1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Archy [21]
3 years ago
12

How do you do this question?

Mathematics
1 answer:
Ksivusya [100]3 years ago
5 0

Answer:

V = (About) 22.2, Graph = First graph/Graph in the attachment

Step-by-step explanation:

Remember that in all these cases, we have a specified method to use, the washer method, disk method, and the cylindrical shell method. Keep in mind that the washer and disk method are one in the same, but I feel that the disk method is better as it avoids splitting the integral into two, and rewriting the curves. Here we will go with the disk method.

\mathrm{V\:=\:\pi \int _a^b\left(r\right)^2dy\:},\\\mathrm{V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy}

The plus 1 in '1 + 2/x' is shifting this graph up from where it is rotating, but the negative 1 is subtracting the area between the y-axis and the shaded region, so that when it's flipped around, it becomes a washer.

V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=\pi \cdot \int _1^3\left(1+\frac{2}{y}\right)^2-1dy\\\\\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\= \pi \left(\int _1^3\left(1+\frac{2}{y}\right)^2dy-\int _1^31dy\right)\\\\

\int _1^3\left(1+\frac{2}{y}\right)^2dy=4\ln \left(3\right)+\frac{14}{3}, \int _1^31dy=2\\\\=> \pi \left(4\ln \left(3\right)+\frac{14}{3}-2\right)\\=> \pi \left(4\ln \left(3\right)+\frac{8}{3}\right)

Our exact solution will be V = π(4In(3) + 8/3). In decimal form it will be about 22.2 however. Try both solution if you like, but it would be better to use 22.2. Your graph will just be a plot under the curve y = 2/x, the first graph.

You might be interested in
Use the hundredths grid to answer the question.
nydimaria [60]

9514 1404 393

Answer:

  C.  0.36 +0.27 = 0.63

Step-by-step explanation:

3 columns and 6 squares of a hundredths grid is a representation of ...

  0.30 +0.06 = 0.36

2 columns and 7 square is a representation of ...

  0.20 +0.07 = 0.27

The total shaded area is the sum of these:

  0.36 +0.27 = 0.63

5 0
2 years ago
Need help with a math question
krek1111 [17]

Answer:

x=13°

Step-by-step explanation:

If BE is an angle bisector, then it divides the angle into two equal angles. This means that

∠ABE=∠EBC

Since ∠ABE=2x+20 and ∠EBC=4x-6, we have

2x+20=4x-6

2x-4x=-6-20

-2x=-26

2x=26

x=13°

4 0
3 years ago
Help could it be any two integers?
Novosadov [1.4K]

Yes, as long as it's between the two numbers

51) -4 and 1

52) -1 and -3

53) -9 and -10

5 0
3 years ago
A ladder is leaning against the side of a building. The building and the ground form a right angle. How high on the
satela [25.4K]

Answer:

15m

Step-by-step explanation:

(see attached)

8 0
3 years ago
Read 2 more answers
(5w7)2
iVinArrow [24]
I think the answer is D
3 0
3 years ago
Read 2 more answers
Other questions:
  • The diameter of a circle is 22 millimeters. What is it's radius
    11·2 answers
  • Help on all pls i need it quick
    14·1 answer
  • Tell whether the value is a solution of the inequality<br><br> r+4 &gt;8;r=2
    5·1 answer
  • 38÷ 177851.4<br><br><br><br><br>HELP ME PLEASE
    9·2 answers
  • What is the slope of the line passing through the points (1, 2) and (5, 4)? A .−2 B.12 C.1 D.2
    6·1 answer
  • 9
    6·1 answer
  • Y=5+6x Y=6x+5 how many solutions
    7·1 answer
  • 850 projects were entered in the science fair. If 86% of the projects did not receive a ribbon, then how many student projects d
    10·1 answer
  • Which equation represents the line that passes through the points (2,1) and (4,-5)
    11·1 answer
  • A regular hexagon is rotated 360° about its center. How many times does the image of the hexagon coincide with the pre image dur
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!