Question

The quantity q varies inversely with the square of m and directly with the product of rand x. When q is 2.5, m is 4 and the

product of r and x is 8. What is the constant of variation?
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Answer 1

5

Explanation:

C on edge

Answer 2

The constant of variation is

`k= 5`

Explanation:

First we must write the relationship as an equality.

If q varies inversely with the square of m, this means that when m ^ 2 increases then q decreases.

If q varies directly with the product of r and x this means that when r * x increases q increases.

Then the relationship is:

`q = k(rx)/(m^2)`

Where k is the constant of proportionality

Then if:

`q=2.5\\\\m=4\\\\r*x=8`

`2.5 = k(8)/(4^2)`

We solve for k

`2.5 = k(8)/(16)`

`2.5 = k(1)/(2)`

`k= 5`