Evaluate the triple integral ∭EzdV where E is the solid bounded by the cylinder y2+z2=81 and the planes x=0,y=9x and z=0 in the first octant.

Answers

Answer 1

Answer:

I = 91.125

Step-by-step explanation:

Given that:

[tex]I = \int \int_E \int zdV[/tex] where E is bounded by the cylinder [tex]y^2 + z^2 = 81[/tex] and the planes x = 0 , y = 9x and z = 0 in the first octant.

The initial activity to carry out is to determine the limits of the region

since curve z = 0 and [tex]y^2 + z^2 = 81[/tex]

∴ [tex]z^2 = 81 - y^2[/tex]

[tex]z = \sqrt{81 - y^2}[/tex]

Thus, z lies between 0 to [tex]\sqrt{81 - y^2}[/tex]

GIven curve x = 0 and y = 9x

[tex]x =\dfrac{y}{9}[/tex]

As such,x lies between 0 to [tex]\dfrac{y}{9}[/tex]

Given curve x = 0 , [tex]x =\dfrac{y}{9}[/tex] and z = 0, [tex]y^2 + z^2 = 81[/tex]

y = 0 and

[tex]y^2 = 81 \\ \\ y = \sqrt{81} \\ \\ y = 9[/tex]

∴ y lies between 0 and 9

Then [tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \int^{\sqrt{81-y^2}}_{z=0} \ zdzdxdy[/tex]

[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{z^2}{2} \end {bmatrix} ^ {\sqrt {{81-y^2}}}_{0} \ dxdy[/tex]

[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{(\sqrt{81 -y^2})^2 }{2}-0 \end {bmatrix} \ dxdy[/tex]

[tex]I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{{81 -y^2} }{2} \end {bmatrix} \ dxdy[/tex]

[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81x -xy^2} }{2} \end {bmatrix} ^{\dfrac{y}{9}}_{0} \ dy[/tex]

[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81(\dfrac{y}{9}) -(\dfrac{y}{9})y^2} }{2}-0 \end {bmatrix} \ dy[/tex]

[tex]I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81 \ y -y^3} }{18} \end {bmatrix} \ dy[/tex]

[tex]I = \dfrac{1}{18} \int^9_{y=0} \begin {bmatrix} {81 \ y -y^3} \end {bmatrix} \ dy[/tex]

[tex]I = \dfrac{1}{18} \begin {bmatrix} {81 \ \dfrac{y^2}{2} - \dfrac{y^4}{4}} \end {bmatrix}^9_0[/tex]

[tex]I = \dfrac{1}{18} \begin {bmatrix} {40.5 \ (9^2) - \dfrac{9^4}{4}} \end {bmatrix}[/tex]

[tex]I = \dfrac{1}{18} \begin {bmatrix} 3280.5 - 1640.25 \end {bmatrix}[/tex]

[tex]I = \dfrac{1}{18} \begin {bmatrix} 1640.25 \end {bmatrix}[/tex]

I = 91.125


Related Questions

) LaTanya is decorating her living room and draws
a floorplan to help look at placement.
10
9
co
A. LaTanya wants to hang a pictur at the center
of the back wall. How do you find the point at
the center between A and B?

Answers

Answer:

56

Step-by-step explanation:

                                   

Can you please help with question 2 and explain your work?

Answers

Answer:

Find AC+CB

Step-by-step explanation:

Answer:

Find [tex]AC + CB[/tex]; 10

Find AB; 10

Step-By-Step Explanation:

[tex]AC (3) + CB (7) = 10[/tex]

Find AB is the same thing, just phrased differently.

