Idk yet I did something like that yesterday
When integrating using shells, the first step is to plot the graph. I personally plotted it with the x and y axis switched, because it aids me in picturing the graph. The integral ranges from 9 to 11, since those are the limits from the two lines y = 9 and y = 11. The reason that these are the limits is because it is rotating around the x, not the y.
![\int\limits^{11}_{9}](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E%7B11%7D_%7B9%7D)
Now that you have the limits of the integral, you have to find what goes inside it.
Because you are integrating using shells, you need to remember to include the
![2\pi y](https://tex.z-dn.net/?f=2%5Cpi%20y)
Again, there is a y here instead of an x, because you are rotating around the x axis. Then you just need to input the function f(y). If you look at the graph that you (hopefully) plotted, you can see that this function ranges between the y axis and the curve
![f(y) = \frac{9}{y}](https://tex.z-dn.net/?f=f%28y%29%20%3D%20%5Cfrac%7B9%7D%7By%7D)
. Put together the pieces, and you have the integral
![\int\limits^{11}_{9} {2 \pi y*f(y)} \, dy](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E%7B11%7D_%7B9%7D%20%7B2%20%5Cpi%20y%2Af%28y%29%7D%20%5C%2C%20dy%20)
After substituting in
![f(y) = \frac{9}{y}](https://tex.z-dn.net/?f=f%28y%29%20%3D%20%5Cfrac%7B9%7D%7By%7D)
, you get
![\int\limits^{11}_{9} {2 \pi y*\frac{9}{y}} \, dy](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E%7B11%7D_%7B9%7D%20%7B2%20%5Cpi%20y%2A%5Cfrac%7B9%7D%7By%7D%7D%20%5C%2C%20dy%20)
Simplified, this is
![18\pi\int\limits^{11}_{9} \, dy](https://tex.z-dn.net/?f=%2018%5Cpi%5Cint%5Climits%5E%7B11%7D_%7B9%7D%20%5C%2C%20dy%20)
Integrating, we get
![18\pi * 2](https://tex.z-dn.net/?f=%2018%5Cpi%20%2A%202)
Therefore, the solution is
![36 \pi](https://tex.z-dn.net/?f=%2036%20%5Cpi%20)
Note: I didn't spend very much time reviewing these integrals, so I may be incorrect.
Answer:
20
Step-by-step explanation:
10+10=20
Answer:
c. it show it to be portioned
Answer:
Answer: k must be 5/2 or 1
Step-by-step explanation:
![{ \tt{ - {2k}^{2} + 7k - 5 = 0}}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7B%20-%20%20%7B2k%7D%5E%7B2%7D%20%20%2B%207k%20-%205%20%3D%200%7D%7D%20)
» Factorise the equation:
![{ \tt{ {2k}^{2} - 7k + 5 = 0 }} \\ { \tt{(2k - 5)(k - 1) = 0}} \\ \\ { \tt{k = \frac{5}{2} \: and \: 1 }}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7B%20%7B2k%7D%5E%7B2%7D%20-%207k%20%2B%205%20%3D%200%20%7D%7D%20%5C%5C%20%20%20%7B%20%5Ctt%7B%282k%20-%205%29%28k%20-%201%29%20%3D%200%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Ctt%7Bk%20%20%3D%20%20%5Cfrac%7B5%7D%7B2%7D%20%20%5C%3A%20and%20%5C%3A%201%20%7D%7D)