[tex]x^2[/tex] and [tex]y[/tex] vary inversely, which means there is some constant [tex]k[/tex] such that
[tex]x^2y=k[/tex]
We're told that [tex]x=2[/tex] when [tex]y=10[/tex], so
[tex]2^2\cdot10=k=400[/tex]
When [tex]y=4000[/tex], we have
[tex]4000x^2=400\implies x^2=10\implies x=\sqrt{10}[/tex]
(taking the positive square root since it's always the case that [tex]x>0[/tex])