(-2.8)^6 (Round to three decimal places as needed)

Answers

-2.8 • -2.8 • -2.8 • -2.8 • -2.8 • -2.8
=481.890

Answer:

481.890

Step-by-step explanation:

481.890304 rounded to the nearest hundredth will be 481.890


Identify the sequence below as arithmetic, geometric, or neither. Then find the next two terms a5 and a6
10, 30, 90, 270,

Answers

Answer:

Geometric sequence of common ratio = 3

a5  would be: 810,

and  a6  = 2430

Step-by-step explanation:

The sequence is a geometric sequence because each term is produced by multiplying the previous one by the factor 3 (called the common ratio)

then terms a5 and a6 would be: 810, and 2430  respectively

Sam can prepare 30 wall paintings in four weeks.How much time will he need to do 90 wall painting s​

Answers

sam needs 12 weeks.

explanation: if he can do 30 paintings in 4 weeks then find out if 30 can go into 90. since it can when you multiply it by 3, then also multiply 4 by 3 since he needs 3 times more than the original amount. in total, he will need 12 weeks

(x-1)2/3+(x-1)1/3-6=0

Answers

Answer:

x=7

Step-by-step explanation:

Add 6 to both sides

Simplify

Expand the parentheses

Add 1 to both sides

A store recorded the number of sweatshirts sold on several days throughout the year. The
scatterplot shows the relationship between the average daily temperature and the number of
sweatshirts sold.
Complete the following statement.
For every 10-degree increase in temperature, the store sells approximately
fewer
sweatshirts
A. 5
B. 10
C 30
D.50

Answers

Answer:

30

Step-by-step explanation:

For every 10-degree increase in temperature, the store sells around 50 fewer sweatshirts. The correct option is D.

What is regression analysis?

Regression analysis is a group of statistical procedures used in statistical modeling to determine the relationships between a dependent variable and one or more independent variables.

A scatter plot is a particular kind of plot or mathematical diagram that displays values for typically two variables for a collection of data. It uses Cartesian coordinates. When the points are coded, a further variable can be seen.

Given that store recorded the number of sweatshirts sold on several days throughout the year. The scatterplot shows the relationship between the average daily temperature and the number of sweatshirts sold.

Here is the scatter plot, it is observed that by increasing the temperature the number of sweatshirts sold is decreasing. For every 10-degree depression of temperature, the number of the sells is decreased by 50.

Therefore, for every 10-degree increase in temperature, the store sells around 50 fewer sweatshirts. The correct option is D.

To know more about regression analysis follow

https://brainly.com/question/26755306

#SPJ2

Question #1:
Select all the statements that are true of a least-squares regression line.
The regression line maximizes the residuals between the observed values and the predicted values.
The slope of the regression line is resistant to outliers.
In the equation of the least-squares regression line, ġ is an observed value when x is known.
The sum of the residuals is always close to zero.
The coefficient of determination measures how much of the variation in the y-values is explained by the regression line.
In the equation of the least-squares regression line, is a predicted value when x is known.

Answers

Answer:

1. The sum of the residuals is always close to zero.

2.The coefficient of determination measures how much of the variation in the y-values is explained by the regression line.

3. In the equation of the least-squares regression line, y hat is a predicted value when x is known

Step-by-step explanation:

The least square regression line is a line that makes distance from data points to the regression line to be as minimal as possible. This line is a best fit for the data points. Let's say we have a collection of numbers and a scatter plot, this line is a line that exists and best fits the data.

Therefore, the least square regression line minimizes sum of squared error to be close to zero. R² measures the extent to which variations in the value of y is explained by the regression line. In the equation of this line, y hat is a predicted value when x is known.

The least square regression line minimizes the sum of squared error such that the sum of the residual is zero or very close to 0. Hence, the true statements from the options given are :

Sum of residuals is always close to 0

The coefficient of determination measures how much of the variation in the y-values is explained by the regression line.

[tex]y_{hat} [/tex] is the predicted value when x is known.

The least square regression Line is used to create a Linear model in the form y = bx + c

The Coefficient of determination R² gives the proportion of the variation explained by the regression line.

The predicted value of y is obtained using the model of the Least Square Regression Line for a given value of x.

Outlier values often affects the performance and accuracy of the Least Square Regression Line.

Learn more :https://brainly.com/question/18405415

can i plz get help? on these ?

