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M varies directly as n and inversely as the square of p. If M = 3,...

Mathematics
WAEC 1996

M varies directly as n and inversely as the square of p. If M = 3, when n = 2 and p = 1, find M in terms of n and p.

  • A. M = 2n/3p
  • B. M = 3n2/2p2
  • C. M = n2/2p
  • D. M = 3n/2p2
  • E. M = 2n/3p2
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Correct Answer: Option D
Explanation

\(M \propto \frac{n}{p^2}\)

\(M = \frac{kn}{p^2}\)

\(3 = \frac{k(2)}{1^2}\)

\(3 = 2k \implies k = \frac{3}{2}\)

\(M = \frac{3n}{2p^2}\)


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