M varies directly as the square of x. If m = 200 when x = 20, find m when x is 32?

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Answer 1 · 2017-03-10T03:05:44

The answer is $512$ $512$

$M$ $M$ varies as $x^{2}$ $x^2$ , so

$\Rightarrow \frac{M}{x^{2}} = k$ $=> M/x^2 = k$

where $k$ $k$ is a non-zero constant.

$M = 200$ $M=200$ and $x = 20$ $x=20$ , hence

$k = \frac{200}{20^{2}} = \frac{1}{2}$ $k=200/20^2 = 1/2$

Now,

$x = 32$ $x=32$

so

$M = \frac{1}{2} \times 32^{2} = 512$ $M = 1/2 xx 32^2 = 512$