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?
- p varies as the square of r
- p varies as the square root of r
- p varies inversely as the square of r
-
p varies inversely as r
The correct answer is: 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.