Question

The variable p varies inversely as the square of q. When p = 36, q = 25.

When p = 4, q=
When q = 10, p =

Answer 1

• p=4: q = 75
• q=10: p = 225

Explanation:

You want to know various values of p and q when p varies inversely as the square of q, and p=36 when q=25.

Variation

A formula describing the variation of one variable with another will generally have a constant of variation, which we choose to represent here by the letter k.

Since p varies inversely as the square of q, the formula can be written as ...

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

Multiplying by q² gives us a way to find the value of k from known values of p and q:

k = p·q²

k = 36·25² = 22500 . . . . . . using the given values of p and q

We can also rearrange the formula to give q as a function of p:

q = √(k/p)

Table of values

We are interested in q for p=4, and in p for q=10.

q = √(22500/4) = 75

p = 22500/10² = 225

• When p=4, q = 75
• When q=10, p = 225