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arlik [135]
3 years ago
13

Please help. NO LINKS. ​

Mathematics
1 answer:
trasher [3.6K]3 years ago
5 0

Answer:

the answer is A

y= 1.9x + 69

y=6x

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The area enclosed by the graphs of y = 1/x, y = 1, and x = 3 is rotated about the line y = -1. Find the volume and show steps.
Natalija [7]

Answer:

A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\approx9.8524

Step-by-step explanation:

Use the Washer Method A=\pi\displaystyle \int\limits_{a}^{b}{\bigr[R(x)^2-r(x)^2\bigr] \, dx where R(x) is the outer radius and r(x) is the inner radius.

If we sketch out the graph, we see that y=1 intersects points (1,1) and (3,1), which will be our bounds of integration.

Here, our outer radius will be R(x)=(-1-1)=-2 and our inner radius will be r(x)=-1-\frac{1}{x}.

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}\\

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

In conclusion, the volume of the solid of revolution will be about 9.8524 cubic units. See the attached graph for a helpful visual!

3 0
2 years ago
15/4÷3/4 I need the ans
Vladimir [108]
Use the stay, change, flip method. 
keep the first fraction the same, change the division to multiplication and flip the last fraction. you may then have the opportunity to cross simplify.
7 0
3 years ago
Read 2 more answers
Freddy poured 1.4 liters of soda pop from a full 2-liter container. How much soda pop was left in the container?
german

Answer:

0.6 liters left

Step-by-step explanation:

So we know that the container is filled with 2 liters.

We also know that he poured 1.4 liters out of the container.

This leads to the conclusion

2 - 1.4 = 0.6

6 0
3 years ago
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Help!!! Whats The answer, Please explain your answer Marking brainlliest:D......
Elina [12.6K]
The answer would be 96 square feet length

6 x (4)^2 = 96
4 0
2 years ago
What type of angles are ∠4 and∠6? Question 2 options: adjacent angles alternate exterior angles alternate interior angles corres
lianna [129]

Angles 4 and 6 are called Alternate Exterior Angles

Step-by-step explanation:

Alternate Exterior Angles are a pair of angles on the outer side of the each of two lines but on opposite sides of the transversal.

When we take two parallel lines they will create 8 angles, such as 1,2,3,4,5,6,7 & 8.

In that angle 6 is 65 degrees.

Angles 1,2,3 & $ are in one line and remaining four angles on other line.

So Angles 4 and 6 are alternate exterior angles.

5 0
3 years ago
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