Find the volume of the solid generated by revolving the region bounded by the x-axis, the curve y = 3x^4 , and the lines x = 1 and x = -1 about the x-axis.

Answers

Answer 1

Answer:

Let's define A as the area given by the integral:

[tex]\int\limits^1_{-1} {3x^4} \, dx[/tex]

Which is the area between the curve y = 3*x^4 and the x-axis between x = -1 and x = 1

To find the volume of a revolution around the x-axis, we need to multiply the area by 2*pi (a complete revolution)

where pi = 3.14

First, let's solve the integral:

[tex]\int\limits^1_{-1} {3x^4} \, dx = \frac{3}{5}(1^5 - (-1)^5) = \frac{3*2}{5} = \frac{6}{5}[/tex]

Then the volume of the solid is just:

V = (6/5)*2*3.14 = 7.536


Related Questions

HOW COULD MAKE 7 TO BECOME EVEN NO. WITHOUT FOUR FUNDAMENTAL PRINCIPLE
LIKE :
PLUS
MINUS
SOBRACTION
DIVISION​

Answers

Answer:

2,4,6,8,10,12,14,16,18,20

Answer:

How do you make the number 7 an even number without addition, subtraction or multiplication?

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22 Answers

Yogesh Rana, B.Sc. Mathematics, University of Delhi (2016)

Answered 4 years ago

You can remove alphabet S from SEVEN.

You can change the convention. Whole mathematics works like that. After all it is just a name, ie, call the numbers divisible by 2 odd and not divisible by 2 even. Everything will still work fine. You got to rename some theorems also.

Introduce and derive a new number system from the current number system, name the symbol 6 as seven and the symbol 7 as Six. Just rename the symbols.

Introducing a new number system and interchange position of 7 with an even number.

If we remove one number before 7 ( 1 - 6 ) with its name, we have again a new number system with base 9 and technically no. 7 is still no. 7 with value = 6.

These are some genuine ways rather than dividing.

ANSWERS OF DIVISION ARE TECHNICALLY WRONG AND RIDICULOUS BECAUSE DIVISION BY ‘x’ is MULTIPLICATION BY ‘1/x’ .

Tom has a steel box that has a capacity of 5 gallons. What is the maximum amount of fluid, in quarts, that this box can hold?
A. 10 qt.
B. 15 qt.
C. 18 qt.
D. 20 qt.

Answers

Answer:

d. 20 qt.

Step-by-step explanation:

4 quarts to a gallon so 4x5= 20

The answer is D

If 4 quarts = 1 gallon, then 5 gallons = 20 quarts
For example, 1/4 = 5/20

what is the ratio of 20cm to 1m​

Answers

9514 1404 393

Answer:

  1 to 5

Step-by-step explanation:

20 cm to 1 m = 20 cm to 100 cm = 20 to 100 = 1 to 5

Find the value of x to the nearest tenth. 2 4 x 8

Answers

192 because if you put 24 into 8 groups there are 192

Find the value of the polynomial when x=1 and y=-2

Answers

Answer:

the answer is : ................

5

The answer is 5 I think

If f(x) is a third degree polynomial function, how many distinct imaginary roots are possible?​

Answers

Answer:

1, 2, or 3

Step-by-step explanation:

if it's third degree then there must me 1 to 3 roots

hope you find this helpful :)

Answer: 0 or 2

Step-by-step explanation:

took test on edge2020

NO LINKS!!!!

Create a table and graph the function.
1. y = (x + 3)^2 + 2


2. y = 2(x - 2)^2 - 4

Answers

Hope this help!!!

Have a nice day!!!

What is the value of h(2)?
0 -2
0 -11
ОО
O 3

Need help fast!!!

Answers

-2 the point is being plot at -2

PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

9514 1404 393

Answer:

  (c) reflection about x-axis, shift right 1

Step-by-step explanation:

The transformation g(x) = p·f(x-h) causes the graph of the function f(x) to be shifted right by h units. It also causes the graph to be vertically scaled by the factor 'p'. When p is negative, the graph is also reflected across the x-axis.

