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
vova2212 [387]
3 years ago
15

Use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves and lines about th

e​ y-axis. =-x^2 , y=6 - 5 x​, x=​0, for x>=0
Mathematics
1 answer:
Nezavi [6.7K]3 years ago
5 0

The two curves intersect when

-x^2=6-5x\implies x^2-5x+6=(x-3)(x-2)=0\implies x=2,x=3

The region bounded by x=0 and the two curves "ends" with a vertex where x=2. So over the interval [0, 2], we have 6-5x\ge-x^2, so that the volume is

\displaystyle2\pi\int_0^2x(6-5x+x^2)\,\mathrm dx=\boxed{\frac{16\pi}3}

That is, each cylindrical shell has a radius of x and height (6-5x)-(-x^2)=6-5x+x^2, and their contribution to the total volume is 2\pi times the radius and height.

You might be interested in
What rations form a proportion ?
igomit [66]
⅔ and 8/12 form a proportion.
7 0
3 years ago
Help me out, please!!!! Need an answer asap!!!
Kazeer [188]

Answer:

D

Step-by-step explanation:


8 0
3 years ago
Read 2 more answers
Three apple pies, all the following shape, are left on a counter. How much total pie has been left?
faltersainse [42]
1 pie is the total pieeeeeeeeeee
6 0
2 years ago
Barb exercise for 14 hours in 1 week how many hour does she exercise in 32 weeks
Blizzard [7]
14 times 1 = 14

14 times 32 = 448

Barb exercised for 448 hours in 32 weeks.
8 0
3 years ago
The following set of coordinates represents what figure?<br><br> (5,5), (7,3), (3,0), (1,2)
posledela
Rectangle. if you simply graph the points, you are able to see the shape they form
6 0
3 years ago
Other questions:
  • What is the $25 fee Maria’s mother paid when Maria visited the doctor
    10·2 answers
  • Help! Marking as brainlyest
    13·1 answer
  • The area of a square gate is 361 feet squared what is the length of any side of the gate
    12·1 answer
  • Two cars start from towns 800800 mi apart and travel toward each other. They meet after 88 hr. Find the speed of each car if one
    5·1 answer
  • How do you find the area of a sphere with a radius of 5 feet
    11·2 answers
  • Solve: -4x = -20 A) -16 B) -5 C) 5 D) 6 Eliminate
    15·2 answers
  • After triangle ACE is dilated by a factor of 6, it has an area of 180 square inches. What was its area before dilation?
    6·1 answer
  • A total of 356 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student t
    15·1 answer
  • Marly drove 15 miles to work and then x miles to the store. How many miles did she travel in total?
    5·2 answers
  • A company had an 8% increase in profits in July. If the July profits were
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!