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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.

A) 36

B) 63

C) 47

D) 81

### 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

## 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