Let's start with the given equation:
[tex]\[ A = \pi r^2 (x + y) \][/tex]
Our goal is to solve for [tex]\( r \)[/tex] and we will assume [tex]\( r > 0 \)[/tex]. Follow these steps to isolate [tex]\( r \)[/tex]:
1. Divide both sides of the equation by [tex]\(\pi (x + y)\)[/tex]:
[tex]\[ \frac{A}{\pi (x + y)} = r^2 \][/tex]
2. Take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt{\frac{A}{\pi (x + y)}} \][/tex]
Since we are given that [tex]\( r > 0 \)[/tex], we take the positive square root:
[tex]\[ r = \frac{\sqrt{A}}{\sqrt{\pi (x + y)}} \][/tex]
Thus, the subject of the formula [tex]\( r \)[/tex] in terms of [tex]\( A\)[/tex], [tex]\(\pi\)[/tex] and the sum [tex]\( (x + y)\)[/tex] is:
[tex]\[ r = \sqrt{\frac{A}{\pi (x + y)}} \][/tex]
