The variable z varies jointly as the second power of x and the third power of y. When x equals 2 and y equals 2.4 , z equals 31.5. Approximate the constant of variation to the nearest hundredth.

The constant of variation, k = 0.57

Step-by-step explanation:

We are given that z varies jointly as the second power of x (x²), and the third power of y (y³).

For a constant of variation, k, z can be written as

z = x²y³k.

We are also given

z = 31.5

x = 2

x = 2.4

31.5 = (2²) (2.4) ³k

31.5 = 4*13.824k

31.5 = 55.296k

k = 31.5/55.296

= 0.57