The values of $x$ and $y$ are always positive, and $x^2$ and $y$ vary inversely. If $y$ is 10 when $x$ is 2, then find $x$ when
$y$ is 4000.
1 answer:
and
vary inversely, which means there is some constant
such that
![x^2y=k](https://tex.z-dn.net/?f=x%5E2y%3Dk)
We're told that
when
, so
![2^2\cdot10=k=400](https://tex.z-dn.net/?f=2%5E2%5Ccdot10%3Dk%3D400)
When
, we have
![4000x^2=400\implies x^2=10\implies x=\sqrt{10}](https://tex.z-dn.net/?f=4000x%5E2%3D400%5Cimplies%20x%5E2%3D10%5Cimplies%20x%3D%5Csqrt%7B10%7D)
(taking the positive square root since it's always the case that
)
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