College algebra help needed

Question

For this statement, find the constant of variation and the variation equation.

y varies jointly as x and the cube of z; y=432 when x=4 and z=3.

Answer 1

Hi, Zoey.

Okay, if y varies jointly as x and the cube of z then the equation is in the form:

y = k(x)(z³)

Where k is the constant of variation.

To solve for k, substitute y = 432 when x = 4 and z = 3:

432 = k(4)(3³)

= k(4)(27)

=108k

k = 4

Therefore, the constant, k, is 4.

Substituting that value into the initial equation you get:

y = 4xz³