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
Lera25 [3.4K]
3 years ago
14

Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of f(x)=x^2+2 for 0≤x≤5 about x

=5.
Mathematics
1 answer:
Irina18 [472]3 years ago
4 0

For each <em>x</em> in the interval 0 ≤ <em>x</em> ≤ 5, the shell at that point has

• radius = 5 - <em>x</em>, which is the distance from <em>x</em> to <em>x</em> = 5

• height = <em>x</em> ² + 2

• thickness = d<em>x</em>

and hence contributes a volume of 2<em>π</em> (5 - <em>x</em>) (<em>x</em> ² + 2) d<em>x</em>.

Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:

\displaystyle 2\pi \int_0^5 (5-x)(x^2+2)\,\mathrm dx=2\pi\int_0^5 (10-2x+5x^2-x^3)\,\mathrm dx=\boxed{\frac{925\pi}6}

You might be interested in
The median income for a sample of people from Chicago is about $60,000 and the
Serhud [2]

Answer:

106,000 is the answer help me with my answer to

5 0
3 years ago
Read 2 more answers
peggy is five years older than peter and susan is two years younger than peter the sum of their ages is 15 years how old is each
spin [16.1K]
Peggy is 9, Peter is 4, and Susan is 2
9+4+2=15
5 0
3 years ago
Solve 3x − 2 = 37. please help me
lyudmila [28]

Answer:

x=13

Step-by-step explanation:

1. Isolate the variable

3x - 2 = 37

     +2 = +2

2. Divide the equation by the coefficient

3x = 39

/3    /3

3. Answer

x = 13

8 0
3 years ago
Read 2 more answers
Free points: this is because of all the kindness I have seen on brainly:
VashaNatasha [74]
The answer is 35450 :)
8 0
3 years ago
Read 2 more answers
Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial function. In y
bekas [8.4K]
F(x) = 2^x; h(x) = x^3 + x + 8

Table


x      f(x) =  2^x             h(x) = x^3 + x + 8

0      2^0 = 1                0  + 0 + 8 = 8

1     2^1 = 2                 1^3 + 1 + 8 = 10

2      2^2 = 4                2^3 + 2 + 8 = 8 + 2 + 8 = 18

3      2^3 = 8                3^3  + 3 + 8 = 27 + 3 + 8 = 38

4      2^2 = 16              4^3 + 4 + 8 = 76

10    2^10 = 1024       10^3  +10 + 8 = 1018

 9      2^9 =   512        9^3 + 9 + 8 = 729 + 9 + 8 = 746

Answer: an approximate value of 10
7 0
3 years ago
Other questions:
  • Evaluate 8x - 3 + y If x = 2 and y = 1
    10·2 answers
  • Complete the statement. Round to the nearest hundredth if necessary. 3 L ≈ qt
    9·2 answers
  • Express (13/15 - 7/10) as a percentage​
    6·1 answer
  • -5/6x = 20 2/3(x - 7) = -2 solve them and show your work! ASAP! I need this done fast!!
    11·1 answer
  • Will give brainliest! and EXTRA points.
    11·1 answer
  • Convert to slope intercept form: <br> 6x-3y=96x−3y=9<br><br> with steps please!!
    7·1 answer
  • The watch at Macys is $400. The store is having a sale and everything is 30% off. What is the discount amount?
    15·1 answer
  • Does anyone know how to solve this math problem?
    10·1 answer
  • Solve for x.<br> 1) 6<br> 2)3<br> 3) 63<br> 4) 32
    6·1 answer
  • Halp u-u
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!