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klio [65]
2 years ago
6

Let W be part of the solid sphere of radius 4, centered at the origin, that lies above the plane z = 2. Set up an integral in cy

lindrical coordinates to find the volume of the region. Do NOT actually integrate.
Mathematics
1 answer:
andriy [413]2 years ago
4 0

Answer:

V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π

Step-by-step explanation:

Since we have the radius of the sphere R = 4, we have R² = r² + z² where r = radius of cylinder in z-plane and z = height² of cylinder.

So, r = √(R² - z²)

r = √(4² - z²)

r = √(16 - z²)

Since the region is above the plane z = 2, we integrate z from z = 2 to z = R = 4

Our volume integral in cylindrical coordinates is thus

V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π

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1 point CA If a rectangular prism has the width of 5. t What would the scale factor be? Round to Type your answer... 3 4 4 1 Giv
Sunny_sXe [5.5K]

We know that the original width was 5, and that after the enlargement the width is 45. To calculate the scale factor we divide the final width between the original one, then:

\frac{45}{5}=9

Therefore the scale factor is 9.

7 0
11 months ago
Alex saved x dollars.
steposvetlana [31]
Answer:
Ethan = 1.(3x)

Step-by-step explanation:
Let's split "Ethan saved 1/3 more than that"
That = x
So, Ethan saved 1/3 more than x
Meaning that Ethan = x + 1/3x
Combine like terms
Ethan = 1 1/3x
which equals to
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Hope this helps :)
Have a great day


4 0
2 years ago
What is the range of the function y=2x+1 for the domain 2<=x<=5?
egoroff_w [7]
So domain is the number you can use
range is the output your get from inputting the domain given
so from 2≤x≤5
since it is linear, we can be sure that we only need to test the endpoints of the domain to find the endpoints of the range

sub 2 for x
y=2(2)+1
y=4+1
y=5

sub 5 for x
y=2(5)+1
y=10+1
y=11

so range is from 5 to 11
in interval notation: [5,11]
in other notation 5≤y≤11
or
R={y|5≤y≤11}
5 0
3 years ago
1. 14=7b<br> 2. -11=k/4<br> 3.6z=-6
Romashka-Z-Leto [24]

Answer:

the anwer is 14-2294-dhi2

Step-by-step explanation:

Because 14 is - 4 you multiple to 5 equal= dhi2

3 0
2 years ago
What is the difference between cross-section and intersection in geometry?
Triss [41]
A cross-section is the shape that would be exposed when cutting straight through a 3-D object. for example, cutting horizontally through a regular cone would expose a circle.

an intersection is where 2 or more shapes (does not matter how many dimensions) overlap. for example, the point at which two lines overlap is the intersection. or the area that two overlapping circles share is the intersection.
5 0
3 years ago
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