Here, we have p=-2, h=1, so the graph is ...

reflected across the x-axisvertically stretched by a factor of 2shifted right 1 unit

This collection of transformations matches the 3rd choice.

_____

Additional comment

The +3 inside parentheses (square brackets) causes the graph to be shifted upward 3 units--before it is reflected and vertically scaled. The reflection across the x-axis causes that upward shift to look like a downward shift, and the vertical stretch causes that shift of 3 units to become a shift of 6 units. (All answer choices agree that the downward shift is 6 units, so we didn't really need to discuss that.)

To evaluate whether or not the intake of a vitamin or mineral is adequate, comparisons are made between the intake distribution and the requirement distribution. Here is some information about the distribution of vitamin C intake, in milligrams per day, for women aged 19 to 30 years:

Percentile (mg/d)
Mean 1st 5th 19th 25th 50th 75th 90th 95th 99th
84.2 31 43 47 60 79 103 126 141 180

Use the 5th, the 50th, and the 95th percentiles of this distribution to estimate the mean (±0.01) and standard deviation (±0.01) of this distribution assuming that the distribution is Normal.

μ = _________
σ = _________

Answers

Answer:

[tex]Mean=79[/tex]

[tex]\sigma=30.3951.[/tex]

Step-by-step explanation:

From the question we are told that:

[tex]Age Bracket :19-20[/tex]

[tex]5th\ percentile = 42[/tex]  

[tex]50th\ percentile = 79[/tex]  

[tex]95th\ percentile = 142.[/tex]

Generally the mean Median and mode of the 50th percentile is are all equal

[tex]Mean=Median=Mode[/tex]

Therefore

[tex]Mean=79[/tex]

Generally for Normal distribution

[tex]5th\ percentile\ = mean - 1.645*\sigma[/tex]  

[tex]95th\ percentile\ = mean + 1.645*\sigma[/tex]

Therefore

[tex](95th\ percentile\ - 5th\ percentile) = 2*(1.645*SD).[/tex]

[tex]\sigma=(95th\ percentile\ - 5th\ percentile)/3.29[/tex]

[tex]\sigma=\frac{142-42}{3.29}[/tex]

[tex]\sigma=30.3951.[/tex]

Name a pair of complementary angles in the diagram above.
21 and 22
Z2 and 23
24 and 25
0 27 and 29

Answers

Answer:

7&9

Step-by-step explanation:

Really, its just because, that's my explanation.

What is the volume of the solid whose cross- sections are circular disks perpendicular to the x-axis and with diameters on the region bounded by the curves y = x and y=x^2?

Answers

Answer:

the volume of the solid is [tex]\frac{\pi }{120}[/tex]

Step-by-step explanation:

Given the data in the question;

y = x and y = x²

so

x = x²

x - x² = 0

Radius will be; r = ( x - x² )/2

Area of the circular disk πr² = π[ ( x - x² )/2 ]²

A = [tex]\frac{\pi }{4}[/tex]( x - x² )²

So, our volume will be;

V = ₀∫¹ A(x) dx

we substitute

= ₀∫¹ [tex]\frac{\pi }{4}[/tex]( x - x² )² dx        

{ lets expand; ( x - x² )² = x(x-x²) -x²(x-x²) = x² - x³ - x³ + x⁴ = x² + x⁴ - 2x³  }

so we have;

=  ₀∫¹ [tex]\frac{\pi }{4}[/tex]( x² + x⁴ - 2x³ ) dx  

= [tex]\frac{\pi }{4}[/tex] [tex][[/tex] [tex]\frac{x^3}{3}[/tex] + [tex]\frac{x^5}{5}[/tex] - [tex]\frac{2}{4} x^4[/tex] [tex]]^1_0[/tex]

= [tex]\frac{\pi }{4}[/tex][ [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{5}[/tex] - [tex]\frac{2}{4}[/tex] ]

= [tex]\frac{\pi }{4}[/tex][ [tex]\frac{1}{30}[/tex] ]

V = [tex]\frac{\pi }{120}[/tex]

Therefore, the volume of the solid is [tex]\frac{\pi }{120}[/tex]

4m + 18 is called a
What expression

Constant
Term
Variable expression
Coefficient

Answers

Answer and Step-by-step explanation:

4m + 18 is an expression.

