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

someone please help me answer this!!

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Answer:

39

Step-by-step explanation:

You should use the pythagorean theorem!

You took out a loan for $15,000 for 3 years with an interest rate of 3.5%. Including interest, how much will you pay total?

Answers

Answer:

39%

Step-by-step explanation:

PLEASE HELP !! ILL GIVE BRAINLIEST !!

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Answer:

jkh and ihk

Step-by-step explanation:

Answer:

<JHK and IHK

Step-by-step explanation:

Help me im stuck answer a b c and d please I don't know if they right

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Answer:

It’s b

Step-by-step explanation:

Look at the photo! Please help

Answers

the answer is A

Explanation:

Who can figure out the answer (3 x 1) +(6x 100)=X

Answers

Answer:

26

Step-by-step explanation:

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:

Bob has a bulb factory that produces two types of bulbs: white light (x) and color light (y). It is known that the standard deviation of service life for the population of white light bulbs is hours and hours for color bulbs, both are normally distributed. He tested the mean service life of those two types of bulbs by randomly drawing a sample of 20 bulbs from each type. The estimated mean service life are hours and hours. Assume that . What is the absolute value of the t-statistic if the null hypothesis is that both types of bulbs have the same service life?

Answers

Answer:

The answer is "3.51".

Step-by-step explanation:

[tex]\to t=\frac{\bar{x}-\bar{y}}{\sqrt{\frac{\sigma_x^2}{n_x}+\frac{\sigma_y^2}{n_y}}}\\\\[/tex]

      [tex]=\frac{960-945}{\sqrt{\frac{14^2}{20}+\frac{13^2}{20}}}\\\\=\frac{15}{\sqrt{\frac{196}{20}+\frac{169}{20}}}\\\\=\frac{15}{\sqrt{\frac{196+169}{20}}}\\=\frac{15}{\sqrt{\frac{365}{20}}}\\\\=\frac{15}{\sqrt{18.25}}\\\\=\frac{15}{4.27}\\\\=3.51[/tex]

PLEASE HELP !! ILL GIVE BRAINLIEST !!

Answers

Answer: angles HIL and MLI are supplementary angles.

Hope this helps! :D

Angle- HIL and angle- JIL are supplementary, explanation

Lincoln Middle School is painting a circle on their playground with a radius of 18 feet. What will be the total area of the circle, in square feet?

Use π = 3.14, and round your answer to the nearest hundredth.

Answers

Answer:

1017.36

Step-by-step explanation:

area = 3.14 (18)square

3.14 (324)

1017.36

What is the ratio of -1,6,-36,216

Answers

Answer:

-6

Step-by-step explanation:

hope this helped <3

sphere has a diameter of 14 ft. What is its surface​ area?

Answers

good morning

A≈615.75ft²

have a great day

Please help!! Due in 45 minutes.

Answers

Answer:

[tex]x = \frac{56}{9} , y =-\frac{26}{3}[/tex]

Step-by-step explanation:

Calculator work :)

I got (56/9, -26/3)

hope this helps ! <3

How would one convert 6 lb to ounces (16 oz = 1 lb)?
O A. 6 lb
16 oz
1 lb
O B.
6 lb
16 OZ
O C. 6 lb x 16 oz
O D. 61bx
1 lb
16 oz

Answers

Answer:

6 * 16

Step-by-step explanation:

One pound is 16oz.

Multiply the number of pounds by 16.

6 * 16 = 96

6 pounds is 96oz.

Hope this helps.

Answer:6lb x 16oz/1lb

Step-by-step explanation:just took the test

Please solve
Step by step

Answers

i believe the answer is C :]

Preston has a car washing business. Last year he washed 20 cars a week. This year, he washed 1,200 cars. How many more cars did he wash this year than last year? *52 weeks=1 year

Answers

Answer:

160 cars

Step-by-step explanation:

The computation of the number of more cars he washed this year is given below;

Last year, he washed 20 cars a week so on yearly basis he washed

= 20 cars × 52 weeks

= 1,040 cars

And, this year he washed 1,200 cars

So, the number of more cars he washed this year is

= 1,200 cars - 1,040 cars

= 160 cars

please help me im stuck on this question​

Answers

Answer:

78.0 kilo

Step-by-step explanation:

85.8- 93.6= 7.8

101.4-93.6= 7.8

85.8-7.8 = 78.0 kilo

The selling price for a classic painting is $16,000, which is $2000 less than two times its original price. What was the original price of the painting?

Answers

Answer:

$9,000

Step-by-step explanation:

$16,000 + $2,000 = $18,000

$18,000/2 = $9,000

I think this is correct but I'm not sure.


Morty spent $54 on tulips and roses and bought a total of 14 flowers. If tulips cost $5 and roses $3

Let t = number of tulips bought

Let r = number of roses bought

a) Write the system.

b) How many of each flower did Morty buy? (Solve the system)

Answers

Answer:

a) Let's define the variables:

t = number of tulips bought

r = number of roses bought

We know that each tulip costs $5, and each rose costs $3.

