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
spin [16.1K]
3 years ago
6

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any meth

od. y = −x^2 + 12x − 35,    y = 0;    about the x-axis
Mathematics
1 answer:
iogann1982 [59]3 years ago
6 0
<span>up vote2down voteacceptedI think your limits of integration are incorrect. If you substitute <span><span>y=4</span><span>y=4</span></span> into <span><span><span>y2</span>−<span>x2</span>=9</span><span><span>y2</span>−<span>x2</span>=9</span></span>, you find that <span><span>x=±<span>7–√</span></span><span>x=±7</span></span>. Therefore, the two curves intersect at <span><span>x=±<span>7–√</span></span><span>x=±7</span></span>. By washer method, we have:<span><span>V<span><span>=π<span>∫<span>7√</span><span>−<span>7√</span></span></span>(4<span>)2</span>−(<span><span><span>x2</span>+9</span><span>−−−−−</span>√</span><span>)2</span>dx</span><span>=2π<span>∫<span>7√</span>0</span>16−(<span>x2</span>+9)dx</span><span>=2π<span>∫<span>7√</span>0</span>7−<span>x2</span>dx</span><span>=2π<span><span>[<span>7x−<span>13</span><span>x3</span></span>]</span><span>7√</span>0</span></span><span>=2π<span>(<span><span>14<span>7–√</span></span>3</span>)</span></span><span>=<span><span>28π<span>7–√</span></span>3</span></span></span></span><span><span>V<span>=π<span>∫<span>−7</span>7</span>(4<span>)2</span>−(<span><span>x2</span>+9</span><span>)2</span>dx</span></span><span>=2π<span>∫07</span>16−(<span>x2</span>+9)dx</span><span>=2π<span>∫07</span>7−<span>x2</span>dx</span><span>=2π<span><span>[<span>7x−<span>13</span><span>x3</span></span>]</span>07</span></span><span>=2π<span>(<span><span>147</span>3</span>)</span></span><span>=<span><span>28π7</span>3</span></span></span></span>And just for fun, let's try the shell method. Here, we have no choice but to find the volume obtained by revolving just the part of the region in the first quadrant, and doubling it.<span><span>VVVVVV</span><span><span>=2×2π<span>∫43</span>y<span><span><span>y2</span>−9</span><span>−−−−−</span>√</span>dy</span><span>=4π<span>∫43</span>y<span><span><span>y2</span>−9</span><span>−−−−−</span>√</span>dy</span><span>=4π<span><span>[<span><span>13</span>(<span>y2</span>−9<span>)<span>32</span></span></span>]</span>43</span></span><span>=4π<span><span>[<span><span>13</span>(<span>y2</span>−9<span>)<span>32</span></span></span>]</span>43</span></span><span>=4π<span>[<span><span>7<span>7–√</span></span>3</span>]</span></span><span>=<span><span>28π<span>7–√</span></span>3</span></span></span></span></span>
You might be interested in
The total arm and blade of a windshield wiper is 12 in. long and rotates back and forth through an angle of 85°. The shaded regi
valkas [14]

Answer:

e

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Is this true or false need answer asap
VLD [36.1K]
Answer: True

Step-by-Step Explanation:

=> 2x + 3y = -7 (Eq. 1)
=> -x = 2y (Eq. 2)
=> x = 1, y = -3

Substitute values of ‘x’ and ‘y’ in Eq. 1 :-

=> 2x + 3y = -7
= 2(1) + 3(-3) = -7
= 2 + -9 = -7
=> -7 = -7
=> LHS = RHS

Therefore, it is a Solution.
3 0
2 years ago
Sets M and F are defined as follows.
a_sh-v [17]

Answer:

intersection is /c,d/

Step-by-step explanation:

circle the common members and list them

6 0
3 years ago
What time what give me 21
Lady bird [3.3K]
21:00 would be 9:00 :)
8 0
3 years ago
You are taking a​ multiple-choice test that has 44 questions. each of the questions has 55 answer​ choices, with one correct ans
Aleks [24]
Since there are 55 choices, we have to have 55 options, and for 44 questions, we multiply how many options there are in 1 question by 44 to get 55*44=2420
6 0
3 years ago
Other questions:
  • Find the relation number between 3 and 4​
    9·1 answer
  • Gregg subtracted some number x from 47, then multiplied the result by two, subtracted 15 and got 45. What was Gregg's number?
    10·1 answer
  • For two variables that are inversely related, what is the result of doubling one variable
    15·2 answers
  • the greatest internet function shown below is defined so that it produces the greatest interger____ or equal to x
    10·2 answers
  • What is the value of 5 in 3,152,308
    9·2 answers
  • The value of tan60° is ______ . * 1 point 1/√3 0 1 √3
    14·2 answers
  • PLZ help thanks!!!! A shipment of 10 tons of sugar is separated into containers of equal size. If the shipment fills 3 3/4 conta
    15·2 answers
  • Please help thank you
    12·2 answers
  • A store sells grape jelly in 16-ounces jars for $ 4.68. How much is the jelly per ounce?
    10·2 answers
  • Pip, David and Bridget share £60 in a ratio 1:2:2. How much money does each person get?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!