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JulijaS [17]
4 years ago
11

Find the volume of the wedge cut from the first octant by the cylinder z=12-3y^2 and the plane x+y=2.

Mathematics
1 answer:
LuckyWell [14K]4 years ago
8 0

Answer:

The wedge cut from the first octant ⟹ z ≥ 0 and y ≥ 0 ⟹ 12−3y^2 ≥ 0 ⟹ 0 ≤ y ≤ 2  

0 ≤ y ≤ 2 and x = 2-y ⟹ 0 ≤ x ≤ 2  

V = ∫∫∫ dzdydx  

dz has changed from zero to 12−3y^2  

dy has changed from zero to 2-x  

dx has changed from zero to 2  

V = ∫∫∫ dzdydx = ∫∫ (12−3y^2) dydx = ∫ 12(2-x)-(2-x)^3 dx =  

24(2)-6(2)^2+(2-2)^4/4 -(2-0)^4/4 = 20

Step-by-step explanation:

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The popular candy Skittles comes in five colors. According to the Skittles website, the five colors are evenly distributed in th
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3 years ago
A and B are independent events. P(S) = 0.40 and P(B) = 0.30. What is P(A and B)
n200080 [17]

The value of the probability P(A and B) is 0.12

<h3>How to determine the probability?</h3>

The given parameters are

P(A) = 0.40

P(B) = 0.30

Given that the events are independent events;, we have:

P(A and B) = P(A) * P(B)

So, we have:

P(A and B) = 0.40 * 0.30

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3 0
2 years ago
Need help please its my last question
Nesterboy [21]

Given:

Radius of circle = 12 units

Area of sector = 24π sq. units.

Central angle = x

To find:

The value of x.

Solution:

We have,

r=12

A=24\pi

\theta = x

We know that, area of a sector is

A=\dfrac{\theta }{360^\circ}\pi r^2

Where, \theta is central angle, r is radius.

24\pi=\dfrac{x}{360^\circ}\pi (12)^2

24\pi=\dfrac{x}{360^\circ}\pi (144)

\dfrac{24\pi}{144\pi}=\dfrac{x}{360^\circ}

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Multiply both sides by 360 degrees.

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4 0
3 years ago
Zalma’s stock investment in March was $120. In October, it was $400.
Goryan [66]

Answer:

In December, Zalma will have $480.

Step-by-step explanation:

The time from March to October is 7 months. In those 7 months, she gains $280. So every month, her investment gains $40.

The time from March to December is 9 months. She will gain $360 during that time. We add her initial $120 with the $360, and Zalma will have $480.

It's not confirmed, but it's what I got. :D

8 0
3 years ago
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