Question

Please help will mark brainliest 25 pts.

Answer 1

Answer:

C^2 = 4πA

Step-by-step explanation:

The first part asks us to isolate r in the equation C = 2πr. We can do that by dividing both sides by C: $r=\frac{C}{2\pi }$. Note that C stands for the circumference of a circle.

The second step is to plug this value of r into the formula for the area of a circle. We know that the area of a circle is πr^2. We are given π and the exponent, so we just need to plug in $\frac{C}{2\pi }$ and we end up getting $A=\pi (\frac{C}{2\pi })^{2}$

The third step is to square the term in the parentheses. Whenever we have to square a fraction, all we have to do is square the numerator and the denominator:

$(\frac{C}{2\pi })^2=\frac{C^2}{(2\pi )^2}=\frac{C^2}{2^2\pi ^2}$

In other words,

$A=\pi *\frac{C^2}{2^2\pi ^2}$

For the fourth step, 2^2 can be evaluated to get 4. We end up getting the following if we do this:

$A=\frac{\pi}{4 } *\frac{C^2}{\pi^2}$

For the fifth step, we can simplify because the π in the numerator of the first fraction and the π^2 in the denominator of the second fraction cancel (π^2 / π leaves π in the denominator and a 1 in the numerator). If we perform this cancellation, we get the following fraction:

$A=\frac{C^2}{4*\pi}$

For the final step, we can isolate C^2 by multiply both sides by 4π. Then, we get that C^2 = 4πA

In other words, the circumference of the circle squared is equal to 4π times the area of the circle

Answer 2

Answer:

1. r = C/2π

2. A = π(C/2π)^2

Step-by-step explanation:

1. C = 2πr^2

C/2π = 2πr/2π

C/2π = r

r = C/2π

2. A = π(C/2π)^2

3. Look at screenshot