Answers

Step-by-step explanation:

she is showing how many wheels are on each bike and skateboard,on each bike there are 2 wheels,on each skateboard there are 4 wheels. sarahs is different because she shows how many wheels are on each of those bikes

a+2a-1=11


Be quick please :D

Answers

Answer:

[tex]a=4[/tex]

Step-by-step explanation:

So we have the equation:

[tex]a+2a-1=11[/tex]

First, combine like terms:"

[tex]3a-1=11[/tex]

Now, add 1 to both sides:

[tex]3a=12[/tex]

Divide both sides by 3:

[tex]a=4[/tex]

And we're done!

solve for y. y/6 = 3/9 simplify your answer as much as possible​

Answers

Answer: y=2

Step-by-step explanation:

y/6 = 3/9        multiply both sides by 6/1 (since 6/1 times y/6 equals 1y or just y)

y = 18/9          now that y is isolated, just simplify 18/9

y=2                 18 divided by 9 is 2

write a sentence as an equation


b is 380 more than the quantity y time 268​

Answers

Answer:

b is → b =

380 more → + 380

y time 268 → 268y

combine

b = 268y + 380

I need help with this ASAP

Answers

Answer:

x=5

Step-by-step explanation

Move all terms containing  x  to the left side of the equation.

4x-8=12

Move all terms not containing  x  to the right side of the equation.

4x=20

Divide each term by  4  and simplify.

x=5

You and two friends pay $40 for tickets. The cost was divided three ways in the ratio 1 : 3 : 6. How much did each person pay

Answers

Answer:

first person payed$4, second person payed$12 and the third person payed $24

Step-by-step explanation:

find the sum of the ratio

find

1 divided by the total ratio time $40 to get first person

follow in that order to get the amount each person payed.

\dfrac{4}{9},-\dfrac{4}{3},4, 9 4 ​ ,− 3 4 ​ ,4,

Answers

Answer:

[tex]-\frac{8}{9}[/tex]

Step-by-step explanation:

[tex]\dfrac{4}{9}-\dfrac{4}{3}\\\\\mathrm{Least\:Common\:Multiplier\:of\:}9,\:3:\quad 9\\\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\\frac{4}{3}=\frac{4\times\:3}{3\times\:3}=\frac{12}{9}\\\\=\frac{4}{9}-\frac{12}{9}\\\\\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\\\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{4-12}{9}\\\\=\frac{-8}{9}\\\\=-\frac{8}{9}[/tex]

Answer:

what?

Step-by-step explanation:

A local library claims it has 2.73x103 books. If there are 42 people in the building, how many books per capita are there?

Answers

Answer:

63 books per capita in the library

Step-by-step explanation:

Given

[tex]Books = 2.73 * 10^3[/tex]

[tex]People = 43[/tex]

Required

Determine the book per capita

To do this, we simply divide the number of books by number of person;

[tex]Average = \frac{Books}{People}[/tex]

[tex]Average = \frac{2.73 * 10^3}{43}[/tex]

[tex]Average = \frac{2.73 * 1000}{43}[/tex]

[tex]Average = \frac{2730}{43}[/tex]

[tex]Average = 63.488372093[/tex]

[tex]Average = 63[/tex] (Approximated)

Hence;

There are 63 books per capita in the library

find two consecutive odd integers such as that 6 times the lesser integer is 7 more than 5 times the greater integer​

Answers

Answer:

The first consecutive integer is 17 while the second is 19

Step-by-step explanation:

Let us say that the first odd integer is x

At this point, the second odd integer will be x+2.

This is because to obtain the next consecutive odd integer, 2 will have to be added to the original number.

From the question, we can set up an equation as shown below:

[tex]6x= 7+5(x+2)[/tex]

from this, we can simply evaluate and find out the value of x

[tex]6x=7 +5x +10\\x=17[/tex]

therefore, the first consecutive integer is 17 while the second is 19

Solve:
1. (12+a) / 47 = - 18

Answers

Answer:

a= -858

Step-by-step explanation:

46 times -18 equals -846

-846-12 equals -858

Answer:

a=-858

Step-by-step explanation:

12+a=846

a=-846-12

a=-858

calculate the length of the base of a parallelogram if the area is 135cm and it's height is 9cm

Answers

Answer:

15cm

Step-by-step explanation:

The formula to calculate the area of a parallelogram is base x height.

Since we know the height and area, we can write the equation:

135 = base x 9

Now we can just divide 9 from both sides to solve for base:

135/9=basex9/9

So we get:

Base = 135/9=15

The length of the base is 15cm.

