What is the volume of the solid generated when the region in the first quadrant bounded by the graph of y=x^3, the x-axis, and the vertical line x=2 is revolved about the x-axis?
Show work.

A
[tex]4[/tex]
B
[tex] \frac{128}{7} [/tex]
C
[tex]4\pi[/tex]
D
[tex] \frac{128\pi}{7} [/tex]

Answers

Answer 1

Answer:

The first thing we need to do is to find the area bounded by:

y = x^3

y = 0

between:

x = 0 and x = 2

This is the integral of the given function between x = 0 and x = 2, written as:

[tex]\int\limits^2_0 {x^3} \, dx = \frac{2^4}{4} - \frac{0^4}{4} = 2^2 = 4[/tex]

This means that the area of the bounded region is 4 square units.

Now, if we do a full rotation around the x-axis, the volume generated will be equal to the area that we obtained times 2*pi units.

The volume is:

V = (4 square units)*(2*pi units) = 8*pi cubic units.

(Notice that no option coincides with this, there may be a mistake in the options)


Related Questions

10.) A book that normally cost $5.50
is marked up by 40%. What is the
selling price of the book?

Answers

Answer:

the answer is seven point seven

4×10^3 times what number is equal to 16×10^5?
Really stuck on this question on my virtual Exam.Could use a little help.

Answers

Answer:

400        or       4 x 10²

Step-by-step explanation:

NEED ANSWER ASAP WILL GIVE BRAINLIEST FOR CORRECT ANSWER

Answers

Answer:

Slope

Step-by-step explanation:

Hope it helps you in your learning process

What is 57 divided by 90?

Answers

Answer:

0.63 should be your answer

Answer;

0.6333333

Step-by-step explanation:

I think it's helps you

How many times greater is the value of 7 in 271,461 than the value of 7 in 927,645?​

Answers

Answer:

3.42 times.

Step-by-step explanation:

We can simply see how many times greater the numbers are from one another.

927,645/271,461 = 3.41723120448 about 3.42 times.

Classify the angle pair using all names that apply

Answers

Answer:

Vertical and supplementary

Step-by-step explanation:

Angles 1 and 2 are Vertically opposite angles and therefore they are equal to each other.

What is the value of the expression 13/4 (8)? *

Answers

Answer: 26

(13/4) (8/1) =(13) (8)/ (4) (1) = 104/4 = 26

Step-by-step explanation:

I think the answer is 26 have a nice day!

10 POINTS FOR THE CORRECT ANSWER PLEASE HELP

Answers

Answer:

Step-by-step explanation:

The Pythagorean theorem says:

[tex]a^2+b^2=c^2[/tex]

where a and b are the two legs of the triangle and c is the hypotenuse.  Here, let's say a = 6 and b = [tex]\sqrt{13}[/tex]. We then get the following equation:

[tex]c^2= (6)^2+(\sqrt{13})^2=49[/tex]

So c = 7. Technically, c can also equal -7 since (-7)^2 = 49 as well but that does not apply here because a side length cannot be <0. So 7 is the answer.

The question: " match each drawing with a triangle congruence postulate that can be used to prove the triangles are congruent, if any."



Possible answers


Side angle side (SAS)

Angel side angle (ASA)

Hypotenuse leg (HL)

Not possible

Answers

Answer:

1 : Hypotenuse leg (HL)

2: Angle side angle (ASA)

3: Side angle side (SAS)

Step-by-step explanation:

Given

See attachment for triangles

Required

Determine the congruence postulate

Figure (1):

From the attachment;

[tex]AC = BD[/tex] --- The hypotenuse

[tex]CB = CB[/tex] --- One other leg

Since the hypotenuse and one other leg of both triangles are congruent, then the postulate is: HL

Figure (2):

From the attachment, we have:

[tex]150^\circ = 150^\circ[/tex] --- Angle

[tex]15^\circ = 15^\circ[/tex] ---- Angle

The horizontal line that divides both triangles show that they have a congruent side.

