Question

Y is inversely proportional to the square of x when y =50, x=2, how do you find an equation connecting y and x?

Answer 1

`2x^2y=25`
`color(white)("XXXX")`(or some variation of that)

Explanation:

If `y` is inversely proportional to the square of `x`, then
`color(white)("XXXX")` `y = c/(x^2)` `color(white)("XXXX")`for some constant `c`

We are told that when `y=50` then `x=2`

So the proportional equation becomes
`color(white)("XXXX")` `50 = c/(2^2)`

`color(white)("XXXX")` `rarr c = 25/2`

So
`color(white)("XXXX")` `y =(25/2)/x^2`
which could also be written as
`color(white)("XXXX")` `x^2y = 25/2`
or
`color(white)("XXXX")` `2x^2y = 25`