Question

x is directly proportional to w²
When w = 4, x = 48

y is inversely proportional to x³
When x = 2, y = 14

Find a formula for y in terms of w.
Give your answer in its simplest form.

Answer 1

The formula for x in terms of w is x = 3w² and the formula for y in terms of x is y = (1/112)x³

Variation

x = k × w²

w = 4, x = 48

48 = k × 4²

48 = k × 16

48 = 16k

k = 48/16

k = 3

So,

x = k × w²

x = 3 × w²

x = 3w²

y = k/x³

x = 2, y = 14

14 = k / 2³

14 × 2³ = k

14 × 8 = k

112 = k

So,

y = k/x³

y = 112/x³

y = (1/112)x³

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