Find the volume of the solid generated by revolving the area bounded by y=x^2 and x-axis from [0,2] around the x-axis

Answers

Answer 1

Answer:  [tex]\dfrac{32\pi }{5}\ \text{unit}^3[/tex]

Step-by-step explanation:

Given

The area is bounded by [tex]y=x^2[/tex] and x-axis from [0,2]

The volume generated for [tex]y=f(x)[/tex] when rotated about the x-axis in the interval [a,b] is

[tex]V=\int_a^b\pi y^2dx[/tex]

Insert the values

[tex]\Rightarrow V=\int_0^2\pi x^4dx\\\\\Rightarrow V=\pi \int_0^2x^4dx\\\\\Rightarrow V=\pi \left[ \dfrac{x^5}{5}\right]_0^2\\\\\Rightarrow V=\dfrac{2^5\pi }{5}\\\\\Rightarrow V=\dfrac{32\pi }{5}\ \text{unit}^3[/tex]


Related Questions

Is Joon lee soo a girl or boy name???​

Answers

Answer:

Girl

Step-by-step explanation:

For me... it sound more like a girl but it could also be a boy's name

a rectangular rug covers 1200 square inches on the floor. The length of the rug is 30 inches .What is the length in inches of the rug

Answers

Answer:

The length is 30 (which you aready said) and the width is 40

Step-by-step explanation:

1200/30=40

(another way)

120/30=4 (multiply each side by ten)

PLEASE HELP ASAP and have a great night ! :D

Answers

Answer:

6-8

Step-by-step explanation:

---------------------

6-8......................

Help me with this hw please

Answers

Answer:

12 = 3 + p

Step-by-step explanation:

She has a total of 12 pencils

3 of them are red

The rest are "p"

p + 3 must equal 12 because she has a total of 12 pencils consisting of 3 red and "p" as the rest

Hello, I am Nazanin. Tomorrow I have to answer a series of math questions. Is there anyone who can help me?​

Answers

It depends what the questions are.

A hovercraft takes off from a platform. The function models the height of the hovercraft above the ground in
meters) as a function of time (in seconds) after it takes off.
Plot the point on the graph of that corresponds to the time when the hovercraft reached its maximum
height.
Height (meters)
6
f

Answers

Answer:(1,8)

Step-by-step explanation:

Which equation could be used to find the length of the hypotenuse?

Answers

Answer:

The first one. 6 squared + 11 squared= c squared

Can somebody help me with this im pretty bad with coordinates ty in advance!​

Answers

I believe your answer is ten, hope this helps

Answer:

the Answer is A. 14 units

Step-by-step explanation:

I counted :)

What is the area of the
triangle?
6 mm
8 mm
square millimeters

Answers

Answer:

24 square millimeters

Step-by-step explanation:

Area of a triangle is half of the base times the height.

[tex]\frac{1}{2} bh[/tex]

Here, that means

[tex]\frac{1}{2}[/tex](8)(6) = 24 square millimeters

Can someone please help me with this algebra

Answers

Answer:

bounce 1

Step-by-step explanation:

1. How can you find answers to the statistical questions?

2. How about answers to non-statistical questions?

Answers

1 The solution involves four steps.

Make sure the sample size is big enough to model differences with a normal population. ...

Find the mean of the difference in sample proportions: E(p1 - p2) = P1 - P2 = 0.52 - 0.47 = 0.05.

Find the standard deviation of the difference. ...

Find the probability.

A circle has a radius of 1.5 meters.
Find its circumference and area.
help bestiess :)

Answers

Answer:

C=9.42

Step-by-step explanation:

Formulas: C=2πr or C=πd

Were gonna use C=2πr

"r"stands for radius from the problem we know that the radius is 1.5 .

Now we substitute the "r" for 1.5, it looks like this C=2π1.5 .

