Find \(d\) when \(c=20\)
\begin{align}c & \propto d^2\\
So \quad c & =kd^2 \\
By \; substitution \quad 15 & =k(3^2)\\
k & =\frac{15}{9}\\
\therefore \quad c & =\frac{15}{9}(d^2)\\
And \; when \; c & =20\\
20 & =\frac{15}{9}(d^2)\\
d^2 & =\frac{9}{15}(20)\\
d^2 & =12\\
\therefore \quad d & = \pm \sqrt{12}
\end{align}
Find \(c\) when \(d=8\)
\begin{align}c & \propto d^2\\
So \quad c & =kd^2 \\
By \; substitution \quad 15 & =k(3^2)\\
k & =\frac{15}{9}\\
And \; when \; d & =8\\
c & =\frac{3}{8}(8^2)\\
\therefore \quad c & =24\\
\end{align}