Hence, the postulate is: ASA

Figure (3):

From the attachment, we have:

A pair of single marks (Side)

A pair of double marks (Side)

A pair of equal angles

Hence, the postulate is: SAS

Your weekly allowance is $15. You spent 30% How much did you spend?

Answers

Answer:

You would have spent $4.50

Step-by-step explanation: Divide 100 by 30 and multiply to 15. So it will look like: 30/100*15= $4.50. I hope this helps

ente. The box plot below shows the heights, in inches, of the 24 students in Brandon's homeroom -- 47 49 51 53 55 57 59 61 63 65 67 69 Select all the statements that describe the dass according to the box plot.​

Answers

Answer:

4+

Step-by-step explanation:

Ms. Jankowski’s art class has a total of 35 students enrolled. Seven of the thirty-five students are girls. What percentage of the class is made up of boys? *

Answers

Answer:

80% of the class is made up of boys

Step-by-step explanation:

7/35 are girls, which means, 28/35 are boys (35 - 7)

To find the percentage, you divide 28 by 35

28/35 = 0.8 or 80%

compare the following pairs of numbers. in each pair,state which is greater​

Answers

a. 759

b. 8769

c. 96699

d. 36754209

The trick is looking at the first numbers for either possible answer. Pick the one that is the greatest going backward. If you're stuck with the same numbers as in d, just continue going back until you see something like the 7 being greater than the 5.

Find the distance between the points (3,7) and (3,2)

Answers

Answer:

5 units.

Step-by-step explanation:

Since the distance is straight up.

You have two options:

Graph those two points and count the spaces separating them

or

Since they have the same x, you would only need to subtract 7-2.

Use the distributive property to multiply the expression.9m (7m+2)

Answers

Answer:

63m^2 + 18m

Step-by-step explanation:

9m x 7m + 9m x 2  

63m^2 + 9m x 2

63m^2 + 18m

the ^2 meaning exponent 2

The height of a triangle is 7 inches greater than the base. The area of the triangle is 225 square inches. Find the length of the base and the height of the triangle.

Answers

Answer:

Height is 25in

Base is 18in

Step-by-step explanation:

225=[x*(x+7)]/2=[x^2+7x]/2

450=x^2+7x

x^2+7x-450=0

(x+25)(x-18)=0

count the numbers of triangles in the figures​

Answers

Answer:

A

Step-by-step explanation:

look it carefully.

Question 5: 10 pts
There are 40 pieces of building blocks in a bag. 10 each of blue, green, red, and yellow. Two pieces are chosen
at random. Identify the probability that both of the pieces chosen are green

Answers

Answer:

The answer is 3/52

Step-by-step explanation:

(2/3)^4=

am very confuse guys help!!!

Answers

Answer:

16/81

Step-by-step explanation:

Lets break it down

When you see ^4, you are multiplying the base ( 2/3 ) by itself 4 times

So lets write the equation

[tex]\frac{2}{3} *\frac{2}{3} *\frac{2}{3} *\frac{2}{3} = x\\[/tex]

[tex]\frac{4}{9} *\frac{4}{9} =x[/tex]

[tex]\frac{16}{81} =x\\x= \frac{16}{81}[/tex]

If my answer is wrong pls correct me.

If you like my answer and explanation then please mark me as Brainliest!

-Chetan K

Airlines monitor the causes of flights arriving late. A total of 75% of flights are late because of weather, while 35% of flights are late because of ground operations. A full 10% of flights are late because of weather and ground operations. What is the joint probability that a flight arrives late because of weather and ground operations

Answers

Answer:

36% is the  joint probability that a flight arrives late because of weather and ground operations

Step-by-step explanation:

Given

% of flight late because of weather = 0.75

% of flight late because of ground operation = 0.35

% of flight late because of both weather and ground operation = 0.10

The probability of joint probability that a flight arrives late because of weather and ground operations is equal to

p (A and B) + {P(A) * P(B)}

0.10 + (0.75 * 0.35)

0.36

or 36%

Answer:36%

Step-by-step explanation:0.10 + (0.75 * 0.35)=0.36 then turn it to a percent which is 36%.

please someone help me with this ASAP with the workout!!

