></div>
<div align="justify">
<br /></div>
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVNUo_5iUlDfP89vpABoLwLhfCy6-x2pFxQ_MEd8twScC3_17l1VhUMZK5LpL17a8Q6hWS4IB24O68OQ17z2uRzD7vmlvBQ3zEsGCWm2bUMURhLlJzeijtGcNJ42t6-5fPXvbFX41JQRY/s1600-h/clip_image002%5B9%5D%5B7%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[9]" border="0" height="23" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdFIhIgOn7_fLdHm0uhK9w1NknVhLBjn18bg6811QgWzf9z-MCsyURWgWPu8Q3tA1MPk1LdO3PrsF67CP_usqMGiq4iVZFC3AgWYrkfy5uwGOvY0vUNVYoLy3RTIJqY8dOo5a_V07M1O4/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[9]" width="259" /></span></a><br />
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S__FEzIkigI/AAAAAAAAAm8/cjpQXXBQO8o/s1600-h/clip_image002%5B11%5D%5B6%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[11]" border="0" height="23" src="http://lh3.ggpht.com/_7wGgh4VGq1A/S__FFb4iXRI/AAAAAAAAAnA/VBnGVj6125E/clip_image002%5B11%5D_thumb%5B4%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[11]" width="271" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<div align="justify">
<br /></div>
<div align="justify">
<br /></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">Onde XY e WZ representam os algarismos que queremos encontrar, que são as idades atuais da avó e da neta. Sendo assim, podemos reescrever estas equações:</span></div>
<div align="justify">
<br /></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfqQvWmZmAvrFj_Z7mDty2ExhE-0Rf3xTUoeKR4TsndyJx_pAtRcRDeuvjzSZ7zvEr5MAImJu2hwDtwZ2r0FbTwh8iQt5A9ChrtTUdExTgJUPndnoPNgmTSIWkA2ueRDbFq69QzZW1DOc/s1600-h/clip_image002%5B19%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[19]" border="0" height="25" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S__FGvbIi-I/AAAAAAAAAnI/2CJIXS5MGhU/clip_image002%5B19%5D_thumb%5B2%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[19]" width="190" /></span></a><br />
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S__FHFyyu9I/AAAAAAAAAnM/iUVwVm-CZ7Y/s1600-h/clip_image004%5B10%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004[10]" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-0fYOnJJ7J3FQqosug7ssiAJBdE6y2kqVgqZDhD2kySKdMoYEv-r3xDG10uXPY7thM-0nJU3Nv8QJ71rnAbhGpgpfYJMQ2EWCu34K7cMRnYFt6lz-lrm0jd-lAWD6XFgUsIBiGy-R9Jo/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[10]" width="201" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<br />
<span style="font-family: Arial; font-size: small;">Agora, vamos decompor os números segundo suas grandezas (unidade e dezena):</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S__FID_b1uI/AAAAAAAAAnU/egJM6G8Avf0/s1600-h/clip_image002%5B17%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[17]" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjbYxrk09-8YJ4fmsYl1mgkb-NirTUDVs6I99q1yxnZt5bXXHGcbMFbBBk2uiyWwBNR_9Rx3sU-FizrZn9SL9y40OQtrwuu94nHXx2-vRS9Tb7f2JpjrAObzQxgEiSIjxbgdT0QCcRjYY/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[17]" width="115" /></span></a><br />
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S__FJWO1y9I/AAAAAAAAAnc/fEKn19uX1cU/s1600-h/clip_image004%5B8%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004[8]" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirhyphenhyphenuza4js6u9ILkL6vnBObSfaSYnAiQvyEgSuvFDQYVFzKlRxdrxr4iCcXPl7My0PXuqcxJNwEJYN_W3S-BbotEcBxyiXS2ByAXUmTa7j9wESiDpDs0UZBqqtdp9w-cf9HvS69aZMVI0/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[8]" width="126" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<br />
<span style="font-family: Arial; font-size: small;">Substituindo os valores decompostos nas equações 1 e 2, temos:</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"><img alt="clip_image002[19]" border="0" height="25" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S__FGvbIi-I/AAAAAAAAAnI/2CJIXS5MGhU/clip_image002%5B19%5D_thumb%5B2%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[19]" width="190" /></span><br />
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/S__FKWO4STI/AAAAAAAAAnk/Z-Uz1vV9L0M/s1600-h/clip_image002%5B15%5D%5B5%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[15]" border="0" height="23" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S__FLCdKzzI/AAAAAAAAAno/FNJO3UpXwBI/clip_image002%5B15%5D_thumb%5B3%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[15]" width="276" /></span></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtbsekRB6tFJRf03bCCMJ1m3POafvyXa0iJ0Mad4EdJYlkgHZqgDjijZkU6ZawuUZKP5-3sn6ZlZixGcSANPTyp3LQxG-NGruf3n9GECkVpZzFL5Ey3hf9WBtKvbXFi5wMsWGOyvoHUIY/s1600-h/clip_image004%5B6%5D%5B5%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004[6]" border="0" height="23" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S__FMkNzLqI/AAAAAAAAAnw/KtkwfRbm_sA/clip_image004%5B6%5D_thumb%5B3%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[6]" width="263" /></span></a><br />
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/S__FNKttHGI/AAAAAAAAAn0/FW5Jtpt-jjI/s1600-h/clip_image006%5B5%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image006" border="0" height="25" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S__FN7-GJgI/AAAAAAAAAn4/WHjcSfj8xsY/clip_image006_thumb%5B2%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image006" width="212" /></span></a><br />
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/S__FOfuzB6I/AAAAAAAAAn8/Dt6k5i6yRZY/s1600-h/clip_image008%5B5%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image008" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqUCWeHNZxI50-Fgz9RReU1H_hQbcVl0soTZ9113XBIyLgfNyFA2VlLa0gTCQgFjQDJXG-zmlO8ShJ3MLcHuQvHvYo8gKUED9Wg0987HATZFHx5UMwVzRwGz_5l6MqTYqhVBM9W0kau5A/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image008" width="133" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S__FPVkqEOI/AAAAAAAAAoE/nagW9-WjSqg/s1600-h/clip_image002%5B23%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[23]" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4qCBQrwKXrxWAsACunzcDDsviRhP75sdcxsWsoLCUoNE-6qnkptG7nSQN9St6KUzhlG-hgrjG1niWo_-jnzhgT5Oy5lghn2ZCOG-X3jKY-ipmUb0ILMMh8d-fFeHQhASla4MzsmInHAE/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[23]" width="158" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"><img alt="clip_image004[10]" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-0fYOnJJ7J3FQqosug7ssiAJBdE6y2kqVgqZDhD2kySKdMoYEv-r3xDG10uXPY7thM-0nJU3Nv8QJ71rnAbhGpgpfYJMQ2EWCu34K7cMRnYFt6lz-lrm0jd-lAWD6XFgUsIBiGy-R9Jo/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[10]" width="201" /></span><br />
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S__FQX9pxJI/AAAAAAAAAoM/NLK-i_xS43k/s1600-h/clip_image002%5B21%5D%5B5%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[21]" border="0" height="22" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S__FQ7EqLsI/AAAAAAAAAoQ/mPwiM1wmO7w/clip_image002%5B21%5D_thumb%5B3%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[21]" width="273" /></span></a><br />
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/S__FRc_YJ7I/AAAAAAAAAoU/zuov6x31_s4/s1600-h/clip_image004%5B12%5D%5B5%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004[12]" border="0" height="23" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S__FR5_pOxI/AAAAAAAAAoY/iZm5K9SsJjs/clip_image004%5B12%5D_thumb%5B3%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[12]" width="271" /></span></a><br />
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/S__FSXpQn_I/AAAAAAAAAoc/lmXUwS9hn8U/s1600-h/clip_image006%5B6%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image006[6]" border="0" height="25" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S__FTBFdtwI/AAAAAAAAAog/-IDGcFwjgkg/clip_image006%5B6%5D_thumb%5B2%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image006[6]" width="213" /></span></a><br />
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S__FTlyIFUI/AAAAAAAAAok/9pdVaobEBJo/s1600-h/clip_image008%5B6%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image008[6]" border="0" height="25" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S__FUEReQ2I/AAAAAAAAAoo/GSu1cMBzQL4/clip_image008%5B6%5D_thumb%5B2%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image008[6]" width="128" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S__FUkD8F1I/AAAAAAAAAos/6quXCjzueIE/s1600-h/clip_image002%5B25%5D%5B3%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[25]" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGS6fgm_hHKOBCDcmUmkBsUPM3H8c5m2Jz4FGRzFuLtE0wt3kH8fMByKIQp02LTnCZ6sYcH-twBQKuxgM8KSn5HFqETnuRVrfB8J7vJtxFVjv1__APItD4lyeoQOJuIGC44XRYUU_CxRQ/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[25]" width="164" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<div align="justify">
