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
Correct Answer: C
Explanation
P ∠1/q3 P = K/q3 q3 = K/P q = K/p[sup]1/[sub]3[/sup][/sub] But q ∠r2 q = Kr2K/p[sup]1/[sub]3[/sup][/sub] = Kr2 r2 = K/p[sup]1/[sub]3[/sup][/sub] x 1/K r2 = 1/p[sup]1/[sub]3[/sup][/sub] r = (1/p[sup]1/[sub]3[/sup][/sub])2 r = 1/p[sup]1/[sub]6[/sup][/sub] r ∠1/p[sup]1/[sub]6[/sup][/sub] ∴ r varies inversely as 6√P
