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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.

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algol13
MN = √2
it comes from √(1^2 + 1^2) = √2 (use phytagoras)

LK = 2 x MN = 2 √2

NK = √(2^2 + 1^2) = √5

ML = NK = √5

so the perimeter
√2 + 2 √2 + √5 + √5
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Answer:

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y = ab^x

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igomit [66]

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3y + 20 = 3(22) + 20 = 66 + 20 = 86 degrees

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The angle opposite 5y - 16 also equals 94 because they are vertical angles.

The angle opposite of 3y + 20 also equals 86 because they are vertical angles

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The first step to finding the developed form is to multiply each term in the parenthesis by 2
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this means that the correct answer to your question is 6x - 20.
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