Answer:
See explanation
Step-by-step explanation:
The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula
![SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx](https://tex.z-dn.net/?f=SA%3D2%5Cpi%20%5Cint%5Climits%5Ea_b%20f%28x%29%5Csqrt%7B1%2Bf%27%5E2%28x%29%7D%20%5C%2C%20dx)
If
then
![f'(x)=2x](https://tex.z-dn.net/?f=f%27%28x%29%3D2x)
and
![b=0\\ \\a=2](https://tex.z-dn.net/?f=b%3D0%5C%5C%20%5C%5Ca%3D2)
Therefore,
![SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx](https://tex.z-dn.net/?f=SA%3D2%5Cpi%20%5Cint%5Climits%5E2_0%20x%5E2%5Csqrt%7B1%2B%282x%29%5E2%7D%20%5C%2C%20dx%3D2%5Cpi%20%5Cint%5Climits%5E2_0%20x%5E2%5Csqrt%7B1%2B4x%5E2%7D%20%5C%2C%20dx)
Apply substitution
![x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctan%20u%5C%5C%20%5C%5Cdx%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B%5Ccos%20%5E2%20u%7Ddu)
Then
![SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du](https://tex.z-dn.net/?f=SA%3D2%5Cpi%20%5Cint%5Climits%5E2_0%20x%5E2%5Csqrt%7B1%2B4x%5E2%7D%20%5C%2C%20dx%3D2%5Cpi%20%5Cint%5Climits%5E%7B%5Carctan%284%29%7D_0%20%5Cdfrac%7B1%7D%7B4%7D%5Ctan%5E2u%5Csqrt%7B1%2B%5Ctan%5E2u%7D%20%5C%2C%20%5Cdfrac%7B1%7D%7B2%7D%5Cdfrac%7B1%7D%7B%5Ccos%5E2u%7Ddu%3D%5C%5C%20%5C%5C%3D%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cint%5Climits%5E%7B%5Carctan%284%29%7D_0%20%5Ctan%5E2u%5Csec%5E3udu%3D%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cint%5Climits%5E%7B%5Carctan%284%29%7D_0%28%5Csec%5E3u%2B%5Csec%5E5u%29du)
Now
![\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B%5Carctan%284%29%7D_0%20%5Csec%5E3udu%3D2%5Csqrt%7B17%7D%2B%5Cdfrac%7B1%7D%7B2%7D%5Cln%20%284%2B%5Csqrt%7B17%7D%29%5C%5C%20%5C%5C%20%5Cint%5Climits%5E%7B%5Carctan%284%29%7D_0%20%5Csec%5E5udu%3D%5Cdfrac%7B1%7D%7B8%7D%28-%282%5Csqrt%7B17%7D%2B%5Cdfrac%7B1%7D%7B2%7D%5Cln%284%2B%5Csqrt%7B17%7D%29%29%29%2B17%5Csqrt%7B17%7D%2B%5Cdfrac%7B3%7D%7B4%7D%282%5Csqrt%7B17%7D%2B%5Cdfrac%7B1%7D%7B2%7D%5Cln%20%284%2B%5Csqrt%7B17%7D%29%29)
Hence,
![SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}](https://tex.z-dn.net/?f=SA%3D%5Cpi%20%5Cdfrac%7B-%5Cln%284%2B%5Csqrt%7B17%7D%29%2B132%5Csqrt%7B17%7D%7D%7B32%7D)
Answer:
A) 370
Explanation:
I will go about solving this using the elimination method.
First, convert the equations.
10x + y = -20
4x + y = -12
Second, find the easiest variable to get rid of and get rid of it! (In this case, y) We will subtract to get rid of y.
6x = -8
Third, you want to solve the equation.
6x = -8 (divide by 6)
x =
![-1 \frac{1}{3}](https://tex.z-dn.net/?f=-1%20%5Cfrac%7B1%7D%7B3%7D%20)
Fourth, solve for y by inserting the answer for x into one of the equations.
10(
![-1 \frac{1}{3}](https://tex.z-dn.net/?f=-1%20%5Cfrac%7B1%7D%7B3%7D%20)
) + y = -20
![-13 \frac{1}{3}](https://tex.z-dn.net/?f=-13%20%5Cfrac%7B1%7D%7B3%7D%20)
+ y = -20 (subtract
![-13 \frac{1}{3}](https://tex.z-dn.net/?f=-13%20%5Cfrac%7B1%7D%7B3%7D%20)
)
y =
![-6 \frac{2}{3}](https://tex.z-dn.net/?f=-6%20%5Cfrac%7B2%7D%7B3%7D%20)
The solution for this system of equations is (
![-1 \frac{1}{3}](https://tex.z-dn.net/?f=-1%20%5Cfrac%7B1%7D%7B3%7D%20)
,
![-6 \frac{2}{3}](https://tex.z-dn.net/?f=-6%20%5Cfrac%7B2%7D%7B3%7D%20)
).
<u><em>You want to leave a 18% tip on a meal that cost $150.</em></u>
<u><em>First, convert the 18% to an actual number that can be used in a calculation. For percents,this is always done by simply dividing the percent (in this case 18%) by 100%.So, the conversational term "18%" becomes 18% / 100% = 0.18 in terms of a real mathematical number.</em></u>
<u><em>Second, you need to find out what 18% of your $150 meal cost is.This is always done by multiplying 0.18 by $150.00, or</em></u>
<u><em></em></u>
<u><em>0.18 x $150.00=$27.00.</em></u>
<u><em>So, the amount of tip you are going to leave is $27.00.</em></u>
<u><em></em></u>
<u><em>This makes the total cost of your meal (to write on your charge slip or other payment)</em></u>
<u><em></em></u>
<u><em>$150.00 + $27.00 = $177.00. </em></u>
<u><em>-By TheRealMarinette</em></u>
<u>Please do not copy N Paste This Answer.</u>
(<u>−1</u>
2 )(n^3)+
<u>1</u>
2 n^2+4.6n+(−
<u>1</u>
2)(n^3)+
<u>1</u>
2 n^2+4.5n
=
<u>−1</u>
2 n^3+
1
2 n^2+4.6n+
−1
2 n^3+
1
2 n^2+4.5n
Combine Like Terms:
=
<u>−1</u>
2 n^3+
<u>1</u>
2 n^2+4.6n+
<u>−1</u>
2 n^3+
<u>1</u>
2 n^2+4.5n
=(<u>−1</u>
2 n^3+
<u>−1</u>
2 n^3)+(
<u>1</u>
2 n^2+
<u>1</u>
2 n^2)+(4.6n+4.5n)
=−n^3+n^2+9.1n
Answer:
=−n^3+n^2+9.1n
Everything underlined means its a fraction/divided hope this helps <em>:D</em>