Question

The square of y varies directly as the cube of x. When x = 4, y = 2. Which equation can be used to find other combinations of x and y?
A. y^2 = 1/16x^3
B. y=1/2x
C. xy=8
D. x^3y^2 = 128

Answer 1

Answer:

A

Step-by-step explanation:

Given y² varies directly as x³ then the equation relating them is

y² = kx³ ← k is the constant of variation

To find k use the condition when x = 4, y = 2

2² = 4³k , that is

4 = 64k ( divide both sides by 64 )

$\frac{4}{64}$ = k , that is

k = $\frac{1}{16}$

y² = $\frac{1}{16}$ x³ → A

Answer 2

Answer:

To find the answer you first need to find the constant of variation K, so according to the question the linear equation should be as follows y² =kx³, substitute the known values then solve for k.

Now the equation becomes 2²=k(4³), 4=64k, k=$\frac{1}{16}$, so the other equation that can solve for the unknown variables is in the following form y²=$\frac{1}{16}$x³ which is choice A

hope it helped you guys, always try to look at the answer from different perspectives and most importantly understand it :)