Answer: [tex]r=44[/tex]
Step-by-step explanation:
The combine variation equation will have the folllowing form:
[tex]y=\frac{kx}{z}[/tex]
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:
[tex]r=\frac{m^2k}{s}[/tex]
Knowing that [tex]r=11[/tex] when [tex]m=6[/tex] and [tex]s=4[/tex], you can substitute values into the equation and solve for "k" in order to find its value:
[tex]11=\frac{6^2(k)}{4}\\\\\frac{11*4}{6^2}=k\\\\k=\frac{11}{9}[/tex]
Now, to find the value of "r" when [tex]m=12[/tex] and [tex]s=4[/tex], you need tot substitute these values and the the constant of variation into [tex]r=\frac{m^2k}{s}[/tex] and then evaluate:
[tex]r=\frac{(12^2)(\fra{11}{9}}{4}\\\\r=44[/tex]
