Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
-$\mathrm { H } = \frac { \mathrm { F } } { \sqrt { \mathrm { F } ^ { 2 } + \mathrm { G } ^ { 2 } } }$, for $\mathrm { F }$
A) $F = H \sqrt { F ^ { 2 } + G ^ { 2 } }$
B) $\mathrm { F } = \frac { \mathrm { GH } } { 1 - \mathrm { H } }$
C) $\mathrm { F } = \frac { \mathrm { GH } } { \sqrt { 1 - \mathrm { H } ^ { 2 } } }$
D) $F = \frac { \sqrt { \mathrm { G } ^ { 2 } + \mathrm { H } ^ { 2 } } } { \mathrm { G } }$

Question

Quizplus · Accepted Answer

To solve for $F$, multiply both sides by the denominator to get $F = H \sqrt{F^2 + G^2}$. Then, square both sides to eliminate the square root, resulting in $F^2 = H^2(F^2 + G^2)$. Rearrange to get $F^2(1-H^2) = H^2G^2$, and solve for $F$ to find $F = \frac{GH}{\sqrt{1-H^2}}$, which matches choice C.

Solve the Formula for the Indicated Letter H=FF2+G2\mathrm { H } = \frac { \mathrm { F } } { \sqrt { \mathrm { F } ^ { 2 } + \mathrm { G } ^ { 2 } } }H=F2+G2​F​

Solve the Formula for the Indicated Letter $\mathrm { H } = \frac { \mathrm { F } } { \sqrt { \mathrm { F } ^ { 2 } + \mathrm { G } ^ { 2 } } }$