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
Maslowich
3 years ago
15

Find the volumes of the solids generated by revolving the triangle with vertices (2, 2)​, (2, 6)​, and (5, 6) about ​a) the​ x-a

xis, ​b) the​ y-axis, ​c) the line x=7​, and ​d) the line y=2.
Mathematics
1 answer:
Vesna [10]3 years ago
7 0
  • About the x-axis (washer method):

\displaystyle\pi\int_2^5\left(6^2-\left(\frac43x-\frac23\right)^2\right)\,\mathrm dx=\frac{16\pi}9\int_2^5(20+x-x^2)\,\mathrm dx=\boxed{56\pi}

  • About the y-axis (shell method):

\displaystyle2\pi\int_2^5x\left(6-\left(\frac43x-\frac23\right)\right)\,\mathrm dx=\frac{8\pi}3\int_2^5x(5-x)\,\mathrm dx=\boxed{36\pi}

  • About x=7 (shell method):

\displaystyle2\pi\int_2^5(7-x)\left(6-\left(\frac43x-\frac23\right)\right)\,\mathrm dx=\frac{8\pi}3\int_2^5(35-12x+x^2)\,\mathrm dx=\boxed{48\pi}

  • About y=2 (washer method):

\displaystyle\pi\int_2^5\left((6-2)^2-\left(\frac43x-\frac23-2\right)^2\right)\,\mathrm dx=\frac{16\pi}9\int_2^5(5+4x-x^2)\,\mathrm dx=\boxed{32\pi}

You might be interested in
What is the 451+451/4​
emmainna [20.7K]

Answer: 563.75

Step-by-step explanation:451+112.75=563.75

6 0
2 years ago
Read 2 more answers
Solve for p: 9(p-4)=-189(p−4)=−18
Alex787 [66]

Answer:

P= 3.27

Step-by-step explanation:

Hope this helps sorry for the crumbled paper

5 0
2 years ago
Read 2 more answers
I’m stuck on this one someone please help?
mylen [45]

Answer:

dude please hurry up and resend the picture I can hardly see it right now

Step-by-step explanation:

3 0
3 years ago
Area of circle with diameter 14cm is​
Alisiya [41]

Answer:

A≈153.94cm²

Step-by-step explanation:

A=πr2

d=2r

Solving forA

A=1

4πd2=1

4·π·142≈153.93804cm²

4 0
2 years ago
This table represents Yasmin's check register. Her checking account had a balance of $556.21 on March 21.
tankabanditka [31]

Answer:

634.11

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • A net for which three-dimensional figure would always have 6 congruent rectangular regions
    14·1 answer
  • If three sides of a right triangle are 10, 45, and 42, which side is the hypotenuse?
    10·1 answer
  • The length of a rectangle is 4 in greater than the width the perimeter of the rectangle is 24 in
    14·2 answers
  • Plzzzzz helpppp <br> If u can help me plz do
    12·2 answers
  • How many Miles will your parents drive in eight hours if you they are traveling 65 mph
    15·1 answer
  • What does x+7/8=4 equal?
    11·2 answers
  • Do the graphs of the two equations parallel lines Y=4x - x and 2y = 4x + 5
    10·1 answer
  • 5x-4=3x-6<br> Solve equation.<br> PLEASE HELP ASAP
    9·1 answer
  • Which of the following expressions are equivalent to - -8/-4
    15·1 answer
  • Can someone help me.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!