<span style="font-family: Arial; font-size: small;">Não é necessário resolver as equações 3 e 4 para encontrar a resposta. Basta ser um pouco observador. Como 10X + Y é igual a XY, temos que XY vale 69. Analogamente, WZ é igual a 19. Então, as idades da avó e da neta são em 1938, respectivamente 69 e 19 anos.</span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">Mas qual é a idade da avó, quando a neta nasceu? Simples, basta fazer a diferença entre as idades:</span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="center">
<span style="font-family: Arial; font-size: small;">69 – 19 = 50</span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">Portanto, a idade da avó quando a neta nasceu é de 50 anos.</span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">____________________________________________________________________________________________</span></div>
<span style="font-family: Arial; font-size: small;">E é isso aí galera, e não percam o desafio da próxima semana!</span><br />
<span style="font-family: Arial; font-size: small;"> </span><br />
<span style="font-family: Arial; font-size: small;"><br />Um abraço! E bom final de semana a todos!</span><br />
<br />
<span style="font-family: Arial; font-size: small;">Marcelo Flora</span><br />
<span style="font-family: Arial; font-size: small;"></span>Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com0tag:blogger.com,1999:blog-7241116304005966082.post-40235645220156065442010-05-25T12:21:00.000-07:002013-11-03T09:33:55.496-08:00Dúvida do Leandro Garcia<div align="justify">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2m5FOjruF3vrIwcYCvgHW3w9L17C55LYZqzVFYh-YMeczHjSwbJUwxl0qSbDkAAxh6d_QSHGZOYCTI5q3RZEoFy1ZzP1xYtC1MQQr0voJmufeue6XzX8BMrPYTKMgE1G68NeNRd5a4cQ/s1600-h/leandro%5B4%5D.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="leandro" border="0" height="130" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S_wiaViHHOI/AAAAAAAAAmA/WGBv3djBcqo/leandro_thumb%5B2%5D.jpg?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="leandro" width="126" /></a><span style="color: black; font-family: Arial; font-size: small;"></span></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="justify">
<br /></div>
<div align="justify">
<span style="font-family: Arial; font-size: small;">Um investidor aplicou certa quantia em um fundo de ações. Nesse fundo, 1/3 das ações eram da empresa A, 1/2 eram da empresa B e as restantes, da empresa C. Em um ano, o valor das ações da empresa A aumentou 20%, o das ações da empresa B diminuiu 30% e o das ações da empresa C aumentou 17%. Em relação à quantia total aplicada, ao final desse ano, este investidor obteve</span></div>
<br />
<a name='more'></a><br /><br />
<span style="font-family: Arial; font-size: small;">(A)lucro de 10,3%</span><br />
<br />
<span style="font-family: Arial; font-size: small;">(B)lucro de 7,0%</span><br />
<br />
<span style="font-family: Arial; font-size: small;">(C)prejuízo de 5,5%</span><br />
<br />
<span style="font-family: Arial; font-size: small;">(D)prejuízo de 12,4%</span><br />
<br />
<span style="font-family: Arial; font-size: small;">(E)prejuízo de 16,5%</span><br />
<span style="font-family: Arial; font-size: small;">____________________________________________________________________________________________</span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Olá Leandro,</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Para resolvermos este exercício, seguiremos as seguintes etapas:</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">1) Calcular o lucro/prejuízo do investidor em cada empresa;</span><br />
<br />
<span style="font-family: Arial; font-size: small;">2) Calcular o lucro/prejuízo total do investidor.</span><br />
<span style="font-family: Arial; font-size: small;">____________________________________________________________________________________________</span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<br />
<span style="font-family: Arial; font-size: small;">1) Sendo x o total aplicado pelo investidor, temos o seguinte:</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Ações em A = 1/3x;</span><br />
<br />
<span style="font-family: Arial; font-size: small;">Ações em B = 1/2x;</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Ações em C = 1 - 1/3x - 1/2x = 1/6x</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Para sabermos o quanto o investidor lucrou em cada empresa, basta multiplicar a fração de x, pelo percentual apresentado no problema. Assim:</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S_wia9TPhkI/AAAAAAAAAmE/jJwN9yd3GO0/s1600-h/clip_image002%5B11%5D%5B8%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[11]" border="0" height="36" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpwxwlfisAu4i3Musc-B4LiJRnr6CYWfLq1Q4oAFdZESDm8KLf_nzkP0QCSho1u-sJWQf3ne-VVEX9iP7K9hFpttJcHLauQziG3PwPeXAM0c0_BNRE8mzBd8hri6-4nHDQ8rte_8ME8EQ/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[11]" width="329" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S_wibpAcibI/AAAAAAAAAmM/as-MRwarHiU/s1600-h/clip_image004%5B7%5D.png"><span style="color: black; font-family: Arial; font-size: small;"><img alt="clip_image004" border="0" height="36" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S_wicNFFeZI/AAAAAAAAAmQ/QgI-vdfEzpU/clip_image004_thumb%5B4%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004" width="295" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/S_wici7huFI/AAAAAAAAAmU/St7VpfDIA1Y/s1600-h/clip_image006%5B7%5D.png"><span style="color: black; font-family: Arial; font-size: small;"><img alt="clip_image006" border="0" height="35" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgle6MdooJugVk_5IQjRHSmkNjMzUgH0xfphjegYWDrgGKqm_RNSyL_NbYIY3cSSjV_o1NR-x34hYad1TZWQAeXPXTG-4YLLoyvNHR4Tr8gCTapUWSrbVR4rspTaal1PNJqD88vs5HNCHM/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image006" width="284" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<br />
<span style="font-family: Arial; font-size: small;">Pronto, podemos passar para a próxima etapa.</span><br />
<span style="font-family: Arial; font-size: small;">____________________________________________________________________________________________</span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<br />
<span style="font-family: Arial; font-size: small;">2) O lucro/prejuízo total do investidor será igual à soma de todos os lucros/prejuízos calculados na etapa anterior. Portanto, temos:</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/S_widzMJeiI/AAAAAAAAAmc/X-M8SK7U04Q/s1600-h/clip_image002%5B13%5D%5B3%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[13]" border="0" height="39" src="http://lh3.ggpht.com/_7wGgh4VGq1A/S_wie9XD5_I/AAAAAAAAAmg/olI-terwZzw/clip_image002%5B13%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[13]" width="240" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<br />
<span style="font-family: Arial; font-size: small;">Nota: O sinal de 3/20x é negativo, pois é um prejuízo (veja o enunciado do problema).</span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Resolvendo esta equação, temos:</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S_wifPnalgI/AAAAAAAAAmk/sdj9_I2pn3Y/s1600-h/clip_image002%5B15%5D%5B6%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[15]" border="0" height="37" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlyrwKoP0dyYJ0UrhgVhWl720HJ18hCgoWJ0K7DVWOBqSSBD_UGjoh7LUtN57kT2lbbIKxgJ25acXM-ApyZbtf0sQAlG3cATrxPCJNUIwERoYa4SS2vyidAnGlnDeIPJsK20jMLk7DCfA/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[15]" width="324" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<br />
<span style="font-family: Arial; font-size: small;">Portanto, a resposta correta é a alternativa (C) prejuízo de 5,5%.</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Qualquer dúvida é só deixar um comentário.</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Um abraço!</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Marcelo Flora <br />____________________________________________________________________________________________ <br />Saiba como enviar suas dúvidas. </span><a href="http://mfmatematica.blogspot.com/2010/01/esclareca-suas-duvidas-em-matematica.html"><span style="font-family: Arial; font-size: small;">Clique aqui!</span></a>Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com12tag:blogger.com,1999:blog-7241116304005966082.post-16283039484192016972010-05-21T09:45:00.000-07:002013-11-03T09:34:36.177-08:00Desafio N#3<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="clear: left; float: left; font-size: small; margin-bottom: 1em; margin-right: 1em;"><img alt="banner_desafio_resolvido cópia" border="0" height="251" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghgtFyEL_PAY_ZsZC-81Iqs4qh7wstSK4hO-lSS7ZPGsWkdoGHs9fqQSGbVS0nUF4DvuahzhodC0jDfz-O2G0ruGDl8YR3AtCVrNC_7-Kg-A0zDhdWaJBt1J9yA91lFBE-uoSeWaTMcPU/?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="banner_desafio_resolvido cópia" width="301" /></span><span style="font-size: small;"> </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<div style="text-align: justify;">
O desafio desta semana foi o seguinte:</div>
