Question

given $a = \frac{1}{2}r^2 + 15b$, solve for $b$

Explanation:

Step1: Subtract $\frac{1}{2}r^2$ from both sides

To isolate the term with \( b \), we subtract \(\frac{1}{2}r^2\) from both sides of the equation \( A=\frac{1}{2}r^2 + 15b \). This gives us \( A-\frac{1}{2}r^2=15b \).

Step2: Divide both sides by 15

Now, to solve for \( b \), we divide both sides of the equation \( A - \frac{1}{2}r^2=15b \) by 15. Using the division operation, we get \( b=\frac{A-\frac{1}{2}r^2}{15} \). We can also simplify this fraction by getting a common denominator in the numerator: \( b = \frac{2A - r^2}{30} \) (by multiplying the numerator and denominator of \(\frac{A}{15}-\frac{r^2}{30}\) by 2 to combine the terms).

Answer:

\( b=\frac{A - \frac{1}{2}r^2}{15} \) (or equivalently \( b=\frac{2A - r^2}{30} \))