Now we multiply 2x1.5=3 . Now you are left with C=3π

Now you need to multiply 3xπ (Instead of π use 3.14) it would look like this 3x3.14= 9.42

Factor the expression below.
x² - 64
A. (x+3)(x-8)
B. (x-8)(x-8)
C. (x - 16)(x - 4)
D. (x+16)(x-2)

Answers

Answer:

(x + 8) (x - 8)

Step-by-step explanation:

To factorise the expression follow the steps:

Think the factorising means you want like:-

  ( x + _ ) ( x + _ )

Now, add the numbers to get 0 & multiple together to get -64

 -64 = 8 x -8

 8 + -8 = 0

Now fill the numbers in the factorising mean which will give you,

( x + _ ) ( x + _ ) --> ( x + 8 ) ( x - 8 )

Therefore, the answer will be: ( x + 8 ) ( x - 8 )

I hope this will help you :)

Answer:

b

Step-by-step explanation:

1) A Jet travels 520 miles in 2 hours. At this rate, how far could the jet fly in 13 hours? What is the rate of speed of the jet? ​

Answers

Answer:

[tex]Speed = \frac{distance}{time} = \frac{520}{2} =260miles \ per \ hour \\\\Distance = Speed * time = 260 * 13 = 3380miles[/tex]

You are designing a rectangular skateboard park on a lot that is on the corner of a city block. The park will have a walkway along two sides. The dimensions of the lot and the walkway are shown in the diagram.

Answers

Answer:

The dimensions of the lot and the walkway are shown in the diagram.

Step-by-step explanation:

Correct I’ll give brainlist no links or will be reported

Answers

Answer:

0

Step-by-step explanation:

If you plug two points into the equation y2-y1/x2-x1, you will find the slope or rate of change. In this case I used the points (0,3) and (2,3). Plug them in to get 3-3/2-0. 0/2=0. Therefore, the rate of change is 0.  

If this helps please mark as brainliest

Answer:

0

Step-by-step explanation:

there is no rate of change. rate of change means what is the slope or the distance the beginning and end of the line. since it is going in a straight line there is no rate of change.

hope this helped

Hi can some one help me !!

Answers

Answer:

50

Step-by-step explanation:

sorry to ask but can i get brainliest

Answer:

A) 50° ✔︎

Step-by-step explanation:

∠D=38°+12=50°

∠B=∠D

∠B=50°

-----------------

hope it helps...

have a great day!!!

Which expression is equivalent to 5x+10y-15
5(x-2y-3)
5(x+2y-10)
5(x+2y-3)
5(x+2y-15)

Answers

5(x+2y-3) is the right answer

if 3 tacos at taco el primo cost $5.31, how much would 8 tacos cost?

Answers

Answer:

[tex]\$14.16[/tex]

Step-by-step explanation:

Since the question implies a constant rate, we can set up the following proportion:

[tex]\frac{3}{5.31}=\frac{8}{x},\\3x=8\cdot 5.31,\\x=\frac{8\cdot 5.31}{3}=\boxed{\$14.16}[/tex]

3t = 5.31

t = 1.77

We're looking for 8t.

t = 1.77

8t = 14.16

Can someone please help me with math.

Answers

Answer:

The answer would be plot D.

Step-by-step explanation:

A recipe for peanut butter cookies uses only peanut butter ,sugar ,syrup and egg in the ratio 5:4:2:1
A) wants to makes 2.4kg of cookies
How much of each ingredient should he use.
B) using this recipe 10ph of syrup is needed to make 15 of these cookies

Answers

The answers is b..........

A)butter= 12

sugar  = 9.6

syrup= 4.8

eggs= 2.4

What is ratio?

A ratio indicates how many times one number contains another.

Given:

5:4:2:1

Let the common ratio be x

So, butter= 5x

sugar= 4x

syrup = 2x

egg= x

As, eggs= 2.4 kg

So, x= 2.4

Now,

butter= 5x = 5* 2.4 = 12

sugar= 4x = 4* 2.4 = 9.6

syrup = 2x  = 2* 2.4 = 4.8

Learn more about ratio here:

https://brainly.com/question/22900753

#SPJ2

Plsss help me !!!!

the public school enrollment of a city is 13,500. Enrollment is declining at a rate of 4.5% per year. predict the enrollment in 5 years.

