Answer:
[tex]r=\frac{32}{15}[/tex]
Step-by-step explanation:
If r varies directly with the square of m and inversely as s,
then [tex]r=\frac{km^2}{s}[/tex] where k is some constant
Given r = 12 when m = 6 and s = 4:
[tex]r=\frac{km^2}{s}[/tex]
⇒ [tex]12=\frac{k6^2}{4}[/tex]
⇒ [tex]\frac{12\times4}{6^2} =k[/tex]
⇒ k = [tex]\frac{4}{3}[/tex]
Therefore, substituting the found value of k into the original equation: [tex]r=\frac{4m^2}{3s}[/tex]
Find r when m = 4 and s = 10:
[tex]r=\frac{4m^2}{3s}[/tex]
⇒ [tex]r=\frac{4\times4^2}{3\times10}[/tex]
⇒ [tex]r=\frac{32}{15}[/tex]
