Answer:
I don't really know I'm just trying to get points!
Step-by-step explanation:
be kind
Step-by-step explanation:
option B is the correct answer
I might be wrong but I'll give it a shot, you subtract the 5x from the right side and put it on the left with makes it 20x=2-3. Then subtract the 3 from the 2 which makes it 20x=-1. So it would be -0.05.
I'm not 100% sure. But his is my guess.
Answer:
![Volume = \frac{384}{7}\pi](https://tex.z-dn.net/?f=Volume%20%3D%20%5Cfrac%7B384%7D%7B7%7D%5Cpi)
Step-by-step explanation:
Given (Missing Information):
;
; ![x=0](https://tex.z-dn.net/?f=x%3D0)
Required
Determine the volume
Using Shell Method:
![V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%5Cint%5Climits%5Ea_b%20%7Bp%28y%29h%28y%29%7D%20%5C%2C%20dy)
First solve for a and b.
and
Substitute 8 for y
![8 = x^\frac{3}{2}](https://tex.z-dn.net/?f=8%20%3D%20x%5E%5Cfrac%7B3%7D%7B2%7D)
Take 2/3 root of both sides
![8^\frac{2}{3} = x^{\frac{3}{2}*\frac{2}{3}}](https://tex.z-dn.net/?f=8%5E%5Cfrac%7B2%7D%7B3%7D%20%3D%20x%5E%7B%5Cfrac%7B3%7D%7B2%7D%2A%5Cfrac%7B2%7D%7B3%7D%7D)
![8^\frac{2}{3} = x](https://tex.z-dn.net/?f=8%5E%5Cfrac%7B2%7D%7B3%7D%20%3D%20x)
![2^{3*\frac{2}{3}} = x](https://tex.z-dn.net/?f=2%5E%7B3%2A%5Cfrac%7B2%7D%7B3%7D%7D%20%3D%20x)
![2^2 = x](https://tex.z-dn.net/?f=2%5E2%20%3D%20x)
![4 =x](https://tex.z-dn.net/?f=4%20%3Dx)
This implies that:
![a = 4](https://tex.z-dn.net/?f=a%20%3D%204)
For ![x=0](https://tex.z-dn.net/?f=x%3D0)
This implies that:
![b=0](https://tex.z-dn.net/?f=b%3D0)
So, we have:
![V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%5Cint%5Climits%5Ea_b%20%7Bp%28y%29h%28y%29%7D%20%5C%2C%20dy)
![V = 2\pi \int\limits^4_0 {p(y)h(y)} \, dy](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%5Cint%5Climits%5E4_0%20%7Bp%28y%29h%28y%29%7D%20%5C%2C%20dy)
The volume of the solid becomes:
![V = 2\pi \int\limits^4_0 {x(8 - x^{\frac{3}{2}}}) \, dx](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%5Cint%5Climits%5E4_0%20%7Bx%288%20-%20x%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%29%20%5C%2C%20dx)
Open bracket
![V = 2\pi \int\limits^4_0 {8x - x.x^{\frac{3}{2}}} \, dx](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%5Cint%5Climits%5E4_0%20%7B8x%20-%20x.x%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx)
![V = 2\pi \int\limits^4_0 {8x - x^{\frac{2+3}{2}}} \, dx](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%5Cint%5Climits%5E4_0%20%7B8x%20-%20x%5E%7B%5Cfrac%7B2%2B3%7D%7B2%7D%7D%7D%20%5C%2C%20dx)
![V = 2\pi \int\limits^4_0 {8x - x^{\frac{5}{2}}} \, dx](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%5Cint%5Climits%5E4_0%20%7B8x%20-%20x%5E%7B%5Cfrac%7B5%7D%7B2%7D%7D%7D%20%5C%2C%20dx)
Integrate
![V = 2\pi * [{\frac{8x^2}{2} - \frac{x^{1+\frac{5}{2}}}{1+\frac{5}{2}}]\vert^4_0](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%7B%5Cfrac%7B8x%5E2%7D%7B2%7D%20-%20%5Cfrac%7Bx%5E%7B1%2B%5Cfrac%7B5%7D%7B2%7D%7D%7D%7B1%2B%5Cfrac%7B5%7D%7B2%7D%7D%5D%5Cvert%5E4_0)
