Question

If pis inversely proportional to the square of q, and p is 23 when q is 4, determine p

when q is equal to 2.

Answer 1

`p\ =\ 92`

Explanation:

Given

`p\ \alpha\ (1)/(q^2)`

`p =23; q=4`

Required

Find p, when
`q = 2`

We have:

`p\ \alpha\ (1)/(q^2)`

Express as equation

`p\ =\ (k)/(q^2)`

Make k the subject

`k =pq^2`

When:
`p =23; q=4`

`k =23 * 4^2`

`k =368`

When
`q = 2`, we have:

`p\ =\ (k)/(q^2)`

`p\ =\ (368)/(2^2)`

`p\ =\ (368)/(4)`

`p\ =\ 92`