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
8- (0.75+2). Plzzz explain it
frosja888 [35]

Answer:

5.25

Step-by-step explanation:

ok so first you add 0.75+2 which is equal to 2.75

and now you will have 8-2.75 which is equal to 5.25

3 0
3 years ago
The surface area of a cylinder?
ioda

Answer:

18. 84 ft² or 18.85 ft² when rounded to the nearest tenth

Step-by-step explanation:

2πrh+2πr²

2× 3.14 × 1 × 2= 12.56

2 × 3.14 × 1² = 6.28

12.56 + 6.28 = 18.84

Have a great day :)

7 0
2 years ago
Read 2 more answers
Help me pls thxxxxxxxxxx
n200080 [17]

Answer:

brooklyn

Step-by-step explanation:if ur brooklyn do it ur self plese and ty -niki minaj

4 0
3 years ago
Please help in math!!
LenaWriter [7]

Answer: C

Step-by-step explanation:

Less than or more than without "or equal" means that the dot is not shaded, otherwise it is.

So the answer is C

6 0
2 years ago
Read 2 more answers
What is a/9 =-4 I really need help on this one
pashok25 [27]
The answer I believe is -36
5 0
3 years ago
Read 2 more answers
Other questions:
  • How do i solve 9j-8=8+9j
    6·1 answer
  • Use the linear combination method to solve this system of equations. What is the value of x?
    12·2 answers
  • Which transformation has been applied?
    8·2 answers
  • Isaac and Shonda can rent a canoe for $12 per hour and a mountain bike for $9 per hour. Together, they have $138 to spend. Let c
    9·2 answers
  • Answer correctly and I will mark you brainless ❤️
    6·1 answer
  • Find the circumcenter of ΔABC with vertices A(12, 0), B(0, -6), C(0, 0)
    5·1 answer
  • Test Your Understar<br>2<br>?<br>273 =​
    11·1 answer
  • The length of a rectangle is 5 yd more than twice the width x. The area is 900 yd?.
    15·1 answer
  • If there are 2 blue, 5 yellow, and 3
    6·1 answer
  • What formula is used for calculating volumes of liquids?.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!