Question

If p is inversely proportional to the square of q, and p is 6 when q is 8, determine p

8
when q is equal to 2.

Answer 1

`p=96`

Explanation:

Because p is inversely proportional to the square of q, we have that
`p(q^2)=k` for some constant k. We know that
`p=6` when
`q=8`, so we have that
`k=(6)(8)^2=6*64=384`.

We want to know what p is when q is equal to 2, so we have that
`p(2)^2=384`, which gives
`4p=384`, which gives
`\boxed{p=96}`.

Note:
`(96)/(6)=((8)/(2))^2`. Coincidence?