![V = 2\pi * [{4x^2 - \frac{x^{\frac{2+5}{2}}}{\frac{2+5}{2}}]\vert^4_0](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%7B4x%5E2%20-%20%5Cfrac%7Bx%5E%7B%5Cfrac%7B2%2B5%7D%7B2%7D%7D%7D%7B%5Cfrac%7B2%2B5%7D%7B2%7D%7D%5D%5Cvert%5E4_0)
![V = 2\pi * [{4x^2 - \frac{x^{\frac{7}{2}}}{\frac{7}{2}}]\vert^4_0](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%7B4x%5E2%20-%20%5Cfrac%7Bx%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D%7D%7B%5Cfrac%7B7%7D%7B2%7D%7D%5D%5Cvert%5E4_0)
![V = 2\pi * [{4x^2 - \frac{2}{7}x^{\frac{7}{2}}]\vert^4_0](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%7B4x%5E2%20-%20%5Cfrac%7B2%7D%7B7%7Dx%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D%5D%5Cvert%5E4_0)
Substitute 4 and 0 for x
![V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [{4*0^2 - \frac{2}{7}*0^{\frac{7}{2}}])](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%28%5B%7B4%2A4%5E2%20-%20%5Cfrac%7B2%7D%7B7%7D%2A4%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D%5D%20-%20%5B%7B4%2A0%5E2%20-%20%5Cfrac%7B2%7D%7B7%7D%2A0%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D%5D%29)
![V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [0])](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%28%5B%7B4%2A4%5E2%20-%20%5Cfrac%7B2%7D%7B7%7D%2A4%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D%5D%20-%20%5B0%5D%29)
![V = 2\pi * [{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}]](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%7B4%2A4%5E2%20-%20%5Cfrac%7B2%7D%7B7%7D%2A4%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D%5D)
![V = 2\pi * [{64 - \frac{2}{7}*2^2^{*\frac{7}{2}}]](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%7B64%20-%20%5Cfrac%7B2%7D%7B7%7D%2A2%5E2%5E%7B%2A%5Cfrac%7B7%7D%7B2%7D%7D%5D)
![V = 2\pi * [{64 - \frac{2}{7}*2^7]](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%7B64%20-%20%5Cfrac%7B2%7D%7B7%7D%2A2%5E7%5D)
![V = 2\pi * [{64 - \frac{2}{7}*128]](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%7B64%20-%20%5Cfrac%7B2%7D%7B7%7D%2A128%5D)
![V = 2\pi * [{64 - \frac{2*128}{7}]](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%7B64%20-%20%5Cfrac%7B2%2A128%7D%7B7%7D%5D)
![V = 2\pi * [{64 - \frac{256}{7}]](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%7B64%20-%20%5Cfrac%7B256%7D%7B7%7D%5D)
Take LCM
![V = 2\pi * [\frac{64*7-256}{7}]](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%5Cfrac%7B64%2A7-256%7D%7B7%7D%5D)
![V = 2\pi * [\frac{448-256}{7}]](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%5Cfrac%7B448-256%7D%7B7%7D%5D)
![V = 2\pi * [\frac{192}{7}]](https://tex.z-dn.net/?f=V%20%3D%202%5Cpi%20%20%2A%20%5B%5Cfrac%7B192%7D%7B7%7D%5D)
![V = [\frac{2\pi * 192}{7}]](https://tex.z-dn.net/?f=V%20%3D%20%5B%5Cfrac%7B2%5Cpi%20%20%2A%20192%7D%7B7%7D%5D)
![V = \frac{\pi * 384}{7}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B%5Cpi%20%20%2A%20384%7D%7B7%7D)
![V = \frac{384}{7}\pi](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B384%7D%7B7%7D%5Cpi)
Hence, the required volume is:
![Volume = \frac{384}{7}\pi](https://tex.z-dn.net/?f=Volume%20%3D%20%5Cfrac%7B384%7D%7B7%7D%5Cpi)
I then the answer is: a^63