This is because it has terms and no equal/inequality sign.

#teamtrees #PAW (Plant And Water)

Answer: Constant

Step-by-step explanation: Its an Constant because every variable is different in the expression.

Find the missing length indicated

Answers

Answer:

D) 20

Step-by-step explanation:

Answer:

D) 20

Step-by-step explanation:

they are asking for the longest length of the triangle. as you can see, 20 is just over 15, and from the diagram, the missing length is just over 15 so we can apply our knowledge to come to the answer of 20.

Use two equations in two variables to solve the problem.
A merchant wants to mix peanuts and cashews, as shown in the illustration, to get 42 pounds of mixed nuts that will be sold at $6 per pound. How many pounds of each should the merchant use?

Answers

Answer:

   

Step-by-step explanation:

Giải các phương trình sau
√3x-√3=√3

Answers

Answer:

2

Step-by-step explanation:

√3x=√3+√3=2√3⇒x=2

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = 2}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \sqrt{3} x - \sqrt{3} = \sqrt{3} [/tex]

➺ [tex] \: \sqrt{3} x = \sqrt{3} + \sqrt{3} [/tex]

➺ [tex] \: \sqrt{3} x = 2 \sqrt{3} [/tex]

➺ [tex] \: x = \frac{2 \sqrt{3} }{ \sqrt{3} } [/tex]

➺ [tex] \: x = 2[/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35☂}}}}⋆[/tex]

Small circular disks are being cut from thin sheets of steel. The steel weighs 1.6 grams per square centimeter. The disks need to have a diameter of 5 centimeters.

(A) find the area of the disk to the nearest hundredth of a square centimeter. Show the steps in your calculation.

Answers

Answer:

[tex]A = 19.63cm^2[/tex]

Step-by-step explanation:

Given

[tex]d =5cm[/tex]

[tex]Weight = 1.6g/cm^2[/tex]

Required

The area (A) of the disk

This is calculated as:

[tex]A = \frac{\pi * d^2}{4}[/tex]

So, we have:

[tex]A = \frac{3.14 * 5^2}{4}[/tex]

[tex]A = \frac{3.14 * 25}{4}[/tex]

[tex]A = \frac{78.5}{4}[/tex]

[tex]A = 19.625[/tex]

[tex]A = 19.63cm^2[/tex] --- approximated

HELP QUICK I NEED ANSWER

Answers

Answer:

The answer is 23

Step-by-step explanation:

Answer:

the answer of the question is 23

What’s the standard form for 1,000,000+80,000+30+3

Answers

Answer:

1080033

Step-by-step explanation:

Answer:  1,080,033

=========================================

Explanation:

1,000,000 = 1 million

80,000 = 80 thousand

Adding those two would get us

1,000,000+80,000 = 1,080,000

Then we change those last two zeros at the end of "1,080,000" to 33 instead to get the final answer  1,080,033. This is done because we're adding 30+3 = 33 at the end.

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

Extra info:

The number 1,080,033 is slightly over 1.08 million1,080,033 = 1 million, 80 thousand, 331,080,033 = one million, eighty thousand, thirty-threeThe use of commas between the words is optional. It's to give a sense of the pacing or pauses when reading out the number.

A website posts evaluations on airlines. It posts the most positive and the most negative comments for each airline. Discuss the usefulness of this feedback for a reader wanting to know about the airline.

choose the correct statement below. SELECT ALL THAT APPLY:

A. The reader can accurately assess the airline based on the posted evaluations.

B. the reader cannot accurately assess the airline because the evaluations are not necessarily representative of all evaluations.

