Math Help Forum

similar triangles

thereddevils — Sun, 08 Nov 2009 06:47:02 GMT

In the diagram , BC is parallel to PQ and NA . Show that PQ:BC =NR:NC

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isosceles triangle

thereddevils — Sun, 08 Nov 2009 06:44:23 GMT

In an isosceles triangle ABC , AB=AC and angle BAC =120 degree. Points D and E lie on BC such that BD=DE=EC . Prove that ADE is an equilateral triangle .

2 triangles

thereddevils — Sun, 08 Nov 2009 06:41:40 GMT

THe diagram shows triangle ABC where points A , B , C and P are coplanar . BC=BP=AP and angle BAC =angle ABP = angle PBC = pi/5 rad

Prove that triangle ABC and BPC are similar triangles . Hence deduce that

(1) BC^2=CP.CA

(2)

I am only stucked with (2) , i am ok with the rest . THanks .

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geometry again .

thereddevils — Sun, 08 Nov 2009 06:36:46 GMT

In the diagram , AN and BM are perpendicular to the tangent at R . O is the centre of the circle with diameter AB . Prove that

(1) triangle ANR and RMB are similar

I managed to prove this part

(2) NR=MR

stuck with this .

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one more problem on dual space

math.dj — Sun, 08 Nov 2009 06:36:32 GMT

Let V be vector space of Polynomial of degree 2 over R.fix t1 Consider p1(x),p2(x),p3(x) in V by requiring that fi(pj) = 1 ,if i=j and 0 ,if i not equals j, i.e; p1(x) = (x-t2)(x-t3)/(t1-t2)(t1-t3) ,
p2(x)=(x-t1)(x-t3)/(t2-t1)(t2-t3) ,
p3(x)=(x-t1)(x-t2)/(t3-t1)(t3-t2) .

Now given c1,c2,c3 in R ,prove that there exist unique p(x) in V such that p(ti)=ci, for all i=1,2,3..

thank you in advance

Not sure where to go

LostMathMan — Sun, 08 Nov 2009 06:27:50 GMT

I am stuck on this question and my friends can't figure it out either. We are all unsure of how to go about solving it.

Let W(s,t)=F(u(s,t),v(s,t)), where F, u, and v are differentiable, and
u(1,0) = 2
us(1,0) = -2
ut(1,0) = 6
Fu(2,3) = -1

v(1,0) = 3
vs(1,0) = 5
vt(1,0) = 4
Fv(2,3) = 10

Find Ws(1,0) and Wt(1,0)

Any help would be great. Thanks

Need 3 Homework problems

Johnny Walker Black — Sun, 08 Nov 2009 06:26:07 GMT

Verify these: [i need help getting started and other help you can throw at me]

1) sin(x + y)cos y - cos (x + y)sin y = sin x

2) cot x = (cos3x + cos x) / (sin 3x - sin x)

3) tan(B/2) = sec B / (sec B csc B + csc B)

Strategy to Solve Proof Questions

BlackBlaze — Sun, 08 Nov 2009 06:12:59 GMT

Hi, I'm not sure how much help you guys can give, since this isn't really a textbook question...More of a "how should I study this".

I find I'm able to do calculations and the like with ease in my linear algebra course, but it's the proofs that really get me. Every time I see a question that says "Show that..." or "Prove that..." I'm not able to figure out a method to complete the question. If I see the answer, I can understand just fine, but I don't understand how any person can think of that method to solve it.

For example, one of the midterm questions I received:
"If A and B are n by n matrices, and given that AB is invertible, prove that B must be invertible."
I draw a blank when I try to solve this question on my own.

When the solutions came up, I understood perfectly. To prove B is invertible, Bx = 0 must only have the trivial solution of x = 0. And then you start off with (AB)x = 0 and can easily go from there.

So, are there some tips or strategies to get better at doing these questions?

Dual space

math.dj — Sun, 08 Nov 2009 06:07:29 GMT

Let V be a vector space over field F.Let g,f1,f2,...fk belong to V* i.e;dual of v,then show that g belongs to span{f1,f2,...,fk} if and only if intersection of kernel(fi) i=1 to k is subset of Kernel(g)..

Thank you in advance..

vectors 4

daphnewoon — Sun, 08 Nov 2009 06:02:15 GMT

(a)Is triangle ABC a right-angled triangle? Justify your answer.
[Note: A right-angled triangle is a triangle with one 90o internal angle.]

Vector AB is ( 3, 6 , 1)
Vector BC is ( 0 , -7 , -4)
Vector CA is ( -3 , 1 , 3)

subgroup

apple2009 — Sun, 08 Nov 2009 05:43:16 GMT

Let H be a group. Let M be a normal subgroup of H. Let K be any subgroup of H. Let MK={m�k: m is an element of M and k is an element if K}
a)Prove: MK is a subgroup of H.
b)Suppose that M intersects K={I}. Let k, k' are elements of K. Prove M�k=M� k' if and only if k= k'. conclude that |MK|=|M||K|

Proofs...

lost1 — Sun, 08 Nov 2009 05:28:31 GMT

Hey I need help with some proving questions....

Q1) Prove the following statement, then write down its converse. Is the converse true or false? Prove
your answer.
�For all x 2 Z, if x ≡ −1 (mod 7) then x^3 ≡ −1 (mod 7).�

For the first part I just sub x into the second congruence. But to how do i do the second part. The answer is that the converse is false, so i guess i just need to find a counter example for that. But how am i meant to know that it is false? also how would i go about finding a counter example.

thanks and im sure ill be posting more of these proving questions soon...

Eigenvalues and Eigenvectors

jkhayer — Sun, 08 Nov 2009 05:23:35 GMT

Find all eigenvalues and eigenvectors for the Sturm-Liouville system

y'' + λy = 0

y'(-π)= 0 and y'(π)= 0

orbit

apple2009 — Sun, 08 Nov 2009 05:21:15 GMT

Let ρ: R�→ R� be a nonidentity rotation about the point P. Describe geometrically the ρ -orbits on the set P of all points of R�. Does this explain why orbits are called orbits?

partition and permutation

apple2009 — Sun, 08 Nov 2009 05:14:13 GMT

List all of the partitions of 6. For each partition π , give a permutation σπ is in S6 whose cycle structure is given by that partition. For each σπ , list all of the powers of σπ and indicate the order of σπ.