a varies inversely as b cubed. If a equals nine fourths when b equals 2​, find a when b is 3.

Answer 1

When you are given "a varies inversely as b cubed" it means:

a = k/b³ where k is the constant of proportionality

To find out what k is, they have given you values for a and for b that allow you to plug them into that equation and solve for k. Then you can re-write a = k/b³ with the value for k in it.

In this case, they said a = 9/4 when b = 2 so that means:

9/4 = k/2³

9/4 = k/8

8*9/4 = k = 72/4 = 18

Therefore a = 18/b³

Now you can plug in b = 3 to find out the corresponding value of a:

a = 18/(3)³

a = 18/27 = 2/3