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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(p \propto q^2\)
\(q\propto\frac{1}{\sqrt{r}\)
\(p = kq^2\)
\(q = \frac{c}{\sqrt{r}}\)
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.
Source: Myschool Past Questions Archive (Record #26605)