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: $r=44$

Step-by-step explanation:

The combine variation equation will have the folllowing form:

$y=\frac{kx}{z}$

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:

$r=\frac{m^2k}{s}$

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:

$11=\frac{6^2(k)}{4}\\\\\frac{11*4}{6^2}=k\\\\k=\frac{11}{9}$

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  $r=\frac{m^2k}{s}$ and then evaluate:

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