Question

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.

Answer 1

`x^2` and
`y` vary inversely, which means there is some constant
`k` such that

`x^2y=k`

We're told that
`x=2` when
`y=10`, so

`2^2\cdot10=k=400`

When
`y=4000`, we have

`4000x^2=400\implies x^2=10\implies x=√(10)`

(taking the positive square root since it's always the case that
`x>0`)

Answer 2

1/10

Explanation: