Question

Y is inversely proportional to the cube of x. When x = 1/2, y = 24.

(a) Find the formula for y in terms of x

Answer 1

y=3/x^3

Explanation:

y = k / x^3

24 = k / 1/2^3

Cross Multiply:

24 × 1/2^3 = k

3 = k

Since k is 3, then:

y=3/x^3

Answer 2

y =
`(3)/(x^3)`

Explanation:

Given y is inversely proportional to x³ then the equation relating them is

y =
`(k)/(x^3)` ← k is constant of proportion

To find k use the condition when x =
`(1)/(2)` , y = 24

24 =
`(k)/(((1)/(2)) ^(3) )` =
`(k)/((1)/(8) )` = 8k ( divide both sides by 8 )

3 = k

y =
`(3)/(x^3)` ← equation of proportion