Answer:
![\frac{784}{15} \pi](https://tex.z-dn.net/?f=%5Cfrac%7B784%7D%7B15%7D%20%5Cpi)
Step-by-step explanation:
According to the given situation, the calculation of volume of the solid is shown below:-
Here we will consider the curves that is
![x = 7y^2, x = 7](https://tex.z-dn.net/?f=x%20%3D%207y%5E2%2C%20x%20%3D%207)
Now, rotating the line for the line x which is equals to 7
![7y^2 = 7\\\\y^2 = 1\\\\ y = \pm1](https://tex.z-dn.net/?f=7y%5E2%20%3D%207%5C%5C%5C%5Cy%5E2%20%3D%201%5C%5C%5C%5C%20y%20%3D%20%5Cpm1)
So, the inner radio is
7 - 7 = 0
and the outer radius is
![7y^2 - 7\\\\ = 7(y^2 - 1)](https://tex.z-dn.net/?f=7y%5E2%20-%207%5C%5C%5C%5C%20%3D%207%28y%5E2%20-%201%29)
Now, the area of cross section is
![A(y) = \pi(7(y^2 - 1))^2\\\\ = 49\pi(y^4 - 2y^2 + 1)](https://tex.z-dn.net/?f=A%28y%29%20%3D%20%5Cpi%287%28y%5E2%20-%201%29%29%5E2%5C%5C%5C%5C%20%3D%2049%5Cpi%28y%5E4%20-%202y%5E2%20%2B%201%29)
The volume is
![V = \int\limits^1_{-1} A(y)dy](https://tex.z-dn.net/?f=V%20%3D%20%5Cint%5Climits%5E1_%7B-1%7D%20A%28y%29dy)
now we will put the values into the above formula
![= \int\limits^1_{-1} 49\pi(y^4 - 2y^2 + 1)dy\\\\ = 49\pi(\frac{y^5}{5} - \frac{2y^3}{3} + y)^{-1}\\\\ = 49\pi(\frac{1}{5} - \frac{2}{3} + 1 + \frac{1}{5} - \frac{2}{3} + 1)\\\\ = 49\pi(2 + \frac{2}{5} - \frac{4}{3} )\\\\ = 49\pi(\frac{30+6-20}{15} )\\\\ = \frac{49\pi}{15} (16)](https://tex.z-dn.net/?f=%3D%20%5Cint%5Climits%5E1_%7B-1%7D%2049%5Cpi%28y%5E4%20-%202y%5E2%20%2B%201%29dy%5C%5C%5C%5C%20%3D%2049%5Cpi%28%5Cfrac%7By%5E5%7D%7B5%7D%20%20-%20%5Cfrac%7B2y%5E3%7D%7B3%7D%20%2B%20y%29%5E%7B-1%7D%5C%5C%5C%5C%20%3D%2049%5Cpi%28%5Cfrac%7B1%7D%7B5%7D%20-%20%5Cfrac%7B2%7D%7B3%7D%20%20%2B%201%20%2B%20%5Cfrac%7B1%7D%7B5%7D%20-%20%5Cfrac%7B2%7D%7B3%7D%20%2B%201%29%5C%5C%5C%5C%20%3D%2049%5Cpi%282%20%2B%20%5Cfrac%7B2%7D%7B5%7D%20-%20%5Cfrac%7B4%7D%7B3%7D%20%29%5C%5C%5C%5C%20%3D%2049%5Cpi%28%5Cfrac%7B30%2B6-20%7D%7B15%7D%20%29%5C%5C%5C%5C%20%3D%20%5Cfrac%7B49%5Cpi%7D%7B15%7D%20%2816%29)
After solving the above equation we will get
![= \frac{784}{15} \pi](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B784%7D%7B15%7D%20%5Cpi)
Answer:
350 plus what will give u 800
Step-by-step explanation:
Answer:
z = x^3 +1
Step-by-step explanation:
Noting the squared term, it makes sense to substitute for that term:
z = x^3 +1
gives ...
16z^2 -22z -3 = 0 . . . . the quadratic you want
_____
<em>Solutions derived from that substitution</em>
Factoring gives ...
16z^2 -24z +2z -3 = 0
8z(2z -3) +1(2z -3) = 0
(8z +1)(2z -3) = 0
z = -1/8 or 3/2
Then we can find x:
x^3 +1 = -1/8
x^3 = -9/8 . . . . . subtract 1
x = (-1/2)∛9 . . . . . one of the real solutions
__
x^3 +1 = 3/2
x^3 = 1/2 = 4/8 . . . . . . subtract 1
x = (1/2)∛4 . . . . . . the other real solution
The complex solutions will be the two complex cube roots of -9/8 and the two complex cube roots of 1/2.
So to find the volume of a cylinder we must use the equation 2πrh+2πr^2. So when we input the numbers we get, 2π(2*4.5)+2π(2)^2. This gives us the answer 26 times pi, or <span>81.6814089933. So your answer is D.</span>
Answer:
18x-30+10x-5=28x-30
Step-by-step explanation:
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