Then the total cost will be:

$5*t + $3*r

We know that Morty spent a total of $54, then we have the equation:

$5*t + $3*r = $54

We also know that he bought a total of 14 flowers, then:

r + t = 14

Then the system of equations is:

$5*t + $3*r = $54

r + t = 14

b) To solve the system, first, we need to isolate one of the variables in one of the equations. I will isolate r in the second one:

r = 14 - t

Now we can replace this into the other equation:

$5*t + $3*r = $54

$5*t + $3*(14 - t) = $54

Now we can solve this for t.

$5*t + $3*14 - $3*t = $54

$2*t + $42 = $54

$2*t = $54 - $42 = $12

t = $12/$2 = 6

t = 6

He bought 6 tulips.

Now we can use the equation r = 14 - t

r = 14 - 6 = 8

r = 8

He bought 8 roses.

A sewing machine sews at a constant rate of 1,500 stitches per minute. If the equation, y = 1,500x represents the relationship between the number of minutes, x, and the total number of stitches, y, what is the independent and dependent variable? (EE.C.9b)​

Answers

Answer:

Step-by-step explanation:

x is the independent variable. y is the dependent variable.

Dependent variables take their values based on values of independent variables. In the considered case, we have:

Independent variable is x = number of minutesDependent variable is y = total number of stitches

What are independent and dependent variables?

Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.

If a variable is taking its values independently of any visible direct cause,  then that variable is called independent variable.

The variables who take their values based on some other variables' values are called dependent variables.

For the considered case, the two variables in consideration are:

x = number of minutesy = the total number of stitches

Time doesn't depend on number of stitches. Its thus, measuring an independent quantity.

The total number of stitches depends on how much time it passed since sewing. So the quantity 'y' depends on the value of 'x'

Thus, variable 'y' is dependent variable.

Therefore, in the considered case, we have:

Independent variable is x = number of minutesDependent variable is y = total number of stitches

Learn more about dependent and independent quantities here:

https://brainly.com/question/19622665

Help me and I’ll give you brainliest

Answers

Answer:

i think its 60

Step-by-step explanation:

Plz help me, ASAP look at the photo

Answers

Answer:

Input     Output

  0             1

  2              2

 -8            -3

100           51

Step-by-step explanation:

Given

The rule: input ⇒ ÷2+1 ⇒ output

Solve

0 ⇒ 0÷2+1 ⇒ 1

2 ⇒ 2÷2+1 ⇒ 2

-8 ⇒ -8÷2+1 ⇒ -3

100 ⇒ 100÷2+1 ⇒ 51

Hope this helps!! :)

Please let me know if you have any questions

Find the value of x in the figure below if RE is parallel to PM.

2.3 units
16 units
21 units
4.6 units

Answers

Answer:

21 units

Step-by-step explanation:

Since,

RE is parallel to PM,

( AR / RP ) = ( AE / EM )

( 7 / x ) = ( 6 / 18 )

( 7 / x ) = ( 1 / 3 )

x × 1 = 7 × 3

x = 21 units

Tiana deposited $500 into an account that earns 6% simple interest. How many years will it take for the value of the account to reach $2000

Answers

Answer:

Number of year = 50 year

Step-by-step explanation:

Given:

Amount deposit in account = $500

Rate of interest = 6 % = 0.06 (Simple interest)

Future amount = $2,000

Find:

Number of year

Computation:

A = P + I

2,000 = 500 + I

Amount of interest I = $1,500

I = PRT

1,500 = 500 x 0.06 x Number of year

1,500 = 30 x Number of year

Number of year = 1,500/30

Number of year = 50 year

What’s the correct answer for this question?

Answers

Answer:

10

Step-by-step explanation:

2(6+1) - |-10| + 3*2

= 2 (7) - (+10) + 6

= 14 - 10 + 6

= 20 - 10

= 10

Answer: 10

Step-by-step explanation:

Given

2 ( 6 + 1 ) - | -10 | + 3 × 2

Expand parenthesis

= 12 + 2 - | -10| + 3 × 2

Simplify absolute value

= 12 + 2 - 10 + 3 × 2

Do multiplication

= 12 + 2 - 10 + 6

Simplify

= 14 - 4

= 10

Hope this helps!! :)

Please me know if you have any questions

Given f(x) = 2x^2 - 3 and g(x) = x + 4.
What is (f g)(x)?

Answers

Answer:

2x³+8x²-3x-12

Step-by-step explanation:

It means function f times by function g.

so fg= (2x²-3)(x+4)=2x³+8x²-3x-12

How do you convert length to cm, in, ml etc.

Answers

Answer:

Use an online converter but there is something you should know

Step-by-step explanation:

There are two systems of measurement. The Imperial system (inch, mile, cups, ounces) and the Metric system (millimeter, centimeter, gram, kilogram).

Converting measurements in the imperial system by memory is very hard, but converting measurements in the metric system is more simple.

It is easier to learn by images so here is an image that explains it

Keep in mind that measurements like inches and centimeters are for distance, while gram and ounces are for weight.

Classify the angle pair using all names that apply

Answers

Answer:

Adjacent

Step-by-step explanation:

∠3 and ∠4 share a common vertex & arm

NEED ANSWER ASAP WILL GIVE BRAINLIEST FOR CORRECT ANSWER

Answers

The answer is the top one

These three side lengths make a triangle.
3 cm, 5 cm, 9 cm

A. True
B. False

Answers

Answer:

aa

Step-by-step explanation:

aaaaaaaaa i need points sorry

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