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

Answer:

$y = \frac{384}{9}$

Step-by-step 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

$k = \frac{24}{9}$

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

$y = kx^2$

$y = \frac{24}{9} * 4^2$

$y = \frac{24}{9} * 16$

$y = \frac{24 * 16}{9}$

$y = \frac{384}{9}$