Question

I need help please!!

Answer 1

Step-by-step explanation:

The domain of A(r) is $r \geq 0.$ The expression for A(r) is

$A(r) = 2\pi r^2 + 16\pi r$

Let's write A(r) as simply A and divide the equation by $2\pi$ to get

$r^2 + 8r = \dfrac{A}{2\pi}$

We can complete the square on the left hand side by adding 16 to both sides:

$r^2 + 8x + 16 = \dfrac{A}{2\pi} + 16$

$\Rightarrow (r + 4)^2 = \dfrac{A}{2\pi} + 16$

Taking the square root of the equation above and then solving for r, we get

$r = -4 \pm \sqrt{\dfrac{A}{2\pi} + 16}$