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AVprozaik [17]
3 years ago
5

A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?

Mathematics
2 answers:
Fiesta28 [93]3 years ago
4 0
The answer is quadrant 4
____ [38]3 years ago
4 0
The answer will be quardrant 4
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Evaluate the triple integral ∭EzdV where E is the solid bounded by the cylinder y2+z2=81 and the planes x=0,y=9x and z=0 in the
dem82 [27]

Answer:

I = 91.125

Step-by-step explanation:

Given that:

I = \int \int_E \int zdV where E is bounded by the cylinder y^2 + z^2 = 81 and the planes x = 0 , y = 9x and z = 0 in the first octant.

The initial activity to carry out is to determine the limits of the region

since curve z = 0 and y^2 + z^2 = 81

∴ z^2 = 81 - y^2

z = \sqrt{81 - y^2}

Thus, z lies between 0 to \sqrt{81 - y^2}

GIven curve x = 0 and y = 9x

x =\dfrac{y}{9}

As such,x lies between 0 to \dfrac{y}{9}

Given curve x = 0 , x =\dfrac{y}{9} and z = 0, y^2 + z^2 = 81

y = 0 and

y^2 = 81 \\ \\ y = \sqrt{81}  \\ \\  y = 9

∴ y lies between 0 and 9

Then I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \int^{\sqrt{81-y^2}}_{z=0} \ zdzdxdy

I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{z^2}{2} \end {bmatrix}    ^ {\sqrt {{81-y^2}}}_{0} \ dxdy

I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix}  \dfrac{(\sqrt{81 -y^2})^2 }{2}-0  \end {bmatrix}     \ dxdy

I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix}  \dfrac{{81 -y^2} }{2} \end {bmatrix}     \ dxdy

I = \int^9_{y=0}  \begin {bmatrix}  \dfrac{{81x -xy^2} }{2} \end {bmatrix} ^{\dfrac{y}{9}}_{0}    \ dy

I = \int^9_{y=0}  \begin {bmatrix}  \dfrac{{81(\dfrac{y}{9}) -(\dfrac{y}{9})y^2} }{2}-0 \end {bmatrix}     \ dy

I = \int^9_{y=0}  \begin {bmatrix}  \dfrac{{81 \  y -y^3} }{18} \end {bmatrix}     \ dy

I = \dfrac{1}{18} \int^9_{y=0}  \begin {bmatrix}  {81 \  y -y^3}  \end {bmatrix}     \ dy

I = \dfrac{1}{18}  \begin {bmatrix}  {81 \ \dfrac{y^2}{2} - \dfrac{y^4}{4}}  \end {bmatrix}^9_0

I = \dfrac{1}{18}  \begin {bmatrix}  {40.5 \ (9^2) - \dfrac{9^4}{4}}  \end {bmatrix}

I = \dfrac{1}{18}  \begin {bmatrix}  3280.5 - 1640.25  \end {bmatrix}

I = \dfrac{1}{18}  \begin {bmatrix}  1640.25  \end {bmatrix}

I = 91.125

4 0
3 years ago
FOR MANY POINTSish
dangina [55]

x will represent the first unknow number

6x will represent the second number

the two numbers together will equal 21

6x + x = 21  combine like terms

7x =21  divide both sides by 7

x =3


Hope that helps.

brainliest is always appreciated.

4 0
3 years ago
How many minutes will it take five people to stack 250 chairs if each person can stack 20 chairs a minute
maria [59]
250/5 = 50.....so each person is stacking 50 chairs...

50/20 = 2.5 minutes....so it takes each person 2.5 minutes to stack 50 chairs.

so ur answer is 2.5 minutes
8 0
3 years ago
Read 2 more answers
What is the solution of the system? 7x+5y=19 and -7x-2y=-16 Need help ASAP
Stells [14]

Answer:

x = 2, y = 1

Step-by-step explanation:

  • 7x + 5y = 19
  • -7x - 2y = -16

Use the elimination method to solve the system of equations. Add the terms from top to bottom. 7x and -7x cancel out.

0 + 3y = 3

Divide both sides by 3.

y = 1

Substitute 1 for y into the first equation.

7x + 5(1) = 19

7x + 5 = 19

Subtract 5 from both sides.

7x = 14

Divide both sides by 7.

x = 2

3 0
3 years ago
What are the square roots of 36/100?
Mekhanik [1.2K]

Question:

What are the square roots of 36/100?

Answer

A. −6/10 and 6/10

6 0
3 years ago
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