passpadi

2006

Mathematics

JAMB

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

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