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.

Accepted Solution

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]