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!
<span>One kilometer is equal to 0.621371 miles. Conversely, one mile is equal to 1.609344 kilometers. One liter is equal to 0.264172 gallons, and one gallon is equal to 3.78541103373138 liters. Thus, 12.4 kilometers per liter is equal to 29.16661 miles per gallon as 1 km/l = 2.352145833 mpg.</span>
Answer:
1.80m + 3 ≤ 25
Step-by-step explanation:
We have a flat rate of $3, which means that's the base value. Now, we see that Jennifer has to pay $1.80 per mile, which means that when she has ridden m miles, she has to pay 1.80m. However, remember to add 3 to this:
1.80m + 3
Jennifer only has $25 to spend, so she can't spend any more than 25. This means that the money she can spend must be less than or equal to $25:
1.80m + 3 ≤ 25
Hope this helps!
12 = 3/4 * x
12 ÷ 3/4 = x
12 * 4/3 = x
48/3 = x
16 = x
Answer: The whole set is 16 counters
I got 1.4 for this one..............