C. the reader cannot accurately assess the airline because the method of choosing the sample is unclear.

D. the reader cannot accurately assess the airline without reading all the evaluations. ​

Answers

Answer:

B. the reader cannot accurately assess the airline because the evaluations are not necessarily representative of all evaluations.D. the reader cannot accurately assess the airline without reading all the evaluations.

Step-by-step explanation:

Using the most positive and the most negative comments to evaluate the airlines will not be an accurate measure of the airline because these are not a good enough sample. The opinions of those who fall in-between the most positive and negative should also be included as they could have some vital details as well.

Also, in order to be completely accurate, all the comments of the airline should have been posted because this would represent the entire population of comments and so would give the best assessment.

Dawn has less than $60. She wants to buy 3 sweaters. What price of sweaters can she afford if all the sweaters are the same price? Let s be the price of each sweater. Write this as an inequality.​


(s will be the variable)

Answers

Answer: s < $20

Step-by-step explanation:

Since Dawn has less than $60 and wants to buy 3 sweaters, then the price of sweaters that she can afford if all the sweaters are the same price will be:

(3 × s) < $60

where,

s = price of each sweater

3s < $60

Divide both side by 3

3s/3 < $60/3

s < $20

The price of each sweater is less than $20

Use your graph to find estimates of the solutions to the equation x^2-x-6=-2

Answers

9514 1404 393

Answer:

  x ≈ -1.5 or 2.6

Step-by-step explanation:

It appears as though your graph crosses the line y = -2 at approximately x = -1.5 and also at x = 2.6.

These are estimates of the solutions to the equation.

  x ≈ {-1.5, 2.6}

Answer:

-2 and 3

Step-by-step explanation:

From the graph, the solution is the points where the curve cuts the x axis. From the graph, you can see that the equation cuts the x axis at two points that is at x=-2 and 3.

Hence the solutions to the equation is -2 and 3


Angles ABC and DBE are vertical angles. If m A. 180°
B. 38°
C. 52°
D. 128°

Answers

I think that the answer is b

(120+2x)+(70+2x)=15,000
not angles, area. also foiling

Answers

Answer:

x =3702.5

Step-by-step explanation:

Given data

(120+2x)+(70+2x)=15,000

Let us open the bracket

120+2x+70+2x=15,000

Collect like terms

120+70+2x+2x=15,000

190+4x=15000

4x=15000-190

4x= 14810

Divide both sides by 4

x=14810/4

x= 3702.5

Hence the value of x =3702.5

Find the margin of error for the 95% confidence interval used to estimate the population proportion. )n=460, x=60

Answers

Is there a picture ?

Is the figure line symmetric? If yes, how many lines of symmetry does the figure have?
Yes
A.No
B. Yes;3 lines of symmetry
C.Yes;6 lines of symmetry
D.Yes; 12 lines of symmetry
Please help. This is due today​

Answers

Answer:

yes 6 lines are symmetry

36 apples cost $6. how many apples can you buy for $1?

Answers

Answer:

16 cents

Step-by-step explanation:

6 divided by 36 = 0.16666667

Solve the inequality 0>_3x-2x

Answers

Answer:

x<0

Step-by-step explanation:

See image below:)

If x = -2, y = 3 and t = 2 then (x/y)t =

Answers

Answer:

-4/3

Step-by-step explanation:

2(-2/3)

= -4/3

Answer:

[tex]( \frac{x}{y} ) \times t \\ \frac{ - 2}{3} \times 2 \\ = \frac{ - 4}{3} [/tex]

determine whether the variable is qualitative or quantitative
street name and adress

Answers

Answer:

C

Step-by-step explanation:

Street name has nothing to do with numerical values, therefore it cannot be quantitative. If we take the two qualitative answers left, one of them says something about numbers, so it cannot be that one. C is the only one left over after process of elimination.

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