Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

If y varies inversely as $x^{2}$ $x^2$ and If y = 2 when x = 6, what is y when x = 3?

1 Answer

May 20, 2016

$y = 8$ $y=color(green)(8)$ when $x = 3$ $x=3$

Explanation:

If $y$ $y$ varies inversely as $x^{2}$ $x^2$
then
$XXX y \cdot x^{2} = c$ $color(white)("XXX")y*x^2=c$ for some constant $c$ $c$

Given that $(x, y) = (6, 2)$ $(x,y)=(6,2)$ is a solution to this inverse relation:
$XXX \to 2 \cdot 6^{2} = c$ $color(white)("XXX")rarr 2*6^2=c$

$XXX \to c = 72$ $color(white)("XXX") rarr c=72$

So the complete relation is
$XXX y \cdot x^{2} = 72$ $color(white)("XXX")y*x^2=72$
or
$XXX y = \frac{72}{x^{2}}$ $color(white)("XXX")y=72/(x^2)$ provided $x \neq 0$ $x!=0$

When $x = 3$ $x=3$
$XXX y = \frac{72}{3^{2}} = 8$ $color(white)("XXX")y=72/(3^2)=8$

Related questions

See all questions in Inverse Variation Models

Impact of this question

4401 views around the world

You can reuse this answer
Creative Commons License