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mestny [16]
3 years ago
12

A solid lies between planes perpendicular to the​ x-axis at x = -2 and x = 2. The​ cross-sections perpendicular to the​ x-axis b

etween these planes are squares whose bases run from the semicircle y = -√(4 - x²) to the semicircle y = √(4 - x²).
Find the volume of the solid.

Mathematics
1 answer:
icang [17]3 years ago
8 0

Answer:

V = 128π/3 vu

Step-by-step explanation:

we have that: f(x)₁ = √(4 - x²);  f(x)₂ = -√(4 - x²)

knowing that the volume of a solid is  V=πR²h, where R² (f(x)₁-f(x)₂) and h=dx, then

dV=π(√(4 - x²)+√(4 - x²))²dx;  =π(2√(4 - x²))²dx ⇒

dV= 4π(4-x²)dx , Integrating in both sides

∫dv=4π∫(4-x²)dx , we take ∫(4-x²)dx and we solve

4∫dx-∫x²dx = 4x-(x³/3) evaluated -2≤x≤2 or too 2 (0≤x≤2) , also

∫dv=8π∫(4-x²)dx evaluated 0≤x≤2

V=8π(4x-(x³/3)) = 8π(4.2-(2³/3)) = 8π(8-(8/3)) =(8π/3)(24-8) ⇒

V = 128π/3 vu

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Answer:

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What is m∠KNL?<br> Enter answer in box
kodGreya [7K]

I want to talk about X's. I'll start by talking about this X - a cross (photo 1). Specifically, a cross made of two perpendicular lines - lines that meet each other at right angles all around. What's special about a cross? There's the religious significance, but in our case, there's also the <em>symmetry</em>. The quick, intuitive definition of symmetry is some quality that a thing has where, if you do something to it, it'll still look the same. Your body is symmetric; the left side of our bodies looks like we took the right side and flipped it - they're mirror images of each other.

One of the symmetries of this cross is right here. (Picture 2) It splits the cross into <em>two identical halves</em>, one a mirror image of the other. Most importantly, <em>the angles on each side of the line are identical</em>. We can draw this same mirror into our problem, too (picture 3). This symmetry tells us that those two unknown angles are exactly the same - <em>equal</em>. So, if angle MNJ is 5x+2 and angle LNK is 3(x+14), we now know that

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7 0
2 years ago
Initially, there were only 197 weeds at a park. The weeds grew at a rate of 25% each week. The following function represents the
olganol [36]

Answer:

 none of the above

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Step-by-step explanation:

If we let x represent days, then x/7 represents weeks and we can rewrite f(x) as ...

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The daily multiplier of 1.03 represents a daily growth rate of

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_____

These answers are not found among the offered choices:

f(x) = 197·1.03^x

3% daily growth

Step-by-step explanation:

8 0
2 years ago
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IgorLugansk [536]

Answer:

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1800 / 166 2/3 = 10.8 hours.

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