Question

Suppose r varies directly as the square of​ m, and inversely as s. If r equals 11 when m equals 6 and s equals 4​, find r when m equals 12 and s equals 4.

Answer 1

Answer:
`r=44`

Explanation:

The combine variation equation will have the folllowing form:

`y=(kx)/(z)`

Where "k" is the constantn of variation.

You know that "r" varies directly as the square of​ "m", and inversely as "s". Then the equation is:

`r=(m^2k)/(s)`

Knowing that
`r=11` when
`m=6` and
`s=4`, you can substitute values into the equation and solve for "k" in order to find its value:

`11=(6^2(k))/(4)\\\\(11*4)/(6^2)=k\\\\k=(11)/(9)`

Now, to find the value of "r" when
`m=12` and
`s=4`, you need tot substitute these values and the the constant of variation into
`r=(m^2k)/(s)` and then evaluate:

`r=\frac{(12^2)(\fra{11}{9}}{4}\\\\r=44`