### Instruction: 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.### Response: I know that inverse variation means that the product of the two variables is constant, so I can write an equation of the form $x^2y=k$, where $k$ is some constant.
To find the value of $k$, I can use the given information that $y$ is 10 when $x$ is 2.
Substituting these values into the equation, I get $2^2(10)=k$, which simplifies to $k=40$.
Now that I have the value of $k$, I can use it to find $x$ when $y$ is 4000.
Plugging in $y=4000$ into the equation, I get $x^2(4000)=40$, which I can solve for $x$ by dividing both sides by 4000 and taking the square root.