maths-variations

a. As x varies directly as y2, let x = ky2, where k is a constant.

Now, y varies inversely as z, let y = m / z, where m is a constant.

So, we have x = k(m / z)2

x = km2 / z2 = c / z2, where c is another constant, c = km2

So, x varies inversely as z2.


b. x = c / z2

Now, z is increased by 10%.

z' = (1 + 10%)z = 1.1z

So, x' = c / (1.1z)2

x' = 1 / 1.21 (c / z2)

x' = x / 1.21

Percentage change of x

= (x' - x) / x X 100%

= (1/1.21 - 1) / 1 X 100%

= -17.4% (cor. to 3 sig. fig.)