If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?
- A.
p varies directly as r^{3} - B.
p varies inversely as r^{6} - C.
p varies inversely as ^{6}√P - D.
p varies directly as r^{6}
Correct Answer: Option C
Explanation
P ∝ ^{1}/_{q3}
P = ^{K}/_{q3}
q^{3} = ^{K}/_{P}
q = ^{K}/_{p1/3}
But q ∝ r^{2}
q = Kr^{2}^{K}/_{p1/3} = Kr^{2}
r^{2} = ^{K}/_{p1/3} x ^{1}/_{K}
r^{2} = ^{1}/_{p1/3}
r = (^{1}/_{p1/3})^{2}
r = ^{1}/_{p1/6}
r ∝ ^{1}/_{p1/6}
∴ r varies inversely as ^{6}√P