Find the volume of the solid of revolution generated by revolving about the x-axis the region under the following curve. y= x from x=0 to x=20 (The solid generated is called a paraboloid.) The volume is (Type an exact answer in terms of n.)

Answers

Answer 1

To start, let's sketch the graph of the curve y = x from x = 0 to x = 20. This is simply a diagonal line that passes through the points (0,0) and (20,20), as shown below:

```
   |
20  |    *
   |   *  
   |  *  
   | *    
   |*    
0  --------------
  0   10   20
```

Now, we want to revolve this curve around the x-axis to create a solid shape. Specifically, we want to create a paraboloid, which is a three-dimensional shape that looks like an upside-down bowl.

To find the volume of this paraboloid, we need to use calculus. The basic idea is to slice the solid into very thin disks, and then add up the volumes of all the disks to get the total volume.

To do this, we'll use the formula for the volume of a cylinder, which is:

V = πr^2h

where r is the radius of the cylinder and h is its height. In our case, each disk is a cylinder with radius r and height h, where:

- r is equal to the y-value of the curve (i.e. r = y = x), since the disk extends from the x-axis to the curve.
- h is the thickness of the disk, which is a very small change in x. We can call this dx.

So, the volume of each disk is:

dV = πr^2dx
  = πx^2dx

To find the total volume of the paraboloid, we need to add up the volumes of all the disks. This is done using an integral:

V = ∫(from x=0 to x=20) dV
 = ∫(from x=0 to x=20) πx^2dx

Evaluating this integral gives us:

V = π/3 * 20^3
 = 8000π/3

So the exact volume of the paraboloid is 8000π/3.

To know more about paraboloid visit:-

https://brainly.com/question/30634603

#SPJ11


Related Questions

help me please I need help

Answers

Answer:

D) 6 in x 4 in

Step-by-step explanation:

3" x 2" scaled up to 1:20 would be 60" x 40"

60" x 40" scaled back to 1:10 would be 6" x 4"

also the scale factor 1:20 is double the scale factor of 1:10

3c + 1 = c + 1
What does c equal

Answers

Answer: c=0

Step-by-step explanation:

first come first served

Answers

Answer:

10. 32 mpg

12. 5 1/3 grams = 1 serving

14. 0.8 cent per can

16. 1/2 kg = 1 foot

18. 8 7/10 meters in 1 hour

Step-by-step explanation:

10. 256/8=32

12. if 4=3/4 then ?=4/4. to find 1/4 divide both by 3, 3/4 divided by 3 = 1/4, 4 divided by 3=1 1/3. then to find 4/4 multiply both by 4, 1/4x4=4/4, 1 1/3x4=5 1/3 so 5 1/3=1

14. 4.8/0.6=0.8

16. if 1/3=2/3 then ?=3/3. to find 1/3 divide both by 2, 2/3 divided by 2=1/3, 1/3 divided by 2 = 1/6. then to find 3/3 multiply both by 3, 1/3x3=3/3, 1/6x3=1/2

18. if 21 3/4=2 1/2 then ?=2/2. to find 1/2 divide both by 5, 2 1/2 divided by 5=1/2, 21 3/4 divided by 5 = 4 7/20. then to find 2/2 multiply both by 2, 1/2x2=2/2, 4 7/20x2=8 7/10

3/11 as a decimal equivalent

Answers

0.27 repeated with the line over the 27

Answer:

The decimal form for this is 0.27 (With a line on top of it.)

Step-by-step explanation:

See this image:

You park in a garage 3 floors below ground level. Then you get in the elevator and go up 12 floors. What floor do you get off the elevator?

Answers

Answer: (B) 6 floors

Step-by-step explanation: Use the equation -3 + 9 to get the amount of floors above ground level.

-3 + 9 = 6

6 floors.

If this helps may I please have a brainliest.

Answer:

you would get off at the 9th floor because in order to reach ground level again your would already go up 3 of the 12 floors. leaving 9 floors left to go up.

Step-by-step explanation:

-3+12=9

4w − 18 = 18 solve for w

Answers

Answer:

hello! :) have a good day!

W = 9

Just give me the answer

Answers

Answer:

y^6 is the simplest form

Answer:

y=6

Step-by-step explanation:

THATS KHANACADEMY RIGHT LOLLL

Help Me ASAP!
Assume the following in the picture: carbon = black oxygen = red hydrogen = blue Which formula represents the given molecule?​

Answers

Answer:

Answer is a

Step-by-step explanation:

You count carbon is c so count the black circles there are 5 and do the same with the rest

Answer:

Step-by-step explanation:

a

Which equations are correct?

Select each correct answer.




−4b3(5b2+3)=−20b6−12b3

−6y4(4y2+2)=−24y8−12y4

−5a4(2a2+4)=−10a6−20a4

−4x2(2x2+5)=−8x4−20x2

Answers

Option C

-5a⁴(2a² + 4)

-10a⁶ - 20 a⁴

What are the x-intercepts of the graph of y = (5x + 7) (2x - 1)(x – 4)?