</div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<div style="text-align: justify;">
<span style="font-size: small;"><i>”Joaquim trabalha em uma empresa de tratamente de água, em que existe um processo onde quatro caixas d’agua de <b>1000 litros </b>são interconectadas através de torneiras, como pode ser visto na figura abaixo.</i> <br /> </span></div>
<div style="text-align: justify;">
<span style="font-size: small;"></span></div>
<a name='more'></a><span style="font-size: small;"><br /></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw9iuzY77LbVQ9UAoakn8jEjGQ8hzhIGwgpDDvwLIfR4yUwmeK4mlUnMAE7EQGj4VNkTU8REaVmVqJNf9BlBL_xf6Av9OkH2AMAsjQSjS7ZyssMekK0Ypl5_Vsrput9i2hr5dkzAkuqlg/s1600/desafio_caixa_d'agua.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: small;"><img border="0" height="333" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw9iuzY77LbVQ9UAoakn8jEjGQ8hzhIGwgpDDvwLIfR4yUwmeK4mlUnMAE7EQGj4VNkTU8REaVmVqJNf9BlBL_xf6Av9OkH2AMAsjQSjS7ZyssMekK0Ypl5_Vsrput9i2hr5dkzAkuqlg/s400/desafio_caixa_d'agua.jpg" width="400" /></span></a></div>
</div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<br />
<span style="font-size: small;"><i>Uma vez ao ano, faz-se a transferência da água contida na caixa 1, para a caixa 4, onde para isso podem apenas abrir sete torneiras de cada vez. <br /> <br />Joaquim foi incumbido de realizar um relatório sobre este processo, onde observou o seguinte:</i> <br /> <br /> <br /><i> </i></span></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;"></span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;"></span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;"></span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><a href="http://lh4.ggpht.com/_7wGgh4VGq1A/S_DEaT6yzCI/AAAAAAAAAh0/TfcVjaYD6uY/s1600-h/prancheta%5B13%5D.jpg"><span style="font-size: small;"><img align="left" alt="prancheta" border="0" height="137" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeGOuNCACCQimeOB6L-siOw6hVRr7Ze56GVHM822ekKHOYFPxNympR8FJeeIUIWKtKtt-8RVzwYEwF9dhIzltOZ78Islb8Xoz0vlf3Cdc6Q2HoK5HxPnklCONBg5UXPNFVo4sGaitGb-E/?imgmax=800" style="border-width: 0px; display: inline; margin-left: 0px; margin-right: 0px;" title="prancheta" width="134" /></span></a><span style="font-size: small;"> 1º) Foram abertas sete torneiras da caixa 1;</span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;">2º) Depois de um determinado tempo, foram fechadas três torneiras da caixa 1, e abertas três da caixa 2;</span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;">3º) Observou-se que as caixas 1 e 2 se esvaziaram exatamente no mesmo tempo;</span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;">4º) Vazias as caixas 1 e 2, abriu-se sete torneiras da caixa 3.</span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;"></span></i></div>
<div align="justify" class="separator" style="clear: both; font-family: arial,helvetica,sans-serif; text-align: center;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;"></span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> </span></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"><i>Nota: No início da operação, a caixa 1 está totalmente cheia, e as demais vazias. No final da operação, a caixa 4 está totalmente cheia, e as demais vazias.</i> <br /> <br /><i>Porém, ao final do processo, Joaquim se deu conta de que havia esquecido de cronometrar o tempo em que a operação foi realizada.</i></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;"></span></i></div>
<div style="font-family: arial,helvetica,sans-serif;">
<br />
<br />
<span style="font-size: small;"><b>Ajude-o descobrindo qual foi o tempo total da operação.</b> <br /> <br /> <br />Obs.: Desconsidere em seus cálculos qualquer característica física que não tenha sido apresentada no problema (por ex: o comprimento das torneiras, aceleração da gravidade, etc.).</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"> </span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;"></span></i></div>
<div style="font-family: arial,helvetica,sans-serif;">
<i><a href="http://lh5.ggpht.com/_7wGgh4VGq1A/S_DEb-alUeI/AAAAAAAAAh8/c8rv1q792nU/s1600-h/cron028rel%5B5%5D.jpg"><span style="font-size: small;"><img alt="cron028rel" border="0" height="258" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S_DEcfxWP8I/AAAAAAAAAiA/AbPadVfk6hw/cron028rel_thumb%5B3%5D.jpg?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="cron028rel" width="268" /></span></a><span style="font-size: small;"> </span></i></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">_________________________________________________________________________________________</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Para resolvermos este problema, vamos analisar os fatos descritos por Joaquim, de modo a descobrir onde foi despendido tempo.</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;">1º) Foram abertas sete torneiras da caixa 1;</span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;"></span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"><i>2º) Depois de um determinado tempo </i><span style="color: red;"><b>(este tempo é igual ao tempo em que as 7 torneiras ficaram abertas. Vamos chamá-lo de T1)</b></span><i>, foram fechadas três torneiras da caixa 1, e abertas três da caixa 2;</i></span></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;"></span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"><i>3º) Observou-se que as caixas 1 e 2 se esvaziaram exatamente no mesmo tempo </i><span style="color: red;"><b>(aqui temos mais um tempo, que foi o tempo em que as caixas 1 e 2 se esvaziaram. Vamos chamá-lo de T2)</b></span><i>;</i></span></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<i><span style="font-size: small;"></span></i></div>
<div align="justify" style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"><i>4º) Vazias as caixas 1 e 2, abriu-se sete torneiras da caixa 3</i> <span style="color: red;"><b>(para finalizar, temos o tempo em que a caixa 3 se esvaziou, com as 7 torneiras abertas. Vamos chamá-lo de T3).</b></span></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="color: red; font-size: small;"><b></b></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;">Assim, concluímos que o tempo total da operação, desconsiderando o tempo de abrir e fechar as torneiras, é igual à soma dos três tempos que encontramos: T1, T2 e T3.</span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span><br />
<span style="font-size: small;"><img alt="clip_image002[49]" border="0" height="25" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2K4PqYCI/AAAAAAAAAig/BU7mVuSrY88/clip_image002%5B49%5D_thumb%5B1%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[49]" width="239" /></span></div>
<div style="font-family: arial,helvetica,sans-serif;">
<span style="font-size: small;"></span></div>
<span style="font-family: Arial; font-size: small;"></span><br />
<br />
<span style="font-family: Arial; font-size: small;">Agora basta calcular cada um dos tempos para encontrarmos a resposta. </span><br />
<span style="font-size: small;">___________________________________________________________________________________________</span><br />
<span style="font-family: Arial; font-size: small;">Calculando T1)</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Podemos relacionar as variáveis do problema da seguinte forma:</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<div align="center">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwGlcDVVXe6X05DrPY0DzRU3wQ5jyaf9WPCQJK_QheDB65P-ZXmm_mlQV5atIgNxYOzMpZmAoJw83eS6iT_wBz2JXbir7WOFg7-BHjzMpQPidr-SKVs5Q7CcxJCj5uLIZZRqS4Rn4I23A/s1600-h/image%5B32%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="image" border="0" height="112" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2MOr5YXI/AAAAAAAAAio/xsQg0xf_gWA/image_thumb%5B18%5D.png?imgmax=800" style="border-width: 0px; display: inline;" title="image" width="240" /></span></a><span style="font-family: Arial; font-size: small;"> </span></div>
<div align="center">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="left">
<br /></div>
<div align="left">
<span style="font-family: Arial; font-size: small;">Multiplicando em cruz, temos:</span></div>
<div align="left">
<br /></div>
<div align="center">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="center">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="center">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvA6GGHyTq3RvFDqAXxiY1p1zQPeiy7XoiWi2cejT_OZ_y1krLvwUe6MeaXcO15HxzUTsY20F378Gl9bBB4_KHAWH0JZxco5T4zwOGDXEtuSgiPVBS2ZjXLcA5P7LHrU3MfQ8QTO53Voc/s1600-h/clip_image002%5B41%5D%5B3%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[41]" border="0" height="25" src="http://lh3.ggpht.com/_7wGgh4VGq1A/S_a2NDsI9KI/AAAAAAAAAiw/--ZQH6qnCmE/clip_image002%5B41%5D_thumb%5B1%5D.png?imgmax=800" style="border-width: 0px; display: inline;" title="clip_image002[41]" width="77" /></span></a></div>
