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JulijaS [17]
2 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]2 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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1 year ago
Tanya walked for 171717 minutes from her home to a friend that lives 1.51.51, point, 5 kilometers away. d(t)d(t)d, left parenthe
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Correct question is;

Tanya walked for 17 minutes from her home to a friend that lives 1.5 kilometers away. D(t) models Tanyas remaining distance to walk in kilometers, t minutes since she left home. What number type is more appropriate for the domain of d?

Answer:

0 ≤ t ≤ 17 ; (0, 17)

Step-by-step explanation:

We are told that she has walked for 17 minutes from her home to a friend that lives 1.5 kilometers away.

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Since she spent 17 minutes, then it means in modeling remaining distance it could be from 0 to 17 minutes as the case may be. Thus, the domain can be written as;

0 ≤ t ≤ 17 ; (0, 17)

6 0
1 year ago
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Step-by-step explanation:

6 0
2 years ago
Maggie bought 3/4 of a pound of bananas and 4 boxes of cereal for $10.11. If each box of cereal cost $2.40, what was the price o
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2 years ago
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JulsSmile [24]
For this case what you should see is that for the interval [9, 11] the behavior of the function is almost linear.
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