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
klemol [59]
3 years ago
14

Find the volume of the given solid: Bounded by the cylinder y^2+z^2=4 and the planes x = 2y, x = 0, z = 0 in the first octant.

Mathematics
1 answer:
rodikova [14]3 years ago
3 0

The solution would be like this for this specific problem:

<span>V = ∫ dV </span><span>
<span>= ∫0→2 ∫ 0→π/2 ∫ 0→ 2·r·sin(φ) [ r ] dzdφdr </span>
<span>= ∫0→2 ∫ 0→π/2 [ r·2·r·sin(φ) - r·0 ] dφdr </span>
<span>= ∫0→2 ∫ 0→π/2 [ 2·r²·sin(φ) ] dφdr </span>
<span>= ∫0→2 [ -2·r²·cos(π/2) + 2·r²·cos(0) ] dr </span>
<span>= ∫0→2 [ 2·r² ] dr </span>
<span>= (2/3)·2³ - (2/3)·0³ </span>
<span>= 16/3 </span></span>

So the volume of the given solid is 16/3. I am hoping that these answers have satisfied your query and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.

You might be interested in
Four numbers from the set 0 to 9, including 0 and 9, are used to create a personal identification number. Once a number is used,
dolphi86 [110]

Answer:

1. 5,040

2. 504

3. 0.1

Step-by-step explanation:

just took the assignment

4 0
3 years ago
WILL NAME BRAINLIEST
ehidna [41]

Answer:

The answer for a different question is 5x

Step-by-step explanation:

DONT CHOOSE THIS. youll get wrong

7 0
3 years ago
Prove that :( 1 + 1/<img src="https://tex.z-dn.net/?f=tan%5E%7B2%7DA" id="TexFormula1" title="tan^{2}A" alt="tan^{2}A" align="ab
Aliun [14]

Answer:

See explanation

Step-by-step explanation:

Simplify left and right parts separately.

<u>Left part:</u>

\left(1+\dfrac{1}{\tan^2A}\right)\left(1+\dfrac{1}{\cot ^2A}\right)\\ \\=\left(1+\dfrac{1}{\frac{\sin^2A}{\cos^2A}}\right)\left(1+\dfrac{1}{\frac{\cos^2A}{\sin^2A}}\right)\\ \\=\left(1+\dfrac{\cos^2A}{\sin^2A}\right)\left(1+\dfrac{\sin^2A}{\cos^2A}\right)\\ \\=\dfrac{\sin^2A+\cos^2A}{\sin^2A}\cdot \dfrac{\cos^2A+\sin^A}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A}\cdot \dfrac{1}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

<u>Right part:</u>

\dfrac{1}{\sin^2A-\sin^4A}\\ \\=\dfrac{1}{\sin^2A(1-\sin^2A)}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

Since simplified left and right parts are the same, then the equality is true.

3 0
3 years ago
What is the value of k?<br>​
poizon [28]
Someone better come get her because she dancing like a s.t.i.p.p.e.r
8 0
2 years ago
What is the rate 470 feet in <br> five years written as feet per <br> year?
MaRussiya [10]

Answer:

94 feet per year

Step-by-step explanation:

470/5 = 94

6 0
2 years ago
Other questions:
  • (b) Write a quadratic function, in standard form, that fits the set of points. Solve it as a system of three equations, and then
    12·1 answer
  • Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern.
    6·2 answers
  • Each month, a phone company charges $30 for 500 minutes of talk time plus $0.45 for each additional minute. Write an expression
    6·1 answer
  • PLS HELP <br> - what is the area of the shape?
    8·1 answer
  • Suppose that a baseball is thrown upward with an initial velocity of 132 feet per second ​(90 miles per​ hour) and it is release
    5·1 answer
  • Which of the following is a problem you might notice using your sense of smell?
    11·2 answers
  • -7(2y+12)-6y=156 how am I supposed to solve this and figure out what hat “y” is?
    9·1 answer
  • I’m not sure what I’m doing here done everything they say to do but I keep getting it wrong pls explain
    14·1 answer
  • PLZ HELP ME SOMEONE!!!!? 17 POINTS!!
    7·2 answers
  • 13. Three friends equally share 12 of a pizza. How much of the pizza does each friend get?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!