Answer:
The constant of variation is
[tex]k= 5[/tex]
Step-by-step 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:
[tex]q = k\frac{rx}{m^2}[/tex]
Where k is the constant of proportionality
Then if:
[tex]q=2.5\\\\m=4\\\\r*x=8[/tex]
[tex]2.5 = k\frac{8}{4^2}[/tex]
We solve for k
[tex]2.5 = k\frac{8}{16}[/tex]
[tex]2.5 = k\frac{1}{2}[/tex]
[tex]k= 5[/tex]
