Question

If y varies inversely as `x^2` and If y = 2 when x = 6, what is y when x = 3?

Answer 1

`y=color(green)(8)` when `x=3`

Explanation:

If `y` varies inversely as `x^2`
then
`color(white)("XXX")y*x^2=c` for some constant `c`

Given that `(x,y)=(6,2)` is a solution to this inverse relation:
`color(white)("XXX")rarr 2*6^2=c`

`color(white)("XXX") rarr c=72`

So the complete relation is
`color(white)("XXX")y*x^2=72`
or
`color(white)("XXX")y=72/(x^2)` provided `x!=0`

When `x=3`
`color(white)("XXX")y=72/(3^2)=8`