<div align="center">
<span style="font-family: Arial; font-size: small;"></span></div>
<div align="center">
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2NuHBWfI/AAAAAAAAAi0/gN2bStvAzCU/s1600-h/clip_image002%5B43%5D%5B3%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[43]" border="0" height="42" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2OR7C9RI/AAAAAAAAAi4/DC6Bg5E58T8/clip_image002%5B43%5D_thumb%5B1%5D.png?imgmax=800" style="border-width: 0px; display: inline;" title="clip_image002[43]" width="101" /></span></a></div>
<div style="text-align: left;">
<span style="font-size: small;">___________________________________________________________________________________________</span></div>
<span style="font-family: Arial; font-size: small;">Calculando T2)</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Analogamente ao cálculo de T1, temos:</span><br />
<br />
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2Om4rcQI/AAAAAAAAAi8/iELWJzt9wK8/s1600-h/image%5B33%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="image" border="0" height="102" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcurd1O_kIjTW2jCrB5yaAJgS0vEIjQ-KfOLDkvznqq4fQdKUnSBzejj4M0UcHoyw5ZP6s57Je6cqFMChyphenhyphenRtdloG4gjiKUm1aUmkl6buF8NB1iyQ_5i9-p76sqV8gLUSgdEHoNgJlHjoA/?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="image" width="290" /></span></a><span style="font-family: Arial; font-size: small;"> </span><br />
<br />
<span style="font-family: Arial; font-size: small;">(1000 – x) significa o quanto ainda restou na caixa 1 quando as 3 torneiras foram fechadas, e 4 permaneceram abertas.</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Multiplicando em curz:</span><br />
<br />
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/S_a2PxJfcqI/AAAAAAAAAjE/T8H-rCwX9Dc/s1600-h/clip_image002%5B35%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[35]" border="0" height="25" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2QbZCmeI/AAAAAAAAAjI/CM0EDPVj22g/clip_image002%5B35%5D_thumb%5B2%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[35]" width="141" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5vj76L4Kl4Nn3mEJ1BFwicgY8CWIxnxd2ZIl7SQj3bsWXwGlS5WpJXChbfO2H8qt8nAUGRuft5ZUoWC0RQmsnbDuA59mXxU5HIMrjapnwn0D-xpvbScWazfpcV0NKbwN4EDyfa7rzGyw/s1600-h/clip_image004%5B11%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004[11]" border="0" height="25" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2SpwHQGI/AAAAAAAAAjQ/Upi8Mtzz5-k/clip_image004%5B11%5D_thumb%5B2%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[11]" width="187" /></span></a><br />
<br />
<span style="font-family: Arial; font-size: small;">Para a caixa d’agua 2:</span><span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2TAidUrI/AAAAAAAAAjU/U10nvGfTTlk/s1600-h/image%5B34%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="image" border="0" height="97" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S_a2TwozlXI/AAAAAAAAAjY/8posOmJ11O0/image_thumb%5B20%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="image" width="240" /></span></a><span style="font-family: Arial; font-size: small;"> </span><br />
<br />
<span style="font-family: Arial; font-size: small;">Multiplicando em curz:</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2UwZ4W1I/AAAAAAAAAjg/SCGqzZVkz_U/s1600-h/clip_image002%5B33%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[33]" border="0" height="25" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2VozxWrI/AAAAAAAAAjk/6T4JvqDPwZY/clip_image002%5B33%5D_thumb%5B2%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[33]" width="118" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2WK4roKI/AAAAAAAAAjo/CfmU_PLFMGU/s1600-h/clip_image004%5B9%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004[9]" border="0" height="45" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2WpyTVUI/AAAAAAAAAjs/TKunja2a5E0/clip_image004%5B9%5D_thumb%5B2%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[9]" width="87" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S_a2XDhYPOI/AAAAAAAAAjw/S22JIAf53bg/s1600-h/clip_image006%5B5%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image006[5]" border="0" height="45" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2YruBOlI/AAAAAAAAAj0/y3bVDGv13pM/clip_image006%5B5%5D_thumb%5B2%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image006[5]" width="66" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-size: small;">___________________________________________________________________________________________</span><br />
<span style="font-family: Arial; font-size: small;">Substituindo o valor de z em (II):</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2Zd1IcnI/AAAAAAAAAj4/337cAG0VeEU/s1600-h/clip_image002%5B39%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[39]" border="0" height="25" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S_a2aJImL1I/AAAAAAAAAj8/rq-hm9kgeUo/clip_image002%5B39%5D_thumb%5B2%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[39]" width="187" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEKC_Rf4TFG_Vald2kkUXSHB42Dh40Revmnx4L4pR4qTxk188ysM5Hps4o2QIs2HYlwPSz69ppEXqRqWdWZJw72W6XYhsHD5KFFTUbY3DgNzS6fE08_H1qvUzk-dD6fCt2yp7EMJG-zsc/s1600-h/clip_image002%5B27%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[27]" border="0" height="45" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2bZ1yW0I/AAAAAAAAAkE/bVHeJZQOZoU/clip_image002%5B27%5D_thumb%5B2%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[27]" width="157" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2bzY0_SI/AAAAAAAAAkI/QrhKfSm7bQk/s1600-h/clip_image002%5B29%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[29]" border="0" height="45" src="http://lh3.ggpht.com/_7wGgh4VGq1A/S_a2cW1f1vI/AAAAAAAAAkM/DcU7-RexOYY/clip_image002%5B29%5D_thumb%5B2%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[29]" width="134" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2dWE6T4I/AAAAAAAAAkQ/cQBhxldHUMs/s1600-h/clip_image002%5B31%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[31]" border="0" height="45" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgY2ef5y8is2u-VmYgM16dmnYcQl3I21EGZdtd_03n_xJpzcBfT0FVhR0-3JzUaW1SCzBofsmoIrHq-pKWlkve4mtKvXmAdmacMqDYYXYMtE_zAiLSIKZ5uSWkt6uQlSFdOXU_Tox1P7gQ/?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[31]" width="76" /></span></a><span style="font-size: small;">___________________________________________________________________________________________</span><br />
<span style="font-family: Arial; font-size: small;">Substituindo o valor de x em (I):</span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjV_QTt43aafUPJ2eF-N2ybYiHoRxTYy8tYH1lN1NZWRLuE-0ldisJIACo1ox5nxltf4IoeDkW9GhcT9QWFXswZQrgqx058rJzPUr4Wn5eMoCWzVkDiC8Appir5yCAUpELc0t0R6YdNfw0/s1600-h/clip_image002%5B45%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[45]" border="0" height="42" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyq_ciFCoeKC2KQUodIpvmqdeBQTe5elVQGZ6ryP_xNiX2UoQK_xMufOw19eue4xdPJF_xs0UCY8wV8suAEJv0Is-0wnt4c_JsPlPvWYdgWPcNh2jdkGYvzb3rFDBjRFLaxwDRKTy1FtY/?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[45]" width="101" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNJ5ej3C6_B9engHrzeESU14r2rsQh_U-h_76nKZ-u4VnXbJIBQRAmA9aZ8bfpr8BXevDn0V6xO_UxuHGNKh1d9ENaPTYhgxAMUs4fkj4ZX0v8TKWOaR7oNbHeNrHUp3o3TRvJUZnC9B4/s1600-h/clip_image004%5B13%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004[13]" border="0" height="60" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2hJZlpyI/AAAAAAAAAkk/Ks0nGswD5UI/clip_image004%5B13%5D_thumb%5B2%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[13]" width="95" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2h3OSE9I/AAAAAAAAAko/ZzMKh3AURnk/s1600-h/clip_image006%5B7%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image006[7]" border="0" height="45" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglDG-NDJ7Bz_i5NdS8FDczjNHcPemc-FcSQXiGMtMcZ4Nh7Jtpef81vdRMERj8xG1crHp8NXnmM0lWV4_VX3rcjgsJO6aPqYlFVoJuOvD9MPi7N2m8Oy1o0AMKPl_FnnmTPTk5GLa4R14/?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image006[7]" width="87" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2i0BKz0I/AAAAAAAAAkw/7Z5IN8nMSxY/s1600-h/clip_image008%5B5%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image008[5]" border="0" height="45" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjH6ODIiSkNhCadan5_75Gf3rrdWCo2pnNrui9E3HZt4L-k2Lwzdi7xwLLNFOjZmw2UHYPhlMBSfwdIXrqAoPZ5Gn8X6vM48w9XQ9DVImROKQs6RD5BtwCPv79WgcKxVt-3lO_lzANsGBU/?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image008[5]" width="77" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-size: small;">___________________________________________________________________________________________</span><br />
<span style="font-family: Arial; font-size: small;">Calculando T3)</span><br />
<br />
