Answer:
2x+
Step-by-step explanation:
hamster=x
guinea pig = x+ 1/4
x+x=2x
then just add the 1/4
Answer:
![A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\approx9.8524](https://tex.z-dn.net/?f=A%3D%5Cpi%5Cdisplaystyle%5Cbiggr%5B%5Cfrac%7B16%7D%7B3%7D-2%5Cln%28%7C3%7C%29%5Cbiggr%5D%5Capprox9.8524)
Step-by-step explanation:
Use the Washer Method ![A=\pi\displaystyle \int\limits_{a}^{b}{\bigr[R(x)^2-r(x)^2\bigr] \, dx](https://tex.z-dn.net/?f=A%3D%5Cpi%5Cdisplaystyle%20%5Cint%5Climits_%7Ba%7D%5E%7Bb%7D%7B%5Cbigr%5BR%28x%29%5E2-r%28x%29%5E2%5Cbigr%5D%20%5C%2C%20dx)
where 
is the outer radius and 
is the inner radius.
If we sketch out the graph, we see that 
intersects points 
and 
, which will be our bounds of integration.
Here, our outer radius will be 
and our inner radius will be 
.
Thus, we can compute the integral and find the volume:
![A=\pi\displaystyle\int\limits^{3}_{1} {(-2)^2-\biggr(-1-\frac{1}{x}\biggr)^2 } \, dx\\ \\A=\pi\displaystyle\int\limits^{3}_{1} {4-\biggr(1+\frac{2}{x}+\frac{1}{x^2} \biggr) } \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {4-1-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {3-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\biggr[3x-2\ln(|x|)+\frac{1}{x}\biggr]\Biggr|_{1}^{3}\\](https://tex.z-dn.net/?f=A%3D%5Cpi%5Cdisplaystyle%5Cint%5Climits%5E%7B3%7D_%7B1%7D%20%7B%28-2%29%5E2-%5Cbiggr%28-1-%5Cfrac%7B1%7D%7Bx%7D%5Cbiggr%29%5E2%20%7D%20%5C%2C%20dx%5C%5C%20%5C%5CA%3D%5Cpi%5Cdisplaystyle%5Cint%5Climits%5E%7B3%7D_%7B1%7D%20%7B4-%5Cbiggr%281%2B%5Cfrac%7B2%7D%7Bx%7D%2B%5Cfrac%7B1%7D%7Bx%5E2%7D%20%20%5Cbiggr%29%20%7D%20%5C%2C%20dx%5C%5C%5C%5CA%3D%5Cpi%5Cdisplaystyle%5Cint%5Climits%5E%7B3%7D_%7B1%7D%20%7B4-1-%5Cfrac%7B2%7D%7Bx%7D-%5Cfrac%7B1%7D%7Bx%5E2%7D%7D%20%5C%2C%20dx%5C%5C%5C%5CA%3D%5Cpi%5Cdisplaystyle%5Cint%5Climits%5E%7B3%7D_%7B1%7D%20%7B3-%5Cfrac%7B2%7D%7Bx%7D-%5Cfrac%7B1%7D%7Bx%5E2%7D%7D%20%5C%2C%20dx%5C%5C%5C%5CA%3D%5Cpi%5Cdisplaystyle%5Cbiggr%5B3x-2%5Cln%28%7Cx%7C%29%2B%5Cfrac%7B1%7D%7Bx%7D%5Cbiggr%5D%5CBiggr%7C_%7B1%7D%5E%7B3%7D%5C%5C)
![A=\pi\displaystyle\biggr[\biggr(3(3)-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3(1)-2\ln(|1|)+\frac{1}{1}\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(9-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3+1\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(\frac{28}{3}-2\ln(|3|)\biggr)-\biggr(4\biggr)\biggr]\\A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\\A\approx9.8524](https://tex.z-dn.net/?f=A%3D%5Cpi%5Cdisplaystyle%5Cbiggr%5B%5Cbiggr%283%283%29-2%5Cln%28%7C3%7C%29%2B%5Cfrac%7B1%7D%7B3%7D%5Cbiggr%29-%5Cbiggr%283%281%29-2%5Cln%28%7C1%7C%29%2B%5Cfrac%7B1%7D%7B1%7D%5Cbiggr%29%5Cbiggr%5D%5C%5C%5C%5CA%3D%5Cpi%5Cdisplaystyle%5Cbiggr%5B%5Cbiggr%289-2%5Cln%28%7C3%7C%29%2B%5Cfrac%7B1%7D%7B3%7D%5Cbiggr%29-%5Cbiggr%283%2B1%5Cbiggr%29%5Cbiggr%5D%5C%5C%5C%5CA%3D%5Cpi%5Cdisplaystyle%5Cbiggr%5B%5Cbiggr%28%5Cfrac%7B28%7D%7B3%7D-2%5Cln%28%7C3%7C%29%5Cbiggr%29-%5Cbiggr%284%5Cbiggr%29%5Cbiggr%5D%5C%5CA%3D%5Cpi%5Cdisplaystyle%5Cbiggr%5B%5Cfrac%7B16%7D%7B3%7D-2%5Cln%28%7C3%7C%29%5Cbiggr%5D%5C%5CA%5Capprox9.8524)
In conclusion, the volume of the solid of revolution will be about 9.8524 cubic units. See the attached graph for a helpful visual!
The set of possible integers is 1, 2, 3, 4, and 5.
The area of a circle with radius of n centimeters = π(n)^2.
So, the set of possible values are:
n area = π(n^2)
1 π
2 4π
3 9π
4 16π
5 25π
And the expected value of the area may be determined as the mean (average) of the five possible areas:
expected value of the area = [ π+ 4π + 9π + 16π + 25π] / 5 = 11π ≈ 34.5575, which rounded to the nearest hundreth is 34.56
Answer: 34.56
I think its y=2x+4 if not im sorry
Answer: i
Step-by-step explanation:
45 into a percent