Answers

Answer:

12x × 1x × 3x = 36x

)))))))))))))))))))

All the x - intercepts of the graph of y = (5x + 7) (2x - 1) (x - 4) will be;

⇒ - 7/5 , 1/2 , 4

What is mathematical expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph of the function,

⇒ y = (5x + 7) (2x - 1) (x - 4)

Now,

Find x - intercept of the equation as;

Substitute y = 0, we get;

⇒ y = (5x + 7) (2x - 1) (x - 4)

⇒ (5x + 7) (2x - 1) (x - 4) = 0

This gives three conditions as;

⇒ 5x + 7 = 0

And, 2x - 1 = 0

And, x - 4 = 0

After solve we get;

⇒ 5x + 7 = 0

⇒ x = -7/5

And, 2x - 1 = 0

⇒ x = 1/2

And, x - 4 = 0

⇒ x = 4

Hence, All the x - intercept = -7/5 , 1/2 , 4.

Therefore, All the x - intercepts of the graph of y = (5x + 7) (2x - 1) (x - 4) will be;

⇒ - 7/5 , 1/2 , 4

Learn more about the mathematical expression visit:

https://brainly.com/question/14462529

#SPJ5

What is the value of the expression 1/2 divided by 6

Answers

Answer: the answer is to divide and you will come up with the answer 1/12

Step-by-step explanation:

Answer:

here is 1/2 divided displayed mathematically

1/2 ÷ 6

1= numerator

2= denominator

3= whole number

to make it fraction from the answer you keep the

numerator by the whole number to make a new

denomiter

___1___ = _1_

2×6 12

thus the answer to 1/2 divided by 6 on fraction form is

1/2 is the answer

which one pls help me i’ll give extra points

Answers

Answer:

C

Step-by-step explanation:

Answer:

A. The doctors will give Charlie an operation

Step-by-step explanation:

-4x < 28
does anyone know the solution and answer?​

Answers

Answer:

x>−7

Explanation:

Let's solve your inequality step-by-step.

−4x<28

Step 1: Divide both sides by -4.

−4x/−4 < 28/−4

x>−7

Answer: x>−7

The residents of a village want to paint a sign that shows the elevation of their village to the sea. Their altimeter shows +2,100 feet. What should their signboard read?

Answers

Answer:

Wassss uppppp

Step-by-step explanation:

i dont know

Can some one solve this

Answers

Answer:

J Monica is right

Step-by-step explanation:

Add three to both sides, divide by 4 you get x[tex]\geq[/tex]4

Answer:

J

Step-by-step explanation:

Transform to slope-intercept form. 1+2y=6x-3

Answers

Hello the slope intercept form is y=3x-2

Answer: Y=3X-2

Step-by-step explanation:

First you are gonna need to combine all like factors.

1+2y=6x-3 (subtract 1 from both sides)

2y=6x-4

Then you need to get the y by itself.

2y=6x-4 (divide all terms by 2)

y=3x-2

now you are in slope intercept form (y=mx+b)

help plz
−86 + (−14) − 23 − (+22) + 16 − (−34)=​

Answers

Step-by-step explanation:

the answer is -86 mark as brainliest or rate this if u found this helpful :)

Answer:

-105

Step-by-step explanation:

-86-14= -100

-100-55= -155

16+34= 50

-155+50= -105

Solve for x.2(-x - 4) = 4x + 16
a) 4
b) 3
c) -3
d) -4

Answers

Answer:

44

Step-by-step explanation:

Answer:

X=-4

Step-by-step explanation:

First, we must solve for the parenthesis so...

-2x-8=4x+16

Then we must simplify this even more so lets add the 8 to 16

-2x=4x+24

Then we must subtract 4x from -2x

-6x=24

we must now divide 24 by -6 so we can isolate the x

x=-4

I hope this helped :)

Find the length of AD if AB = 24, DE = 8, and DC = 12.
a.8
b.12
c.14
d.10

HELP PLS

Answers

Answer:

AD = 12

Step-by-step explanation:

Find the diagram attached

From the given diagram, it can be inferred that;

AB = AD+DB and AD = DB

AB = AD + AD

AB = 2AD

AD = AB/2

Given that AB = 24

AD = 24/2

AD = 12

Hence the length of AD is 12

Answer: 10

Step-by-step explanation:

I got it right after trying the answer of 12 on CAOLA

what does the ! after a number mean.
explain in your own words and give 5 examples.

Answers

Answer: it means that you multiply the number by the numbers counting to 0

Step-by-step explanation:4!=4•3•2•1

Priya's family exchanged 250 dollars for 4,250 pesos. Priya bought a sweater for 510 pesos. How many dollars did the sweater cost? Pesos dollars 4,250 250 25 1 3 510

Answers

Answer:

$30

Step-by-step explanation:

since they exchanged them we can assume they are worth the same

250=4250

First find how many pesos is worth 1 dollar

4250/250= 17

Then divide the amount the sweater costs by how much 1 dollar would be

510/17= 30

The sweater would cost 30 dollars.

