Solve for the specified variable. Assume that all other variables are nonzero
-$$\mathrm { S } = \lambda \left( \mathrm { b } ^ { 2 } + \mathrm { B } ^ { 2 } \right) \mathrm { w } ; \text { for } \mathrm { b }$$
A) $b = \pm \sqrt { \frac { S - \lambda w B ^ { 2 } } { \lambda w } }$
B) $b = \pm \sqrt { \frac { S - B ^ { 2 } } { \lambda w } }$
C) $b = \pm \sqrt { \frac { S } { \lambda w } } - B ^ { 2 }$
D) $b = \pm \sqrt { \frac { S } { \lambda w } } - B$

Question

Quizplus · Accepted Answer

To solve for $b$, first isolate $b^2$ by subtracting $\lambda w B^2$ from both sides of the equation, giving $S - \lambda w B^2 = \lambda w b^2$. Then, divide both sides by $\lambda w$ to isolate $b^2$, resulting in $b^2 = \frac{S - \lambda w B^2}{\lambda w}$. Finally, take the square root of both sides to solve for $b$, yielding $b = \pm \sqrt{\frac{S - \lambda w B^2}{\lambda w}}$.

Solve for the Specified Variable S=λ(b2+B2)w; for b\mathrm { S } = \lambda \left( \mathrm { b } ^ { 2 } + \mathrm { B } ^ { 2 } \right) \mathrm { w } ; \text { for } \mathrm { b }S=λ(b2+B2)w; for b

Solve for the Specified Variable $\mathrm { S } = \lambda \left( \mathrm { b } ^ { 2 } + \mathrm { B } ^ { 2 } \right) \mathrm { w } ; \text { for } \mathrm { b }$