## Intermediate Algebra (12th Edition)

$F=\dfrac{Mm}{r^2}$
$\bf{\text{Solution Outline:}}$ To solve the given formula, $r=\sqrt{\dfrac{Mm}{F}}$ for $F ,$ square both sides and then use cross-multiplication to isolate the needed variable. $\bf{\text{Solution Details:}}$ Squaring both sides of the given formula results to \begin{array}{l}\require{cancel} (r)^2=\left( \sqrt{\dfrac{Mm}{F}} \right)^2 \\\\ r^2=\dfrac{Mm}{F} .\end{array} Since $\dfrac{a}{b}=\dfrac{c}{d}$ implies $ad=bc$ or sometimes referred to as cross-multiplication, the equation above is equivalent to \begin{array}{l}\require{cancel} r^2(F)=1(Mm) \\\\ Fr^2=Mm \\\\ F=\dfrac{Mm}{r^2} .\end{array}