Given that p is inversely proportional to the square of q, then these two variables are related by the next formula:
[tex]p=\frac{k}{q^2}[/tex]where k is some constant.
Substituting with p = 10 and q = 10, and solving for k:
[tex]\begin{gathered} 10=\frac{k}{10^2} \\ 10=\frac{k}{100} \\ 10\cdot100=\frac{k}{100}\cdot100 \\ 1000=k \end{gathered}[/tex]Substituting with q = 5 and k = 1000, we get:
[tex]\begin{gathered} p=\frac{1000}{5^2} \\ p=\frac{1000}{25} \\ p=40 \end{gathered}[/tex]