Question

The quantity y varies directly with the square of x. If y=24 when x=3, find y when x is 4

Answer 1

`y = (384)/(9)`

Explanation:

Given

`y\ \alpha\ x^2` --- direct variation

`(x,y) = (3,24)`

Required

y when x = 4

`y\ \alpha\ x^2`

Express as an equation

`y = kx^2`

Substitute:
`(x,y) = (3,24)`

`24 = k*3^2`

`24 = k*9`

Solve for k

`k = (24)/(9)`

To solve for y when x = 4, we have:

`y = kx^2`

`y = (24)/(9) * 4^2`

`y = (24)/(9) * 16`

`y = (24 * 16)/(9)`

`y = (384)/(9)`