Modeling Using Variation

Question

Suppose that z varies jointly with the cube of x and the square of y.

Find the constant of proportionality k if z = 2188.8 when y = 3 and x = 4.

k = 

Using the k from above write the variation equation in terms of x and y.

z =   

Using the k from above find z given that y = 10 and x = 6.

z = 

If needed, round answer to 3 decimal places.

Enter DNE for Does Not Exist, oo for Infinity

Answer 1

Hi Cameron,

The general equation is z = k x³ y²

Substituting the values given: 2188.8 = k (3)³(4)²

Then 2188.8 = 432k

and k = 75/16 or about 5.07

the the equation asked for is z = 75/16x³y²

^{If y = 10 and x = 6}

then

z = 75/16(6)³(10)² = 109440

Happy to help!