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 r3
B
p varies inversely as r6
C
p varies inversely as 6√P
D
p varies directly as r6
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
P ∝ 1/q3
P = K/q3
q3 = K/P
q = K/p1/3
But q ∝ r2
q = Kr2
K/p1/3 = Kr2
r2 = K/p1/3 x 1/K
r2 = 1/p1/3
r = (1/p1/3)2
r = 1/p1/6
r ∝ 1/p1/6 = p = \(\frac{1}{r^6}\)
∴ p varies inversely as \(r^6\)
Source: Myschool Past Questions Archive (Record #9035)