Solve the equation for the indicated variable. Assume no denominator is 0.
-$A = 2 \pi a ^ { 2 }$, for a
A) $a = \frac { \pm A \sqrt { 2 \pi } } { 2 \pi }$
B) $a = \frac { \pm \sqrt { 2 \pi \mathrm { A } } } { 2 \pi }$
C) $a = \sqrt { 2 \pi \mathrm { A } }$
D) $a = \frac { \pm \sqrt { \mathrm { A } \pi } } { 2 }$

Question

Quizplus · Accepted Answer

To solve for $a$, we start with the given equation $A = 2 \pi a^2$. Dividing both sides by $2\pi$ gives $a^2 = \frac{A}{2\pi}$. Taking the square root of both sides to solve for $a$ yields $a = \pm \sqrt{\frac{A}{2\pi}}$, which simplifies to $a = \frac{\pm \sqrt{2\pi A}}{2\pi}$, matching choice B.

Solve the Equation for the Indicated Variable A=2πa2A = 2 \pi a ^ { 2 }A=2πa2

Solve the Equation for the Indicated Variable $A = 2 \pi a ^ { 2 }$