## Intermediate Algebra (12th Edition)

$K=\dfrac{mV^2}{2}$
$\bf{\text{Solution Outline:}}$ To solve the given formula, $V=\sqrt{\dfrac{2K}{m}}$ for $K ,$ 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} (V)^2=\left( \sqrt{\dfrac{2K}{m}} \right)^2 \\\\ V^2=\dfrac{2K}{m} .\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} V^2(m)=1(2K) \\\\ mV^2=2K \\\\ \dfrac{mV^2}{2}=K \\\\ K=\dfrac{mV^2}{2} .\end{array}