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Y is inversely proportional to the square of x when y =50, x=2, how do you find an equation connecting y and x?

1 Answer

Aug 1, 2015

$2 x^{2} y = 25$ $2x^2y=25$
$XXXX$ $color(white)("XXXX")$ (or some variation of that)

Explanation:

If $y$ $y$ is inversely proportional to the square of $x$ $x$ , then
$XXXX$ $color(white)("XXXX")$ $y = \frac{c}{x^{2}}$ $y = c/(x^2)$ $XXXX$ $color(white)("XXXX")$ for some constant $c$ $c$

We are told that when $y = 50$ $y=50$ then $x = 2$ $x=2$

So the proportional equation becomes
$XXXX$ $color(white)("XXXX")$ $50 = \frac{c}{2^{2}}$ $50 = c/(2^2)$

$XXXX$ $color(white)("XXXX")$ $\to c = \frac{25}{2}$ $rarr c = 25/2$

So
$XXXX$ $color(white)("XXXX")$ $y = \frac{\frac{25}{2}}{x^{2}}$ $y =(25/2)/x^2$
which could also be written as
$XXXX$ $color(white)("XXXX")$ $x^{2} y = \frac{25}{2}$ $x^2y = 25/2$
or
$XXXX$ $color(white)("XXXX")$ $2 x^{2} y = 25$ $2x^2y = 25$

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