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2j-oygCI/AAAAAAAAAk4/r4hj-o0NvVc/s1600-h/image%5B38%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="image" border="0" height="93" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2kpjnH3I/AAAAAAAAAk8/GfntoENxPbI/image_thumb%5B22%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="image" width="240" /></span></a><span style="font-family: Arial; font-size: small;"> </span><br />
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S_a2k7RJAxI/AAAAAAAAAlA/Yi4zrBH6ICY/s1600-h/clip_image002%5B47%5D%5B3%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[47]" border="0" height="25" src="http://lh3.ggpht.com/_7wGgh4VGq1A/S_a2lhBaU2I/AAAAAAAAAlE/NAboPERq7RY/clip_image002%5B47%5D_thumb%5B1%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[47]" width="108" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2mKIzV7I/AAAAAAAAAlI/oT2HauB5yIo/s1600-h/clip_image004%5B15%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image004[15]" border="0" height="45" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S_a2mjOA78I/AAAAAAAAAlM/J9T42Wu4DQA/clip_image004%5B15%5D_thumb%5B2%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[15]" width="87" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Pronto! Agora que já temos T1, T2 e T3, podemos calcular o tempo total.</span><br />
<span style="font-size: small;">___________________________________________________________________________________________</span><br />
<span style="font-family: Arial; font-size: small;">Calculando o Tempo Total:</span><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S_a2nFk_ApI/AAAAAAAAAlQ/fxtise8U9XU/s1600-h/clip_image002%5B49%5D%5B3%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[49]" border="0" height="25" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2K4PqYCI/AAAAAAAAAig/BU7mVuSrY88/clip_image002%5B49%5D_thumb%5B1%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[49]" width="239" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqoWL1u5WUp4ozL8Jr5MJawV24F_0ZewXCwLAnCypZ9kTdxIVS1GurD9X1d7ImLTJ5jV7pNmCZ-diwQhnshi1ziBh5jMHwzUEL-Boxhar620BmI_J1Rej7CwK3qeghB4u0XHFhJeDkZOY/s1600-h/clip_image002%5B51%5D%5B8%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[51]" border="0" height="40" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S_a2o6PX53I/AAAAAAAAAlY/jkEOYwTw3cw/clip_image002%5B51%5D_thumb%5B6%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[51]" width="240" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S_a2pVj_1JI/AAAAAAAAAlc/aI568PGlRRs/s1600-h/clip_image002%5B53%5D%5B3%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[53]" border="0" height="45" src="http://lh3.ggpht.com/_7wGgh4VGq1A/S_a2p-fp9pI/AAAAAAAAAlg/xLaGyF3a4TA/clip_image002%5B53%5D_thumb%5B1%5D.png?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[53]" width="225" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<a href="http://lh4.ggpht.com/_7wGgh4VGq1A/S_a2qbQQhVI/AAAAAAAAAlk/qwA99LGXVYA/s1600-h/clip_image002%5B57%5D%5B4%5D.png"><span style="font-family: Arial; font-size: small;"><img alt="clip_image002[57]" border="0" height="45" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0gKVpVPha-Du7tJUauIo8-OBvtSK9Eeec51NLqdlNGluEN46JusUEsFzDn3GHUOqkcJlwFjNtehfR7X_faSLWqQt8y3voeIZrxslXju_xmWDW-IlL_yxVdjdhyYAoePBNm_ObAAjPFWw/?imgmax=800" style="border-width: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[57]" width="228" /></span></a><br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-family: Arial; font-size: small;">Se dividirmos 1840 por 49, temos aproximadamente 37,55 horas, onde 0,55 horas em minutos é igual a 33.</span><br />
<br />
<span style="font-family: Arial; font-size: small;"></span><br />
<span style="font-size: small;"><span style="font-family: Arial;">Assim, o tempo total será de aproximadamente <b>37 horas e 33 minutos.</b></span> ___________________________________________________________________________________________</span><br />
<span style="font-family: Arial; font-size: small;">E é isso aí galera, e não percam o desafio da próxima semana!</span><br />
<span style="font-family: Arial; font-size: small;"> <br />Um abraço! E bom final de semana a todos!</span>Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com2tag:blogger.com,1999:blog-7241116304005966082.post-26176041824941064262010-05-15T12:19:00.000-07:002013-11-03T09:35:38.953-08:00Dúvida do Kléber <span style="clear: left; float: left; font-family: arial; font-size: small; margin-bottom: 1em; margin-right: 1em;"><img alt="duvida2" border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUOTKxOOj31WN8n2aTRc-uPOtTHiM0vJOj5HWKEX4N_pR8vL0jMWvbNUWhkSL4I4I6hJUn3m1mEklUaeYsMT1FZ-SzXExp420U9xJ5hnjy0qINnAzYPDjQ5-sHj7q3PhFMc2kCOt6w6_8/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="duvida2" width="192" /></span><br />
<span style="font-family: arial;">Olá Marcelo,</span><br />
<br />
<span style="font-family: arial; font-size: small;">Minha dúvida é a seguinte:</span> <br />
<br />
<span style="font-family: arial; font-size: small;">Qual é a metade do número 2^21 + 4^12? </span> <br />
<br />
<span style="font-family: arial; font-size: small;">Desde já agradeço.</span> <br />
<span style="font-family: arial; font-size: small;"> </span> <br />
<span style="font-family: arial; font-size: small;"> </span> <br />
<br />
<span style="font-family: arial; font-size: small;"></span><br />
<a name='more'></a><span style="font-family: arial; font-size: small;"><br /></span><br />
<span style="font-family: arial; font-size: small;"><br /></span>
<span style="font-family: arial; font-size: small;"><br /></span>
<span style="font-family: arial; font-size: small;">Olá Kléber,</span> <br />
<br />
<div align="justify">
<span style="font-family: arial; font-size: small;">Para resolvermos este exercício, basta saber as propriedades da </span><a href="http://pt.wikipedia.org/wiki/Exponencia%C3%A7%C3%A3o"><span style="font-family: arial; font-size: small;">exponenciação</span></a><span style="font-family: arial; font-size: small;">. Nem pense em desenvolver a potência destes números, pois assim você iria perder muito tempo.</span></div>
<div align="justify">
<br /></div>
<span style="font-family: arial; font-size: small;"></span> <br />
<span style="font-family: arial; font-size: small;">Vamos à resolução.</span> <br />
<span style="font-family: arial; font-size: small;">____________________________________________________________________________________________</span> <br />
<div align="justify">
<br /></div>
<div align="justify">
<span style="font-family: arial; font-size: small;">Primeiramente, vamos colocar as duas potências em bases iguais para que possamos somá-las:</span></div>
<div align="justify">
</div>
<span style="font-family: arial; font-size: small;"></span> <br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJO42qb7fh34sWjB0VfVb1rNuQ-pgvzWtS741vcQaqJOZbIPHhAzEGQOwIcOnwz7OAhAWXpLyO_GhIDS80koRu9uvW6wuRMAH5Gb9WBnrPrCMAulZ14tLVIlBU0JKFRtwR6JPu3km-MSI/s1600-h/clip_image002%5B4%5D%5B5%5D.gif"><span style="font-family: arial; font-size: small;"><img alt="clip_image002[4]" border="0" height="19" src="http://lh3.ggpht.com/_7wGgh4VGq1A/S-7y2Qkn0QI/AAAAAAAAAhQ/5RRB6axuL0Q/clip_image002%5B4%5D_thumb%5B3%5D.gif?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[4]" width="269" /></span></a> <br />
<span style="font-family: arial; font-size: small;"></span> <br />
<div align="justify">
</div>
<div align="justify">
<br />
<span style="font-family: arial; font-size: small;">Agora que vem a parte mais importante: vamos colocar 2^21 em evidência, de modo a facilitar nosso cálculo.</span> <br />
<br /></div>
<div align="justify">
</div>
<div align="justify">
<span style="font-family: arial; font-size: small;"></span></div>
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S-7y238carI/AAAAAAAAAhU/toTq_ih6cBc/s1600-h/clip_image004%5B3%5D.gif"><span style="font-family: arial; font-size: small;"><img alt="clip_image004" border="0" height="19" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S-7y3W7-lpI/AAAAAAAAAhY/tRIWS0sHIVw/clip_image004_thumb.gif?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004" width="240" /></span></a> <br />
<span style="font-family: arial; font-size: small;"></span> <br />
<div align="justify">
</div>
<div align="justify">
<br />
<span style="font-family: arial; font-size: small;">Como nos é perguntado a metade do número, basta dividir por 2.</span></div>
<div align="justify">
<br /></div>
<span style="font-family: arial; font-size: small;"></span> <br />
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S-8LdReqZ9I/AAAAAAAAAhk/RRed-5BLLc4/s1600-h/clip_image002%5B3%5D.gif"><img alt="clip_image002" border="0" height="38" src="http://lh6.ggpht.com/_7wGgh4VGq1A/S-8Ld-HTA0I/AAAAAAAAAho/4y2947HnAlU/clip_image002_thumb.gif?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002" width="114" /></a> <br />
<span style="font-family: arial; font-size: small;"></span> <br />
