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

Question

asked Feb 6, 2022 158k views

1 Answer

NZJames · Answer 1 · 2022-02-12T00:43:27+0000

Answer:

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)