Given that (Ppropto frac{1}{sqrt{r}}) and p = 3 when r = 16, find the value of r when p =-5
-
A.
48 -
B.
64 -
C.
72 -
D.
324
Correct Answer: Option B
Explanation
(P propto frac{1}{sqrt{r}} P=3hspace{1mm}r=16\
P = frac{k}{sqrt{r}}Rightarrow 3 = frac{k}{sqrt{16}}Rightarrow frac{3}{1} = frac{k}{4} \ Rightarrow K = 12 Rightarrow K = 12; Psqrt{r} = k Rightarrow sqrt{r} = frac{k}{p}\
r = frac{(k)^2}{P}=12^2 div frac{3}{2}=left(frac{12}{1}times frac{2}{3}right)=8^2\
r = 64)