Hope this helped!

Answer:

lol

Step-by-step explanation:

2. haha

3. haha.5.jsj

jayden has two jobs. his full time job pays $17 an hour. a part time job pays $9 an hour. last week jayden worked 32 hours at his full time job and 14 hours at his part time job

Answers

Answer:

670

Step-by-step explanation:

32 hours at 17  plus 14 hours at 9

32 *17 + 14 *9

544+126

670

Answer:

job 1 = 544 dollars he made job 2 = 126$

Step-by-step explanation:

You multiply the amount he made for 1 hour by the total hours same thing with job 2.

Find each product. Then determine which conclusion can be drawn based on the results.

√2•√2
√5•√7
√ 2•18
√2•√6
The product of two irrational numbers is always rational.
The product of two irrational numbers can be rational or irrational.
The product of two irrational numbers is always irrational.
The product of two irrational numbers cannot be determined.

Answers

Answer:

Second answer:

"The product of two irrational numbers can be rational or irrational"

Step-by-step explanation:

notice from the first product

[tex]\sqrt{2} \,* \,\sqrt{2} = \sqrt{4} = 2[/tex]

that the product of two irrational numbers can give us a rational one.

from the other three examples, the answer for the products always contains a square root that cannot be reduced, so they all result in an irrational number.

Then, depending on the type of irrationals used, the product can be either rational or irrational.

70% of 120 = 120x70/100
How do you figure this out

Answers

10% of 120 = 12
12 x 7 = 84
70% = 84

120 x 70 = 8400
8400 / 100 = 84

It’s either showing you that both sides of the equation equal to the same thing or that you can find 70% of 120 by using the steps on the right

HELP PLZ NEED ASAP AND BRAINLIEST Simplify the complex fraction. In complete sentences, explain the process that you followed to simplify the fraction. Include the LCD and simplified form in your answer. Complete your work in the space provided or upload a file that can display math symbols if your work requires it.

A-9/a / 1-3/a=

Answers

Answer:

the answer is a+9/2

Step-by-step explanation:

a-9/a/1-3/a

=a-9/a/-2/a

=a+9/a/2/a.

( dividing two negatives is equal to positive)

=a+9/a*a/2

doing reciprocal

=a+9*1/2

reduce the expression"a"

=a+9/2

find the product

answer is a+9/2

Hello what is 50+3 ? c h a t w i t h p e p s

Answers

Answer:

50+3=53

Step-by-step explanation:

mark as Brainliest

Answer:

53

Step-by-step explanation:

5+5+5+5+5+5+5+5+5+5+1+1+1

The function g is defined below . g(x) = (x - 5)/(x ^ 2 - 36) Find all values of x that are NOT in the domain of g. If there is more than one value, separate them with commas.

Answers

Answer:

-6, 6

Step-by-step explanation:

So we have the rational function:

[tex]g(x)=\frac{x-5}{x^2-36}[/tex]

The domain of a rational function is all real numbers except for when x is a zero of the denominator.

Thus, to determine the domain restrictions, set the denominator to 0 and solve for x:

[tex]x^2-36=0[/tex]

Add 36 to both sides:

[tex]x^2=36[/tex]

Take the square root of both sides:

[tex]x=\pm 6[/tex]

So, the values that are not in the domain of g is: -6, 6.

And we're done!

Mr.rodriguez invests half money in land a tenth in stocks and a twentieth in bonds he puts the remaining 35,000 in his savings account what is the total amount of money that Mr Rodriguez saves and invests

Answers

Answer:

Step-by-step explanation:

find the mode in the set 3,5,7,13,7,9,3

Answers

Answer:

3 and 7

Step-by-step explanation:

The mode of a set is the number that appears the most frequently. There can be multiple modes in a set. Looking at the given set, we see that the numbers that show up the most are 3 and 7 so that is our answer.

