Solution for Problem 2.5.2

Find the constant of proportionality.
z is inversely proportional to the cube of w.  If w = 2, then z = 3.  

Solve

Step

The goal is to find k, the constant. Plug in the values 
Use the formula for inverse variation 
If w = 2, then z = 3.   Given
Plug in w and z
Cube 2 and multiply both sides by 8
k = 24 constant of proportionality
Plug 45 in formula for k

Check

 
If w = 2, then z = 3.  

 
z = 3