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
aleksklad [387]
2 years ago
5

Find the volume of the solid in the first octant bounded by the coordinate planes, the cylinder X^2+Y^2=4 and the plane X+Z=4.

Mathematics
1 answer:
stira [4]2 years ago
5 0

Answer:

4\pi- \frac{8}{3}

Step-by-step explanation:

The solid that you described is shown in the image of below. To compute the volume we use triple integrals. Observe that

0\leq x\leq 2

0\leq y \leq \sqrt{4-x^2}

0\leq z \leq 4-x

So, the volumen of the solid is given by

\int_{0}^{2}\int_{0}^{\sqrt{4-x^2}}\int_{0}^{4-x}1\, dzdydx=\int_{0}^{2}\int_{0}^{\sqrt{4-x^2}}4-x\, dydx=\int_{0}^{2}(4-x)\sqrt{4-x^2}\,dx

This last integral equals 4\pi -\frac{8}{3}

You might be interested in
Kerri has a germen shepherd that has a mass of 30,000 grams. how many kilograms is 30,000 grams
wolverine [178]
Answer: 30 kilograms

explanation: Each 1000 grams converts to 1 kilogram
8 0
2 years ago
A runner runs a distance of 450 metres in a time of 50 seconds. What is his average speed?
vekshin1

Answer:

0.279 miles / 0.449 km

Step-by-step explanation:

convert the meters into miles/kilometers to get your answer

4 0
2 years ago
2. The price of a gallon of gas was $2.95 on Monday. On Wednesday, the price of a gallon of gas rose to $3.15. How much did the
wolverine [178]

Answer:

0.2

Step-by-step explanation:

2.95-3.15

6 0
2 years ago
Please help me in this anwer for my test thx.
julsineya [31]

Answer:

-4.5

Step-by-step explanation:

Maths

7 0
3 years ago
I think it’s A am I right
Mandarinka [93]

Pi(r)(r)(2) + pi(diameter)(height)

3.14(4)(4)(2)+ 3.14(8)(1.5)

138.16

4 0
2 years ago
Read 2 more answers
Other questions:
  • Pls help ASAP I need it for tomarrow
    5·1 answer
  • 5d-2/3c if d =4 and c =3 evaluate fast fast
    15·1 answer
  • What is the value of x? Please help. Will mark brainliest ASAP
    7·2 answers
  • Kevin is a quarterback on the football team.he completed 36 passes during the season.his second-string replacement,Mark complete
    14·1 answer
  • HELP PLZZZZZ OMGGGGGGG
    11·1 answer
  • Prove that the circumcenter of a triangle is equidistant from its vertices.
    13·1 answer
  • Please help me! (please no links!)​
    11·2 answers
  • A conclusion drawn based on evidence from the story is:
    6·2 answers
  • Help me with elar pls
    6·1 answer
  • Help ur friend out would ya mate?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!