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Shalnov [3]
3 years ago
6

I need help please!!

Mathematics
1 answer:
Evgesh-ka [11]3 years ago
6 0

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}

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