Step-by-step explanation:
The domain of A(r) is
The expression for A(r) is
![A(r) = 2\pi r^2 + 16\pi r](https://tex.z-dn.net/?f=A%28r%29%20%3D%202%5Cpi%20r%5E2%20%2B%2016%5Cpi%20r)
Let's write A(r) as simply A and divide the equation by
to get
![r^2 + 8r = \dfrac{A}{2\pi}](https://tex.z-dn.net/?f=r%5E2%20%2B%208r%20%3D%20%5Cdfrac%7BA%7D%7B2%5Cpi%7D)
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](https://tex.z-dn.net/?f=r%5E2%20%2B%208x%20%2B%2016%20%3D%20%5Cdfrac%7BA%7D%7B2%5Cpi%7D%20%2B%2016)
![\Rightarrow (r + 4)^2 = \dfrac{A}{2\pi} + 16](https://tex.z-dn.net/?f=%5CRightarrow%20%28r%20%2B%204%29%5E2%20%3D%20%5Cdfrac%7BA%7D%7B2%5Cpi%7D%20%2B%2016)
Taking the square root of the equation above and then solving for r, we get
![r = -4 \pm \sqrt{\dfrac{A}{2\pi} + 16}](https://tex.z-dn.net/?f=r%20%3D%20-4%20%5Cpm%20%5Csqrt%7B%5Cdfrac%7BA%7D%7B2%5Cpi%7D%20%2B%2016%7D)
The equation of the vertical line passing through point -4,7 would be X = -4.
If Nick starts with 20, we can just plug it into p/2 - 12 to get 10-12 or -2. This means Nick did not get 20 cards. Now we have answered both. Two-liner!
26/25 aka 1 1/25
explanation
the first drawing has 11 shaded out of 25
11/25
The second one has three out of 5
5 times 5 is 25
3 times 5 is 15
there fore it would have 15 shaded out of 25
15/25
and 15/25 plus 11/25 is 26/25
Answer:
76 in
Step-by-step explanation:
20+20+18+18=76