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
seraphim [82]
3 years ago
14

Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = 49, bounded above by the plane z = x and below by

the xy-plane.
Mathematics
1 answer:
fiasKO [112]3 years ago
4 0
\displaystyle\iiint_R\mathrm dV=\int_{y=-7}^{y=7}\int_{x=-\sqrt{49-y^2}}^{x=0}\int_{z=x}^{z=0}\mathrm dz\,\mathrm dx\,\mathrm dy

Converting to cylindrical coordinates, the integral is equivalent to

\displaystyle\iiint_R\mathrm dV=\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}\int_{z=r\cos\theta}^{z=0}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta
=\displaystyle\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}-r^2\cos\theta\,\mathrm dr\,\mathrm d\theta
=-\displaystyle\left(\int_{\theta=\pi/2}^{3\pi/2}\cos\theta\,\mathrm d\theta\right)\left(\int_{r=0}^{r=7}r^2\,\mathrm dr\right)
=\dfrac{2\times7^3}3=\dfrac{686}3
You might be interested in
What is the aquare root of 200​
Anton [14]

Answer:

=10\sqrt{2}

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors.

Like this :

5 0
3 years ago
a carpet is laid on a rectangular floor which measures 4meters by 5meters. if the carpet covers 60% of the floor find the area o
Yuri [45]

Answer:

12 m²

Step-by-step explanation:

Area of the floor:

area = length * width

area = 4 m * 5 m

area = 20 m²

area of carpet = 60% of area of the floor

area of carpet = 0.6 * 20 m²

area of carpet = 12 m²

3 0
3 years ago
I am too unmotivated to do any math even if its easy please help :)
Marta_Voda [28]

Answer:

40% increase

Step-by-step explanation:

First, find the difference:

161-115=46

Then divide by the past price to get the percent increase:

46/115=.4=40%

4 0
3 years ago
Question is down below, best answer gets Brainliest! Good luck!
Westkost [7]

Answer:

976cm^2

Step-by-step explanation:

Surface area:

Ara of cross section x 2 = 1/2 x 2 x 14 x 24 = 14 x 24 = 336

Area of base = 14 x 10 = 140

area of slope x 2 = 25 x 10 x 2 = 500

Total surface area = 500+140+336 = 640 + 336 = 973cm^2

7 0
3 years ago
Read 2 more answers
What is the area of a circle with a radius of 10.2 feet? 10.2 ​
klasskru [66]
Answer:

326.85 ft^2

Explanation:

The area of a circle is A=πr2
If we substitute the value of 10.2 feet into this formula we get 326.85 ft^2
6 0
2 years ago
Read 2 more answers
Other questions:
  • Surveys indicate that two-thirds of all voters in Ward 5 plan on choosing Spike Jones for commissioner. If there are 500 voters
    9·1 answer
  • A pink crayon is made with 12 mL of red wax for every 5 mL of white wax.
    13·1 answer
  • No clue on this need help please
    6·2 answers
  • Does anyone know this
    8·1 answer
  • A clock on sale for $215 was regularly priced at $565 find the percent of discount
    15·1 answer
  • Given a cube with a volume of 27 cm³ what is the volume of a square piramid that can fit perfectly inside the cube?
    7·1 answer
  • It has been determined that 60% of the people in a certain midwest city who are responsible for preparing the evening meal have
    10·1 answer
  • Please help, correct answers please<br> PLEASE I DO NOT UNDERSTAND
    11·2 answers
  • What is the exact value of cos(195°)?
    5·2 answers
  • Solve 4.62 + (−12.3).<br><br> 56.83<br> 5.85<br> −7.68<br> −16.92
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!