Chapter 11 - Polynomial and Rational Functions - 11.1 Power Functions and Proportionality - Exercises and Problems for Section 11.1 - Exercises and Problems - Page 440: 22

$c=16.2$ when $d=5$ and $k=405$

We are given that $c=45, d=3$ $c$ is inversely proportional to the square of $d$. So, we can write $c=\dfrac{k}{d^2}~~~~(1)$ Plug $c=45, d=3$ in equation (1) to obtain: $45= \dfrac{k}{3^2} \implies k=405$ Thus, we have: $c=\dfrac{405}{d^2} ~~~~(2)$ Now, plug $d=5$ in Equation (2) to obtain: $c=\dfrac{405}{5^2} \implies c=16.2$ Therefore, we get $c=16.2$ when $d=5$ and $k=405$