Suppose that $a$ varies inversely with $b^2$. If $a=9$ when $b=2$, find the value of $a$ when $b=3$.
Since $a$ varies inversely with $b^2$, that means there is some constant $k$ such that $a=k/b^2$. To find $k$, I can use the given values of $a$ and $b$: $9=k/2^2$, so $k=9\times 4=36$. Now that I have $k$, I can plug in any other values of $a$ and $b$ to find the missing variable. For example, if $b=3$, then $a=36/3^2=36/9=4$. 