2006

Mathematics

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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: p varies inversely as 6√P

Explanation

P ∝ 1/q³ P = K/q³ q3 = K/P q = K/p^1/3 But q ∝ r² q = Kr² K/p^1/3 = Kr²² r² = K/p^1/3x 1/K r² = 1/p^1/3 r = (1/p1/3)² r = 1/p^1/6 r ∝ 1/p^1/6 ∴ r varies inversely as 6√P

P ∝ 1/q³ P = K/q³ q3 = K/P q = K/p^1/3 But q ∝ r² q = Kr² K/p^1/3 = Kr²² r² = K/p^1/3x 1/K r² = 1/p^1/3 r = (1/p1/3)² r = 1/p^1/6 r ∝ 1/p^1/6 ∴ r varies inversely as 6√P

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