The values of $x$ and $y$ are always positive, and $x^2$ and $y^2$ vary inversely. If $y$ is 10 when $x$ is 2, then find $x$ when $y$ is 4000.
y^2 = k / x^2
10^2 = k / 2^2
100 = k / 4
4 * 100 = k = 400 = the proportionality constant
So
(4000)^2 = 400 / x^2 rearrange as
x^2 = 400 / ( 4000)^2 take the sqrt of each side
x = sqrt (400) /sqrt (4000^2)
x = 20 / 4000
x = 2/400
x = 1 / 200
+230 
