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