Answers

The answer is 18 cm
Half of 72 is 36
Since YZ is 30, you would subtract 30 from 36 in order to get XY, so you would get 6 for XY
Half of circle W is 24, since it says the diameter of it is 48
So you would subtract XY from half of the diameter of W in order to get WX
It would look like this:
24-6=18

Answer:

18cm

Step-by-step explanation:

How many pairs of opposite sides are parallel

Answers

One pair is parallel
1 of the sides are parallel

Distance between Train 1 and Train 2 = 95 miles.
Average speed of Train 1 = 45 mph.
Average speed of Train 2 = 60 mph.
If both trains leave at the same time and travel toward each other but on parallel tracks, in how much time will their engines be opposite each other? (Hint: When the engines are opposite each other, together the trains will have traveled 95 miles. Their relative speed of travel is the sum of their respective speeds, or 105 mph.)
Travel time = hours.

Answers

9514 1404 393

Answer:

  19/21 hours, about 54 minutes 17 seconds

Step-by-step explanation:

The time is found from ...

  time = distance/speed

  time = (95 mi)/(105 mi/h) = 95/105 h = 19/21 h

The trains will meet after 19/21 hours, about 54 minutes, 17 seconds.

Answer:

19

Step-by-step explanation:

How do I get from step 2 to step 3?

Answers

Answer:

do the floss

Step-by-step explanation:

I think you divide 16 on both sides and add them together.
But I really don’t know
Sorry :(


Given f(x) = 6(1-x), what is the value of f(-8)?

Answers

Answer:

7/3

Step-by-step explanation:

1x6

1x(-x)

subtract and solve

Beth wants to buy Christmas lights to decorate her new home. At various stores, Beth found lights priced from $6.99 a strand to $25.99 a strand. Beth bought almost $200 worth of the cheapest lights so that she could have as many lights on her house as possible. For Beth, Christmas lights are a(n) _____.

Answers

Answer:

Christmas lights are price based shopping products

Step-by-step explanation:

From the question we understand that, Beth bought as many cheapest lights as possible. This means that she places value over quantity than quality.

The above is an illustration of price based shopping products where customers (in this case, Beth) see all products (in this case, Christmas lights) as similar products, irrespective of their different qualities (after all, they all light Christmas trees).

Because of this, the customer will opt for least expensive items, leaving the more expensive items.

C = 172.7 cm
Use the formula, c = ad, and x = 3.14, to find the diameter of this circle whose circumference equals 172.7 cm.
A. 55 cm
B. 27.5 cm
O c. 542.278 cm
D. 5.5 cm
O E. 86.35 cm

Answers

Answer:

B

Step-by-step explanation:

Does anyone know what the answer please???

Answers

Answer: 8

As you can see, ABCD is similar to FECG which means its just a bigger or smaller version of the other. The sides change by a specific amount like times 2 or divided by 2

In this case abcd is 2x bigger thab fecg. You can see this by the side BC being 10 and it is the same side on the other shape being 5 so you know FECG is just ABCD x 1/2

Because of this since we know what FG is (4) on FECG we know y is 2x that side so it is 8.

Tom read 20 books, 12 magazines, and 18 newspaper articles last year.
Based on this data, what percentage of the material that Tom read is a magazine?

Answers

Answer:

Step-by-step explanation:

20 dude hahah

Pls help I’ll addd extra points

Answers

Answer: 3/5

Step-by-step explanation:6/10 6 divide by 2 and 10 divide by 2

hoped this helped:)

Answer:

[tex] \frac{3}{5} [/tex]

Step-by-step explanation:

[tex] \frac{6}{10} \div \frac{2}{2} [/tex]=

[tex] \frac{3}{5} [/tex] ....

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