<span style="font-size: small;"><span style="font-family: arial;"> Pronto! A metade de 2<sup>21</sup> + 4<sup>12</sup> é 9* 2<sup>20</sup></span></span> <br />
<div align="justify">
<br /></div>
<sup><span style="font-family: arial; font-size: small;"></span></sup> <br />
<sup><span style="font-family: arial; font-size: small;"><span style="font-size: small;">Qualquer dúvida, deixe aí seu comentário.</span></span></sup> <br />
<br />
<div style="font-family: arial,helvetica,sans-serif;">
Um abraço! E bom final de semana!</div>
<div style="font-family: arial,helvetica,sans-serif;">
<br /></div>
<div style="font-family: arial,helvetica,sans-serif;">
Marcelo Flora <br />
____________________________________________________________________________________________ <br />
Saiba como enviar suas dúvidas. <a href="http://mfmatematica.blogspot.com/2010/01/esclareca-suas-duvidas-em-matematica.html">Clique aqui!</a></div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com5tag:blogger.com,1999:blog-7241116304005966082.post-45089371429856591632010-05-14T07:28:00.000-07:002013-11-03T09:37:09.007-08:00Desafio N#2<div style="font-family: Arial,Helvetica,sans-serif;">
</div>
<div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;">
</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
</div>
<div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;">
</div>
<div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;">
</div>
<div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;">
<br /></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz1uLZzblqLyz2nSmOHo7QSHcDRxlChV8G0cXm2ICa3CghAb028gHQoyaUo38eQhMP2StdtSBhT_-oUsFwvo8nLIEZUthi91XTGjqiLrIgq4yLeVb8k1_pLZespPLEIjvpTY1R-J1n15Y/s1600/banner_desafio_resolvido%232.jpg" imageanchor="1" style="clear: left; float: left; font-family: Arial, Helvetica, sans-serif; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz1uLZzblqLyz2nSmOHo7QSHcDRxlChV8G0cXm2ICa3CghAb028gHQoyaUo38eQhMP2StdtSBhT_-oUsFwvo8nLIEZUthi91XTGjqiLrIgq4yLeVb8k1_pLZespPLEIjvpTY1R-J1n15Y/s320/banner_desafio_resolvido%232.jpg" /></a><span style="font-family: Arial,Helvetica,sans-serif;">O desafio desta semana foi o seguinte:</span><br />
<br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">
"</span><i style="font-family: Arial,Helvetica,sans-serif;">Durante uma aula de geometria, o professor Jacó fez um arco de
circunferência na lousa, e propôs aos seus alunos o seguinte desafio:</i><br />
<br />
<i style="font-family: Arial,Helvetica,sans-serif;">- Quero que vocês descubram qual foi o tamanho da abertura do
compasso que utilizei para desenhar este arco! Tudo o que vocês precisam
pra descobrir está escrito na lousa!"</i><br />
<i style="font-family: Arial,Helvetica,sans-serif;"></i><br />
<a name='more'></a><i style="font-family: Arial,Helvetica,sans-serif;"><br /></i><br />
<i style="font-family: Arial,Helvetica,sans-serif;"><br /></i>
<i style="font-family: Arial,Helvetica,sans-serif;"><br /></i>
<i style="font-family: Arial,Helvetica,sans-serif;"><br /></i>
<br />
<div class="separator" style="clear: both; font-family: Arial,Helvetica,sans-serif; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWOv7YwgNiiMbJaW5T3F3ta2QSnSyx1J3U9-CPyFsQICsZ8i3v2345wNe5GULsTwI0t4OXWl2Edq5l8DZuaRdZhhAKAPSM1m8MlJy-vroa4sKZNf2JsIjkaPA4sK1DHbNBSsm6urTjt54/s1600/lousa.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWOv7YwgNiiMbJaW5T3F3ta2QSnSyx1J3U9-CPyFsQICsZ8i3v2345wNe5GULsTwI0t4OXWl2Edq5l8DZuaRdZhhAKAPSM1m8MlJy-vroa4sKZNf2JsIjkaPA4sK1DHbNBSsm6urTjt54/s400/lousa.jpg" width="400" /></a></div>
<br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">E quem resolveu o desafio do Prof. Jacó foi o </span><b style="font-family: Arial,Helvetica,sans-serif;">André Lucas O. Duarte!</b><span style="font-family: Arial,Helvetica,sans-serif;"> Parabéns!</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Como prometido, segue a sua resolução abaixo:</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<div style="text-align: justify;">
<span style="font-family: Arial,Helvetica,sans-serif;">1) Sendo CD mediatriz do segmento AB e sabendo que todos os pontos da mediatriz são equidistantes das extremidades do segmento, temos que a reta que passa por CD também passa pelo centro da circunferência que vou chamar de O.</span></div>
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<div style="text-align: justify;">
<span style="font-family: Arial,Helvetica,sans-serif;">2) Ligando-se o ponto A ao ponto O, obtemos um triângulo retângulo ACO.</span></div>
<div style="text-align: justify;">
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Arial,Helvetica,sans-serif;">3) Como é conhecida a medida de CD, se chamarmos a medida de AO por x, a medida de CO fica sendo x-2.E ainda temos que AC = AB/2 = 4√2/2 = 2√2.</span></div>
<div style="text-align: justify;">
<span style="font-family: Arial,Helvetica,sans-serif;"><br />4) Usando a Relação de Pitágoras,</span></div>
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<div style="text-align: center;">
<span style="font-family: Arial,Helvetica,sans-serif;">x² = (2√2)² + (x-2)²</span></div>
<div style="text-align: center;">
<span style="font-family: Arial,Helvetica,sans-serif;"><br />x² = 8 + x² - 4x + 4</span></div>
<div style="text-align: center;">
<span style="font-family: Arial,Helvetica,sans-serif;"><br />4x = 12</span></div>
<div style="text-align: center;">
<span style="font-family: Arial,Helvetica,sans-serif;"><br />x = 3</span></div>
<span style="font-family: Arial,Helvetica,sans-serif;"><br />5) Logo, a abertura do compasso foi de 3 unidades de comprimento.</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">E é isso aí galera, e não percam o desafio da próxima semana!</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br />Um abraço! E bom final de semana a todos!</span><br />
<div style="font-family: Arial,Helvetica,sans-serif;">
</div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com0tag:blogger.com,1999:blog-7241116304005966082.post-1718012324875880102010-05-12T20:45:00.000-07:002013-11-03T09:37:50.951-08:00Dúvida da Neri<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhboYmK3_goBgNsoNy6-n146n8oDjZtcw2JB2ftYgtlNbi2fLWPUPG2-1JkudBc0OTDMivfXaQvN23CLE52LUz8aixcUm7KRrNYH3HJENh9epNLw5SaWE0WgHh0x3gPLDa7iDRSBhoRrYs/s1600/ne.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhboYmK3_goBgNsoNy6-n146n8oDjZtcw2JB2ftYgtlNbi2fLWPUPG2-1JkudBc0OTDMivfXaQvN23CLE52LUz8aixcUm7KRrNYH3HJENh9epNLw5SaWE0WgHh0x3gPLDa7iDRSBhoRrYs/s320/ne.jpg" /></a></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
Oi Marcelo!</div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
</div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
Gostaria que você fizesse o favor de esclarecer uma duvida minha... Tenho muitos exercícios deste tipo aqui e não sei resolver. </div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<i>“Uma caixa d'agua com capacidade para 850 m³ possui uma tubulação que a alimenta e que a enche em 7 horas. Possui também um ‘ladrão’ que a esvazia em 12 horas. Com a água jorrando, enchendo a caixa e o ‘ladrão’ funcionando simultaneamente, em quanto tempo a caixa d' agua ficará cheia?”.</i></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<i></i></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<br />
<a name='more'></a><br /></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<br />
A resposta é 16h e 48 min.</div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
Obrigada pelo espaço!</div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
Neri</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
____________________________________________________________________________________________</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Olá Neri,</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Para resolvermos este exercício, basta fazer regra de três. É bem mais simples do que se imagina.</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Vamos à resolução.</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
____________________________________________________________________________________________</div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
Iremos seguir os seguintes passos:</div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
1) Calcular o quanto a caixa d’agua esvazia em 7 horas (Sabendo isto, podemos calcular o passo 2);</div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
2) Calcular o quanto a caixa d’agua enche com o ladrão aberto, em 7 horas (Sabendo isto, podemos calcular o passo 3);</div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div align="justify" style="font-family: Arial,Helvetica,sans-serif;">
3) Calcular o tempo de enchimento da caixa, com o ladrão aberto, para 850 m³ (Que é a resposta).</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
