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: Option 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.