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Gennadij [26K]
3 years ago
9

HELP ME I AM CRYING SO MUCH ALSO LMK IF U CANT SEE

Mathematics
1 answer:
Wittaler [7]3 years ago
3 0
Send a better picture so I can help.
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Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving
harina [27]

Answer:

The volume of the solid is 714.887 units³

Step-by-step explanation:

* Lets talk about the shell method

- The shell method is to finding the volume by decomposing

 a solid of revolution into cylindrical shells

- Consider a region in the plane that is divided into thin vertical

 rectangle

- If each vertical rectangle is revolved about the y-axis, we

 obtain a cylindrical shell, with the top and bottom removed.

- The resulting volume of the cylindrical shell is the surface area

  of the cylinder times the thickness of the cylinder

- The formula for the volume will be:  V = \int\limits^a_b {2\pi xf(x)} \, dx,

  where 2πx · f(x) is the surface area of the cylinder shell and

  dx is its thickness

* Lets solve the problem

∵ y = x^{\frac{5}{2}}

∵ The plane region is revolving about the y-axis

∵ y = 32 and x = 0

- Lets find the volume by the shell method

- The definite integral are x = 0 and the value of x when y = 32

- Lets find the value of x when y = 0

∵ y = x^{\frac{5}{2}}

∵ y = 32

∴ 32=x^{\frac{5}{2}}

- We will use this rule to find x, if x^{\frac{a}{b}}=c, then=== x=c^{\frac{b}{a}} , where c

 is a constant

∴ x=(32)^{\frac{2}{5}}=4

∴ The definite integral are x = 0 , x = 4

- Now we will use the rule

∵ V = \int\limits^a_b {2\pi}xf(x) \, dx

∵ y = f(x) = x^(5/2) , a = 4 , b = 0

∴ V=2\pi \int\limits^4_0 {x}.x^{\frac{5}{2}}\, dx

- simplify x(x^5/2) by adding their power

∴ V = 2\pi \int\limits^4_0 {x^{\frac{7}{2}}} \, dx

- The rule of integration of x^{n} is ==== \frac{x^{n+1}}{(n+1)}

∴ V = 2\pi \int\limits^4_0 {x^{\frac{9}{2}}} \, dx=2\pi[\frac{x^{\frac{9}{2}}}{\frac{9}{2}}] from x = 0 to x = 4

∴ V=2\pi[\frac{2}{9}x^{\frac{9}{2}}] from x = 0 to x = 4

- Substitute x = 4 and x = 0

∴ V=2\pi[\frac{2}{9}(4)^{\frac{9}{2}}-\frac{2}{9}(0)^{\frac{9}{2}}}]=2\pi[\frac{1024}{9}-0]

∴ V=\frac{2048}{9}\pi=714.887

* The volume of the solid is 714.887 units³

5 0
3 years ago
Can someone please give me the (Answers) to this? ... please ...
Korvikt [17]

Answer:

6:A

7;B

8;c

9;A

10:c

11;b

12:A

3 0
2 years ago
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What is 35.6 × 10−4 in standard form?
Fittoniya [83]

35.6\times10^{-4}=35.6\times0.0001=0.00356


a^{-n}=\dfrac{1}{a^n}\\\\10^{-4}=\dfrac{1}{10^4}=\dfrac{1}{10000}=0.0001

8 0
3 years ago
You have $3.20 in quarters and dimes. You have four fewer quarters than dimes. What would the associated system of equations loo
Harlamova29_29 [7]
 The equation is 
Dimes is x

x+x-4=3.20


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Which triangles illustrate the Side Angle Side Similarity theorem (abbreviated S A S).
worty [1.4K]

Answer:

Triangles a, b, and d

Step-by-step explanation:

The three triangles have a side length measurement, an angle measure, then another side length measurement

in that order (the order matters)

6 0
1 year ago
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