Answer
$c=125$ when $d=5$ and $k=5$
Work Step by Step
We are given that $c=45; d=3$
$c$ is directly proportional to $d^2$.
We can write $c=kd^2~~~~(1)$
Plug $c=45, d=3$ in equation (1) to obtain:
$45=k(3)^2\implies k=5$
Thus, we have: $c=5d^2 ~~~~(2)$
Now, plug $d=5$ in Equation (2) to obtain:
$c=5(5)^2 \implies c=125$
Therefore, we get $c=125$ when $d=5$ and $k=5$.