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If M varies directly as N and inversely as the root of P. Given that M = 3, N = ...


Question

If M varies directly as N and inversely as the root of P. Given that M = 3, N = 5 and P = 25. Find the value of P when M = 2 and N = 6.

Options

A) 36

B) 63

C) 47

D) 81

The correct answer is D.

Explanation:

\(M \propto N \) ; \(M \propto \frac{1}{\sqrt{P}}\).
\(\therefore M \propto \frac{N}{\sqrt{P}}\)
\(M = \frac{k N}{\sqrt{P}}\)
when M = 3, N = 5 and P = 25;
\(3 = \frac{5k}{\sqrt{25}}\)
\(k = 3\)
\(M = \frac{3N}{\sqrt{P}}\)
when M = 2 and N = 6,
\(2 = \frac{3(6)}{\sqrt{P}} \implies \sqrt{P} = \frac{18}{2}\)
\(\sqrt{P} = 9 \implies P = 9^2\)
P = 81

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Dicussion (1)

  • \(M \propto N \) ; \(M \propto \frac{1}{\sqrt{P}}\).
    \(\therefore M \propto \frac{N}{\sqrt{P}}\)
    \(M = \frac{k N}{\sqrt{P}}\)
    when M = 3, N = 5 and P = 25;
    \(3 = \frac{5k}{\sqrt{25}}\)
    \(k = 3\)
    \(M = \frac{3N}{\sqrt{P}}\)
    when M = 2 and N = 6,
    \(2 = \frac{3(6)}{\sqrt{P}} \implies \sqrt{P} = \frac{18}{2}\)
    \(\sqrt{P} = 9 \implies P = 9^2\)
    P = 81

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