y varies jointly as x and the cube of z; y=432 when x = 4 and z=3. find the constant variation of k and the variation equation

Answer: constant of variation k = 36 the variation equation, y = 36xz^3

Step-by-step explanation:

y varies jointly as x and the cube of z. This means that y varies directly as x and directly as z^3

In order to remove the "variation" symbol and replace it with "equal to" symbol, we will introduce a constant of variation, k

y = kxz^3

y=432 when x = 4 and z=3

We will substitute these values of x, y and z into the equation to determine the value of k

432 = k * 4 * 3

432 = 12k

k = 432/12 = 36

We will substitute the value of k into the equation. Substituting k = 36 into equation y = kxz^3

The equation becomes

y = 36xz^3