Question

Suppose r varies directly with the square of m and inversely as s. If r= 12 when m = 6 and s=4, find r when m = 4 and s 10

Answer 1

Answer:

$r=\frac{32}{15}$

Step-by-step explanation:

If r varies directly with the square of m and inversely as s,

then $r=\frac{km^2}{s}$ where k is some constant

Given r = 12 when m = 6 and s = 4:

       $r=\frac{km^2}{s}$

⇒    $12=\frac{k6^2}{4}$

⇒ $\frac{12\times4}{6^2} =k$

⇒     k = $\frac{4}{3}$

Therefore, substituting the found value of k into the original equation: $r=\frac{4m^2}{3s}$

Find r when m = 4 and s = 10:

   $r=\frac{4m^2}{3s}$

⇒ $r=\frac{4\times4^2}{3\times10}$

⇒ $r=\frac{32}{15}$