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John has twin sisters. The sum of the ages of John and his twin sisters is 39. In 4 years’ time the twins will be 18. How old will John be in 4 years’ time?

With a problem like this first you must pull the necessary information out of the question. It can make it more familiar if we assign single letters to the unknowns. In this case the unknowns are, Johns age ...
FW
Answered by Finlay W. • Maths tutor
6139 Views

Calculate the area of a sector which has an acute angle of 30 degrees and a radius of 5cm.

Sector area = (angle/360) + πr 2 Therefore the answer would be: Area = (30/360) + (π x 5 2 ) = 78.62 degrees to 2dp
PH
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P (–1, 4) is a point on a circle, centre O which is at the origin. Work out the equation of the tangent to the circle at P. Give your answer in the form y = mx + c

A tangent makes an angle of 90 degrees with the radius of a circle.Using this fact, we find the gradient of the radius going through P = -4Therefore gradient of the tangent to the circle at P is -1/-4 = 1/4T...
CG
Answered by Charlie G. • Maths tutor
10320 Views

n is an integer greater than 1. Prove algebraically that n^2-2-(n-2)^2 is always an even number

We want to show that this gives an even number, so we need to get it into a form that it is 2 multiplied by some positive integer. We start by expanding the (n-2) 2 out, remember that (n-2) 2 =(n-2)(n-2). Th...
JC
Answered by Jacob C. • Maths tutor
27188 Views

Find the length of the hypotenuse of a right-angled triangle using i) Pythagoras Theorem ii) Trigonometry. The triangle has sides of lengths 3cm and 4cm and an acute angle of 30 degrees.

Part i Pythagoras Theorem states a 2 = b 2 + c 2 , where a is the hypotenuse.Using this the lengths can be substituted into the equation as b and c, a 2 = 3 2 + 4 2 a 2 = 25a = sqrt(25) = 5cm Part ii Trigono...
ZS
Answered by Zaakir S. • Maths tutor
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