____________________________________________________________________________________________</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
1) Como sabemos que a caixa esvazia 850m³ em 12 horas, para saber em 7, basta fazer a regra de três:</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div align="center" style="font-family: Arial,Helvetica,sans-serif;">
Esvazia ====== Tempo</div>
<div align="center" style="font-family: Arial,Helvetica,sans-serif;">
850m³ ========= 12h</div>
<div align="center" style="font-family: Arial,Helvetica,sans-serif;">
x m³ =========== 7h</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Multiplicando em cruz, temos:</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
7*850 = 12x</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
5950 = 12x</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
x = 5950/12 (Simplificando por 2)</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
x = 2975/6</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Portanto, a caixa d’agua esvazia 2975/6 m³ de água em 7 horas.</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
____________________________________________________________________________________________</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
2) O quanto a caixa d’agua enche <b>com o ladrão aberto</b> em 7 horas, será igual ao quanto ela <b>enche</b> em 7 horas, <b>menos</b> o quanto ela <b>esvazia</b> em 7 horas. Assim, temos:</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S-tvf5go6WI/AAAAAAAAAfE/y0uD_N126Hg/s1600-h/clip_image002%5B6%5D%5B3%5D.png"><img alt="clip_image002[6]" border="0" height="36" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S-tvgUjvCnI/AAAAAAAAAfI/pAni2f9mxAY/clip_image002%5B6%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[6]" width="189" /></a></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Fazendo o mmc de 1 e 6, e depois “dividindo pelo debaixo, e multiplicando pelo de cima”, fica:</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/S-tvgz9mrFI/AAAAAAAAAfM/Jf44Gxicw-A/s1600-h/clip_image004%5B4%5D%5B3%5D.png"><img alt="clip_image004[4]" border="0" height="36" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S-tvhZh43BI/AAAAAAAAAfQ/8sibMGKW9Po/clip_image004%5B4%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[4]" width="210" /></a></div>
<div align="center" style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div align="center" style="font-family: Arial,Helvetica,sans-serif;">
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/S-tvh4NqpNI/AAAAAAAAAfU/jmVsXePPloE/s1600-h/clip_image006%5B4%5D%5B3%5D.png"><img alt="clip_image006[4]" border="0" height="36" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S-tviaQzjOI/AAAAAAAAAfY/sBUQcE-_uXE/clip_image006%5B4%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image006[4]" width="197" /></a></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S-tvi9OzyxI/AAAAAAAAAfc/f8SBhwOU0BM/s1600-h/clip_image008%5B4%5D%5B3%5D.png"><img alt="clip_image008[4]" border="0" height="36" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S-tvjenQFNI/AAAAAAAAAfg/EaSWNjppcxM/clip_image008%5B4%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image008[4]" width="147" /></a></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Portanto a caixa d’agua enche, com o ‘ladrão’ aberto, 2125/6 m³ de água em 7 horas.</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
____________________________________________________________________________________________</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
3) Agora basta fazer outra regra de três com o resultado anterior. Assim:</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div align="center" style="font-family: Arial,Helvetica,sans-serif;">
Enche ====== Tempo </div>
<div align="center" style="font-family: Arial,Helvetica,sans-serif;">
2125/6m³ ========= 7h </div>
<div align="center" style="font-family: Arial,Helvetica,sans-serif;">
850 m³ =========== x h</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Multiplicando em cruz, temos: </div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<a href="http://lh6.ggpht.com/_7wGgh4VGq1A/S-tvjvI4M8I/AAAAAAAAAfk/U3hJL11OJuQ/s1600-h/clip_image002%5B8%5D%5B3%5D.png"><img alt="clip_image002[8]" border="0" height="36" src="http://lh5.ggpht.com/_7wGgh4VGq1A/S-tvkZX0E_I/AAAAAAAAAfo/AIIP5I4P4nc/clip_image002%5B8%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[8]" width="123" /></a></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbxvcUj2Wtg5Uf9PK7fEThIG3TuQZJ4G1M74-PH_uuKBVKwMVzC5gRGL358JqUNsTFX2bFK8szcO3QrYE3RUEKipcJigZHnvDITuqukqkfFuLxbZFp3Fq12FYoUw1DlFi7B62XUtgETao/s1600-h/clip_image004%5B6%5D%5B3%5D.png"><img alt="clip_image004[6]" border="0" height="20" src="http://lh3.ggpht.com/_7wGgh4VGq1A/S-tvlMqTNYI/AAAAAAAAAfw/WRSBXBq0PxA/clip_image004%5B6%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image004[6]" width="141" /></a></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCaOkCx_0VqYtMgBGD9I5PbEVJv4ozKvQY3xCC-dK15y808UmM1KA-LFZlvVFkQim6c5JM53RnJtNht1pIFCv6BeB3kKcNhnqCSvsEG5638DFvtEraIpbh_Zt064RWnSss8q157Z52P7Q/s1600-h/clip_image006%5B6%5D%5B3%5D.png"><img alt="clip_image006[6]" border="0" height="20" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbp5_BctODyR9xrLK60VWScnDEoS6vFXedoZKCv-wiYRQIBt3IBVLjGkxbTw_j6DRErOYQieQ45XFQWZp3kjy0cYbDWIZjGGaxcPr71ei8e2E0d_yNK7dPonZmk4hOxOsSyBMWM0oeo78/?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image006[6]" width="114" /></a></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8gvaeNlbIVXXtQRn7hEbpyrYUgzg1GYp8CKsNHGpSRS-6t2UWEDw2MGBe1p0FTJzSBnVYliKEpbNS6jgAsmPhNT6bAv_vdWY2qB8cRCK9-tyiXLVCDLPLQpY3z_zUakYE0b7jid-Pkbc/s1600-h/clip_image008%5B6%5D%5B3%5D.png"><img alt="clip_image008[6]" border="0" height="36" src="http://lh4.ggpht.com/_7wGgh4VGq1A/S-tvnJTgV1I/AAAAAAAAAgA/u1HPM1e-nPA/clip_image008%5B6%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image008[6]" width="68" /></a></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg93E6HuoqMCLudC64f8AYf5yqK11hICSpxdUFhTkzgIWWiFtLhBPk23TWeBFf53zMfAIMbKMCiZVEjkRr3mPN1wCRGSkOHnpklC6xjxt3j4euUOx1HSfR8VhhGrlcNHnjnCIedKdDfd9I/s1600-h/clip_image002%5B10%5D%5B3%5D.png"><img alt="clip_image002[10]" border="0" height="20" src="http://lh3.ggpht.com/_7wGgh4VGq1A/S-tvn06cOsI/AAAAAAAAAgI/RLSAH9a5ORw/clip_image002%5B10%5D_thumb%5B1%5D.png?imgmax=800" style="border: 0px none; display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[10]" width="99" /></a></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Para transformar as 0,8 horas em minutos, basta multiplicar 0,8 por 60 min.</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div align="center" style="font-family: Arial,Helvetica,sans-serif;">
0,8*60 = 48 min.</div>
<div align="center" style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div align="left" style="font-family: Arial,Helvetica,sans-serif;">
Portanto, a resposta é <b>16 horas e 48 minutos</b>.</div>
<div align="left" style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Qualquer dúvida é só deixar um comentário.</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Um abraço! E até a próxima!</div>
<div style="font-family: Arial,Helvetica,sans-serif;">
<br /></div>
<div style="font-family: Arial,Helvetica,sans-serif;">
Marcelo Flora <br />
____________________________________________________________________________________________ <br />
Saiba como enviar suas dúvidas. <a href="http://mfmatematica.blogspot.com/2010/01/esclareca-suas-duvidas-em-matematica.html">Clique aqui!</a></div>
Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com1tag:blogger.com,1999:blog-7241116304005966082.post-74953257111235920482010-04-29T20:09:00.000-07:002013-11-03T09:39:57.809-08:00Desafio N#1<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMLOdpmsvRbmW6uFSXagg3ZSIekQEcVzVeezP1gSTieM0btQgMlNpNGy5buQjeAUrxfUV3d7MChTIvEOnWfbJ67fYAf84KmvGBM00z7_KpnBpq2K7-79KUOi_kgk6M1HMMLRapPz8LRjM/s1600/banner_desafio_resolvido.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMLOdpmsvRbmW6uFSXagg3ZSIekQEcVzVeezP1gSTieM0btQgMlNpNGy5buQjeAUrxfUV3d7MChTIvEOnWfbJ67fYAf84KmvGBM00z7_KpnBpq2K7-79KUOi_kgk6M1HMMLRapPz8LRjM/s320/banner_desafio_resolvido.jpg" /></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;">O desafio desta semana foi o seguinte:</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">“Considere o quadrado ABCD e a circunferência de origem O mostrados na figura abaixo.</span></em><br />
<em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></em>
<em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"></span></em><br />
<a name='more'></a><em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></em><br />
<em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></em>
<em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></em>
<em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></em>
<em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></em>
<em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></em>
