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?
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Correct Answer: Option 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
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