PLEASE HELP ASAP ILL GIVE BRAINLY

Answers

Step-by-step explanation:

x= (70+83+90)/3= 81

85=(89+75+y)/3

255=89+75+y

y=91

92=(86+a+a)/3

276=86+2a

2a=190

a=95

93=(b+b+b)/3

279=3b

b=93

Can somone help please? Thx​

Answers

Answer:

I would say the answer is 0.69

Step-by-step explanation:Because if you multiply 7 times 0.69 it gives you 4.83

Answer:

The answer is 1.45

Step-by-step explanation:

Divide 7 and 4.83 and the answer is 1.447.

Plz help me !!!!!!!!!!

Answers

C i think?????????????????????  :D

C is the answer ! :)

A baseball player earns $3 million in 2015. During the next 15 years, the earnings increase 4% each year.

a. Write an exponential growth model giving the earnings y (in millions of dollars) t years after 2015. Write the base of the model as a decimal.

An exponential growth model is y=
b. In which year will the player's earnings first exceed $5,000,000?

Answers

Answer:

[tex]y=3*1.04^{t}[/tex]

in 2029

Step-by-step explanation:

[tex]y=3*1.04^{t}[/tex]

[tex]when y=5\\t=\frac{ln(5/3)}{ln(1.04)} =13.02 ..[/tex]

have to round it up to 14 to exceed

Help Please........ ​

Answers

Answer:

4

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(4 x 2)/2 + (4 x (6-2))/2 = 12

A hexagonal prism has.............vertices.

Answers

Step-by-step explanation:

A hexagonal prism has 12 vertices.

Hope this answer will help you.

Have a great time

Pensé dos números. Sumados dan 38 y restados dan 2. ¿Qué números son?

Answers

Answer:

sorry I cannot help you sir can you translate it into English

What pair of angles is congruent?

Answers

Answer:

angle f angle g and angle h are congruent as they are 90 degree

Which polynomial represents the difference below?
2x +7X+6
(3x? – X
A. - x + 6x + 6
B. 2x2 + 4x + 6
c. 2x2 + 5x + 6
D. - x2 + 3x + 6

Answers

Answer:

-x²-8x+6

Step-by-step explanation:

Given the polynomial expression

2x²+7x+ 6 and 3x² – X

Taking their difference

2x²+7x+ 6  - (3x² – X)

2x²-3x²+7x+x+6

-x²-8x+6

Hence the required difference is -x²-8x+6

Answer:

-x²+8x+6

Step-by-step explanation:

Ape-x

Other Questions
Which three statements accurately describe the effects of the economic policies on individuals? 3. The slope of a line shows the___for that line. This means it tells us how far ____ the line moves each time you move over one unit on the x-axis.for that line. Which instructions would the nurse provide when teaching nutritional therapy to a patient recovering from renal stones composed of calcium oxalate A rock displaces 1.65 L of water. The volume of the rock is: Simplify the expression PLSSS HELP !!!!Which statement best explains how the phrase "At three paces from her, seated in a chair which he balanced on two legs" impacts the meaning of the story?1) By describing the scene this way, the reader can get a better understanding of what the men of the Catalans are like.2) By highlighting the point that Fernand is sitting so close to Mercds, the author shows us how tenacious he is.3) By including this information, the reader can tell that Fernand doesn't care about what Mercds has to say.4) By showing Fernand is close by and balancing on a chair, the reader gets a glimpse of Fernand's personality. A proton moving along the positive x-axis enters a uniform magnetic field which is directed along the positive y-axis. If the magnitude of the field is 0.7 T, and the charge and speed of the proton are 1.5 x10-19 C and 3.0 x 106 m/s respectively. Calculate the force acting on the proton Question -Define Myself? Meteorologists use weather balloons to carry weather instruments high into the atmosphere. when it is first released at earths surface, a weather balloon typically appears underinflated. what happens to the balloons volume and pressure as it rises into the atmosphere? check all that apply. the pressure in the balloon decreases. the pressure in the balloon increases. the volume of the balloon increases. the volume of the balloon decreases. 20 pts and brainliest Jackson invested $4,200 in an account paying an interest rate of 9 1/2 compounded continuously. Julia invested $4,200 in an account paying an interest rate of 8 7/8 compounded quarterly. To the nearest hundredth of a year, how much longer would it take for Julia's money to double than for Jackson's money to double? Unlike what the framers of the constitution originally intended, modern presidents? Identify the characteristics of homologous chromosomes and sister chromatids. Men are expected to have _________ character traits like strength, self-confidence, assertiveness, and ambition. Group of answer choices progressive agentic modern expressive The definition of _____ is a negative emotional state occurring in response to events that are perceived as taxing or exceeding a person's resources or ability to cope. the periodic table contains alot of information in it with the help of that information calculate the number neutrons present in the non metalic elements of the periodic table (1) Compute the total variable cost per unit. (2) Compute the total fixed costs. (3) Compute the income from operations for sales volume of 16,000 units. (4) Compute the income from operations for sales volume of 20,000 units. The sum of a number and its reciprocal is 122/11. Find thenumber.O -1109O 11 6 out of 24 as a percentage what is the volume of a sphere with a radius of 6 inches