Query: A sector of a circle radius r subtends an angle of theta at the centre. The perimeter of the sector is 3m and the area is A sq.m. Show that A=0.5r(3-2r).
Response: Please click on the graphic to view the solution.
Query: A sector of a circle radius r subtends an angle of theta at the centre. The perimeter of the sector is 3m and the area is A sq.m. Show that A=0.5r(3-2r).
Response: Please click on the graphic to view the solution.
Query: How do I estimate the height of this mast (see diagram)?
Response: The man's height has to be estimated first. Next, you calculate how many men of the same height (i.e. standing on each other's heads) it would take to reach the top of the mast.
Click on the graphic below to see how you would show this.
Query: What is the order of rotational symmetry of this shape?
Response: If you rotate the shape you can see that it will fit its own outline four times in each complete revolution.
Hence the order of rotational symmetry is 4.
Query: John's pulse rate is taken every 6 hours over a three day period. The graph shows his pulse rate in beats per minute. [Please click on the graph to see it full size]
Find the difference between his lowest and highest pulse rate on the 3rd of May.
Response: From the graph the highest rate is 102 and the lowest is 97. Hence the difference is 102-97=5 beats per minute.
Query: I'm given that the cost of a taxi fare is made up of a fixed charge of $4.20 and 45 cents per mile travelled. How do I find the cost of a 30 mile journey?
Response: You'll need to work out 30 x 45 cents (use $0.45 in a calculator) and then add the $4.20 fixed charge to this.
The answer is $17.70.