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MATHEMATICS

JAMB 2006 - Question 41

Mathematics 2006 JAMB Past Questions - Question 41: 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?

Choose the most appropriate option for the gap .

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

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Correct Answer

Explanation

P ∝ 1/q3P = K/q3q3 = K/Pq = K/p1/3But q ∝ r2q = Kr2K/p1/3 = Kr2r2 = K/p1/3 x 1/Kr2 = 1/p1/3r = (1/p1/3)2r = 1/p1/6r ∝ 1/p1/6 = p = 1r6∴ p varies inversely as r6