Answer:

3 and 7

Step-by-step explanation:

The mode means the number that appears the most.

hope this helps you :)

Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise. The number of ducks and pigs in a field totals 38. The total number of legs among them is 100. Assuming each duck has exactly two legs and each pig has exactly four legs, determine how many ducks and how many pigs are in the field. ducks pigs

Answers

5 legs because its 1000

what decimal is longer than 8.5 cm

Answers

Answer:

8.5555

Step-by-step explanation:

This number is not only larger, but also longer in digits than 8.5.

___________________________________________________I AM ALWAYS HAPPY TO HELP :)

I need help with #2 and 4 please help me T^T

Answers

Answer:

2. w = -90

4. b = 8

Step-by-step explanation:

Multiply both sides by the reciprocal of the number multiplying the variable.

2.

[tex] -\dfrac{2}{3}w = 60 [/tex]

[tex] -\dfrac{3}{2} \times (-\dfrac{2}{3}w) = -\dfrac{3}{2} \times 60 [/tex]

[tex] w = -\dfrac{180}{2} [/tex]

[tex] w = -90 [/tex]

4.

[tex] 9.6 = 1.2b [/tex]

[tex] \dfrac{1}{1.2} \times 9.6 = \dfrac{1}{1.2} \times 1.2b [/tex]

[tex] 8 = b [/tex]

[tex] b = 8 [/tex]

Other Questions
Read the excerpt from the Declaration of Independence.We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creatorwith certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. That tosecure these rights, Governments are instituted among Men, deriving their just powers from the consent ofthe governed, - That whenever any Form of Government becomes destructive of these ends, it is the Right ofthe People to alter or to abolish it, and to institute new Government.Which best describes the language in this excerpt?objective and timidO personal and casualcomplex and intellectualpassionate and logicalMark this and returnSave and ExitNextSubmit After learning how to fly, Wendy reduced her daily commute time by 75\%75%75, percent. Previously, her commute took mmm minutes.Which of the following expressions could represent Wendy's commute time, in minutes, after she learned how to fly? Which would best be described as abiotic?water in a streamfish in a streambacteria in the soilroots in the soil The area of the surface of the largest known star is about 1015 square miles. The area of the surface of the Earth is about 1011 square miles. How many times larger is the star's area? Which theory of the origin of government has to do with families growing into the role of ruling? what is the purpose of the cause and effect signal word therefore? 1. What are the "Big Five" personality factors? 2. How do they affect your leadership abilities and capabilities? 3. Which factor(s) was most strongly associated with leadership? 4. Discuss which of these personality traits you feel you possess and give a personal example of how they benefited you in a leadership context. The quotient of 1/3 and 4/3 The bottom number of a time signature shows how many beats there are per measure.TrueFalse Metal sphere A has a charge of ????. An identical metal sphere B has a charge of +2????. The magnitude of the electric force on sphere B due to sphere A is F. The magnitude of the electric force on A due to B must be:______. I need the percentage of the shaded area. B IS WRONG HEADS UP Select the correct answer.James is in a class at high school that his regular teachers teach. When he graduates, he plans on enrolling in the locatransfer some of the classes that he took while in high school. Why, can he do this?A.He won't be able to transfer any credits into his community college..His high school participated in the Dual Credit program.C.His community college doesn't take any high school credits.D.His community college takes articulated credits.Next PLZ HELP ASAP! ANSWER ALL FOR BRAINLIEST The number of hours a group of 12 children in Mrs. Smith's kindergarten class read in a day. The following information is available for Sandhill Company at December 31, 2017, regarding its investments.Securities Cost Fair Value2,500 shares of Myers Corporation Common Stock $36,200 $45,300900 shares of Cole Incorporated Preferred Stock 24,300 20,800 $60,500 $66,100Prepare the adjusting entry (if any) for 2017, assuming no balance in the Fair Value Adjustment account at January 1, 2017. Neither of Sandhills investments result in significant influence. Assume the securities as trading securities. Given f(x) = -4(6x - 5) + 60, what is the value of f(4)? PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :) 1. Ma maison2. La salle de bains3. Manger4. La tlvision5. Ma chambre6. Ranger7. Faire le lit8. Ma famille9. La cuisine10. Le sofa i dont know what to in this question true or false: the height from which cliff divers jump affects the velocity at which they will fall. velocity is speed in a certain direction.