<em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></em>
<em><br /></em>
<div class="separator" style="clear: both; text-align: center;">
<em style="margin-left: 1em; margin-right: 1em;"><img src="http://img706.imageshack.us/img706/1253/desafio1.jpg" style="display: block; float: none; margin-left: auto; margin-right: auto;" /></em></div>
<br />
<div align="justify">
<em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></em>
<em><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Sabendo que o lado AB do quadrado tangencia a circunferência em um ponto AB/2, que as extremidades do quadrado interceptam a circunferência nos pontos C e D, e que o raio da circunferência é igual a 5, determine a área do quadrado ABCD.”</span></em></div>
<div align="justify">
<span class="Apple-style-span" style="color: #555555; font-size: 13px; line-height: 19px;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">____________________________________________________________________________________________</span></span></div>
<br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Achou complicado? Então vai cair de costas quando ver a resolução!</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Para resolvê-lo, basta aplicar o teorema de pitágoras, como mostrado na figura abaixo.</span><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8E5mWw7V1I4GnqCpM3vZ_6NhpZUfJsTriq6EXfuJ3M3OqK3fpNTPTp1vJczcYYbbtUrR0-QvGJl_nY5wPAqWYCosoFvdexsmv0wffIA6DPItjTXVzF9bVkxgoLkz21h4M_1SIb05mneg/s1600/resolu%C3%A7%C3%A3o_desafio+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="250" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8E5mWw7V1I4GnqCpM3vZ_6NhpZUfJsTriq6EXfuJ3M3OqK3fpNTPTp1vJczcYYbbtUrR0-QvGJl_nY5wPAqWYCosoFvdexsmv0wffIA6DPItjTXVzF9bVkxgoLkz21h4M_1SIb05mneg/s400/resolu%C3%A7%C3%A3o_desafio+1.jpg" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Coloquei este como primeiro desafio só para provar que as vezes não é necessário ter um conhecimento matemático muito grande para resolver problemas, basta ter força de vontade, e ser um bom observador. Portanto, não desanime de uma questão de prova só de ler o enunciado.</span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Bom, é isso pessoal. Um bom final de semana a todos, e não se esqueçam que segunda-feira tem novo desafio!</span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Um abraço!</span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Marcelo Flora</span></div>
<br />Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com3tag:blogger.com,1999:blog-7241116304005966082.post-29324160283886329592010-04-28T11:03:00.000-07:002013-11-03T09:40:52.530-08:00Dúvida do Crisley<br />
<div style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;">
<img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi96zVOczboRRhS23uWJqaqCHNtl-i3o1E9QlZWQho6uRP8ff6jqtvqOEKSA_IohqDKWXkzVX7RtSK-oMiiINyJXCDEiUzzbROm_tPY63atqenS4hx0kj2o4L6w24jydl_ba99whoEbwHdn/s200/duvida2.jpg" style="display: block; float: none; margin-left: auto; margin-right: auto;" /></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;">Olá!</span><br />
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Me chamo Crisley, e gostaria que me ajudasse nesta questão. Parece ser fácil, contudo não consigo resolvê-la. Obrigado desde já.</span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">(UFES) Quantos fatores primos distintos tem o número N = 1999² − 1997² − 1998 ?</span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">a) 1 b) 2 c) 3 d) 4 e) 5 </span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"></span><br />
<a name='more'></a><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Resposta: C</span></div>
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">____________________________________________________________________________________________</span><br />
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Olá Crisley,</span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Para resolver exercícios deste tipo, devemos ter em mente que é inviável realizar a operação apresentada diretamente, pois perderíamos muito tempo. Ao invés disso, temos que encontrar um meio de simplificá-la.</span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Vamos à resolução.</span></div>
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">____________________________________________________________________________________________</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Analisando a equação N = 1999² − 1997² − 1998, é possível perceber que temos a diferença de dois quadrados, ou seja, 1999² − 1997².</span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Pelo método da diferença de quadrados, sabemos que:</span></div>
<div align="justify">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<a href="http://lh5.ggpht.com/_7wGgh4VGq1A/S9MVq8fSMNI/AAAAAAAAAd0/cKog-vzLZAU/s1600-h/clip_image002%5B8%5D%5B2%5D.gif"><img alt="clip_image002[8]" border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlN9wOIrxFvVTdLHGFG8CDegDM8i1MiDShsgbfPNs5wmRaDuYQHoy87mDGdo5-V43PNSGkoCJF6OY_ZqaXLRn7JH535KxOZ5JoOfHpzQK1EKb_dUJVjSEdhB9jLw9P0dztfY4l7ca9A4E/?imgmax=800" style="display: block; float: none; margin-left: auto; margin-right: auto;" title="clip_image002[8]" width="203" /></a><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Assim, podemos transformar nossa equação para a seguinte forma:</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<div align="center">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">N = (1999 + 1997)(1999 - 1997) − 1998</span></div>
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Desenvolvendo esta equação:</span><br />
<div align="center">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">N = (1999 + 1997)(1999 - 1997) − 1998</span></div>
<div align="center">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="center">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">N = (3996)(2) − 1998</span></div>
<div align="center">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="center">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">N = 7992 – 1998</span></div>
<div align="center">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="center">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">N = 5994</span></div>
<div align="center">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div style="text-align: left;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Agora temos que decompor 5994 em fatores primos. Para isso, basta ir dividindo o número em questão pelos números primos, e ir escrevendo os quocientes, e os números, um abaixo do outro. Assim:</span></div>
<div style="text-align: left;">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="left">
<a href="http://lh3.ggpht.com/_7wGgh4VGq1A/S9h3BPSGWcI/AAAAAAAAAec/ZoAae4yWaR0/s1600-h/image%5B3%5D.png"><img alt="image" border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkedcCfi1Bwu_hmmvygNn4jh3CNO7fK5XBp2vXfD4C3kpQjk7BOQEqPK-XH0lVHMA3y3YMNh3ab7jdLwGqqxn5v-tINa5qT8oIhzdwTdAXDtjmVACI1LzgAc9Tt_A2zv737dhl-JHWmlI/?imgmax=800" style="border-bottom: 0px; border-left: 0px; border-right: 0px; border-top: 0px; display: block; float: none; margin-left: auto; margin-right: auto;" title="image" width="86" /></a><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"> </span></div>
<div align="left">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Quantos fatores primos </span><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">distintos</span></strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"> tem o número?</span></div>
<div align="left">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="left">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Analisando a figura acima, vemos que são 2, 3 e 37.</span></div>
<div align="left">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="left">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Portanto, é correta a </span><strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">alternativa c) 3.</span></strong></div>
<div align="left">
<strong><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></strong></div>
<div align="left">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Qualquer dúvida é só deixar um comentário.</span></div>
<div align="left">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div align="left">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Um abraço! E até a próxima!</span></div>
<div align="left">
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Marcelo Flora <br />____________________________________________________________________________________________<br />Saiba como enviar suas dúvidas. </span><a href="http://mfmatematica.blogspot.com/2010/01/esclareca-suas-duvidas-em-matematica.html"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Clique aqui!</span></a>Marcelo Florahttp://www.blogger.com/profile/08800851349561481319noreply@blogger.com1