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grin007 [14]
2 years ago
7

Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y=x+2 and the parabol

a y=x^2 about the following lines.
(A) The line x=2
(B) The line x=-1
(C) The​ x-axis
(D) The line y=4
Mathematics
1 answer:
Viktor [21]2 years ago
4 0

Answer:

8 π or

25.13 unit^3 to the nearest hundredth.

Step-by-step explanation:

(A)

The height of the shell is (2 + x - x^2) and  the radius is (2 - x).

V = 2π ∫(2 - x)(x + 2 - x^2) dx  between the limits x = 0 and x = 2.

=  2π ∫ (2x + 4 - 2x^2 - x^2 - 2x + x^3) dx

 = 2π ∫ (x^3 - 3x^2 + 4 ) dx

= 2π [ x^4/4 - x^3 + 4x ]  between x = 0 and x = 2

= 2 π [4 - 8 + 8 )

= 2 π * 4

= 8π

= 25.13 unit^3 to the nearest hundredth.

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iris [78.8K]

Answer:

Step-by-step explanation:

From the picture attached,

Addition of the blocks in first row is 60

a + a + a + 12 = 60

3a + 12 = 60

3a = 60 - 12

3a = 48

a = 16

For second row,

(b + 5) + (b + 5) + (b + 5) + (b + 5) = 60

4(b + 5) = 60

b + 5 = 15

b = 10

For third row,

(a + b) + c = (b + 5) + (b + 5) + (b + 5)

a + b + c = 3(b + 5)

16 + 10 + c = 3(10 + 5) [Since, a = 16 and b = 10}

26 + c = 45

c = 45 - 26

c = 19

For fourth row,

3c + d = 60

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8 0
2 years ago
20n^4+n^3+10n^2) / 10n^2
Zina [86]
Divide them
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3 0
2 years ago
Help and I’ll kiss u again mwah mwah
ElenaW [278]

Answer:

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Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Find the surface area of the cube.
Mrac [35]
<h3><u>Given</u>:-</h3>

\rightarrow Side(a) of the cube = \sf{\frac{1}{3}ft}.

<h3><u>To Find</u>:-</h3>

\rightarrow Surface Area of the cube with side \sf{\frac{1}{3}ft.}

<h3><u>Formula Used</u>:-</h3>

\rightarrow Surface area of cube = \sf{6a^2}

<h3><u>Solution</u>:-</h3>

\rightarrow Surface area of cube = \sf{6a^2} (putting the value of a from the above given)

\rightarrow \sf{=\:6×(\frac{1}{3})^2}

\rightarrow \sf{=\:6×\frac{1}{9}}

\rightarrow \sf{=\:\frac{6}{9}}

\rightarrow \sf{=\:\frac{2}{3}ft^2}

Therefore, surface area of the given square = \sf{=\:\frac{2}{3}ft^2}

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Hope it helps you:)

3 0
2 years ago
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Answer:

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Step-by-step explanation:

Three equations

Look for x

Look for y

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__________________

Note that all of these are questions can be answered through isolating the variable.

Let's start with x :

Get x alone :

2(x + 5) = 3x + 1

Distribute :

(2(x) + 2(5))

2x + 10 = 3x - 1

Add 1 to both sides of the equation :

2x + 11 = 3x

Subtract 2x from both sides :

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Next is y :

Isolate y :

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Add 4 to both sides :

3y = 10 - 2y

Add 2y to both sides :

5y = 10

Divide 5 from both sides to get y by itself :

y = 2

Lastly is n :

Isolate n :

3(n + 2) = 9(6 - n)

Distribute :

(3(n) + 3(2)) = (9(6) - 9(n))

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Subtract 54 from both sides :

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-48 = -12n

-12n = -48

Divide -12 from both sides :

n = 4

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