Given that p varies as the square of q and q varies inversely as the square root of r. How does p vary with r?
A. p varies as the square of r B. p varies as the square root of r C. p varies inversely as the square of r D. p varies inversely as r
Correct Answer: D
Explanation
\(p \propto q^2\) \(q \propto \frac{1}{\sqrt{r}\) \(p = kq^2\) \(q = \frac{c}{\sqrt{r}}\) where c and k are constants. \(q^2 = \frac{c^2}{r}\) \(p = \frac{kc^2}{r}\) If k and c are constants, then kc\(^2\) is also a constant, say z. \(p = \frac{z}{r}\) p varies inversely as r.