Answers

Answer:

The enrollment after 5 years is 10,724

Step-by-step explanation:

Generally, we can have the depreciation formula written as follows;

A = P(1 - r)^t

A is the number of enrollment in after a certain number of years t

P is the initial population which is 13,500

r is the rate of depreciation which is 4.5% = 4.5/100 = 0.045

t = 5 years

Substituting these values, we have it that;

A = 13,500(1-0.045)^5

A = 10,723.84

Solve for X

x = ___ (Round to the nearest hundredth)

Answers

Answer:

12.62

Step-by-step explanation:

imagine a circle with the center at the corner (let's call it A) with the 31 degree angle. the radius is AB.

so,

x = sin(31)×AB

and

21 = cos(31)×AB

therefore,

AB = 21/cos(31) = 24.4993...

=> x = sin(31)×24.4993... = 12.62 (12.61807...)

solve pleas really important ​

Answers

Answer:

bleasssss

Step-by-step explanation:

Answer:

B negative 3

Step-by-step explanation:

just did this u wont reget

What is the ratio of the side length of the smaller square to the side length of the larger square?

FAST RESPONSE PLEASE!!!

Answers

Answer:

the smaller square length is 3cm

the larger square length is 6cm

hence their ratio will be 3:6

Simplify the ratio

we have our final answer to be 1:2

The required ratio of the side length of the smaller square to the side length of the larger square is 1 : 2.


What is the Ratio?

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Side of smaller square, a = 3
Side of the larger square, b = 6

According to the question,

The ratio of the side length of the smaller square to the side length of the larger square,

= a / b = 3 / 6
= 1 / 2

Thus, the required ratio of the side length of the smaller square to the side length of the larger square is 1 : 2.

Learn more about Ratio here:

brainly.com/question/13419413

#SPJ2

what is the circrumfrence of a circle with a diameter of 7 feet? Use 3.14 for pi

Answers

Answer:

Step-by-step explanation:

if you take the diameter of a circle and put it around the circumference you will need to have 3 and a bit more (pi=3.14) of diameters to cover the whole circumference.

C = pi*d = 3.14 * 7 = 21.98 feet

please help me ill give you the crown thing if its right

Answers

24.75
ft.
Explanation:
We essentially have the following ratio:
4
9
:
11
x
where
x
is the length of the actual billboard.
We can solve this by cross-multiplying. We get
4
x
=
99
Dividing by
4
, we get
x
=
99
4
, or
24.75
ft.
Hope this helps!

Answer:

C 22cm  I really hope this helps and is right! Sorry if its wrong

Step-by-step explanation:

:)

An angle that measures 100° is an angle
a. acute
b. plain
c. straight
d. obtuse​

Answers

Answer:

obtuse

Step-by-step explanation:

Help, I dont get it, Like how do I do the division?

Answers

The answer is 10 units^3

Answer:

Step-by-step explanation:

you actually dont have to do any division in this problem. since you know the area of the square and its depth, you simply multiply to two fractions, so [tex]\frac{25}{4} *\frac{8}{5}[/tex] when you multiply fractions all you do is multiply the tops and and bottoms, so 25 * 8=200 and 5 * 4=20, so the fraction is now 200/20, so when divide both sides by 20, the answer is 10. another way to demonstrate this in case you didnt understand is that you can rewrite your equation as [tex]\frac{25 * 8}{4 * 5}[/tex] then all you have to do is perform the opperation.

if you have any questions, leave them in the comments and i will try to answer them, if this helped, pls give brainliest

Shows the termination of the parking lot of Helen healings health food store parking lot is how many square yards

Answers

Answer:

1100 yd²

Step-by-step explanation:

The parking lot can be divided into 2 rectangles :

Area of a rectangle = Length * Width

First rectangle :

Dimension = 40 yards by 20 yards

Area = 40 * 20 = 800 yd²

Rectangule 2 :

30 yards by 10 yards

Area = 30 * 20

Area = 30 * 10 = 300 yd²

Total area of parking lot :

800 + 300 yd²

= 1100 yd²

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