Set up an integral that represents the area of the surface obtained by rotating the given curve about the x-axis. x = t + e, y=et, ostsi 6'( dt Use a calculator or computer to find the surface area correct to four decimal places.

Answers

Answer 1

A ≈ 2π√(1 + e²) ∫[0,6] et dt ≈ 2π√(1 + (2.71828)²) ∫[0,6] et dt  surface area

To find the area of the surface obtained by rotating the curve x = t + e, y = et (where t ranges from 0 to 6) about the x-axis, we can use the formula for the surface area of revolution.

The formula for the surface area of revolution is given by:

A = ∫[a,b] 2πy√(1 + (dy/dx)²) dx

In this case, we need to express y and dy/dx in terms of t. Let's start by finding dy/dx.

Given:

x = t + e

y = et

Differentiating y with respect to x:

dy/dx = dy/dt ÷ dx/dt

dy/dt = e (differentiation of et with respect to t)

dx/dt = 1 (differentiation of t + e with respect to t)

So, dy/dx = e/1 = e.

Now, we can rewrite the integral using the parameter t:

A = ∫[a,b] 2πy√(1 + (dy/dx)²) dx

A = ∫[0,6] 2π(et)√(1 + e²) dt

A = 2π√(1 + e²) ∫[0,6] et dt

To evaluate the integral, we can use a calculator or computer. Substituting the values a = 0, b = 6, and e ≈ 2.71828 (the base of natural logarithm), we can calculate the surface area:

A ≈ 2π√(1 + e²) ∫[0,6] et dt ≈ 2π√(1 + (2.71828)²) ∫[0,6] et dt

Evaluating this integral using a calculator or computer will yield the surface area of the rotated curve around the x-axis, correct to four decimal places.

learn more about "surface area":- https://brainly.com/question/16519513

#SPJ11


Related Questions

Please Help


How is an object's acceleration affected by its mass and the forces acting on it?

Answers

Answer:

Step-by-step explanation:

The acceleration of an object increases with increased forced and decreases with increased mass which is in the same direction as the force.

Which of the following activities is not associated with the purchase and payments business process? Select one: a. Buying products and services O b. Receiving goods O c. Recording payments to vendors d. Selling products and services

Answers

The activity that is not associated with the purchase and payments business process is Selling products and services.

therefore d. Selling products and services is correct.

Business process is a set of activities carried out in a systematic manner, aimed at achieving specific results.

The purchase and payment process are important in businesses as it involves the payment of vendors for goods and services bought.

The activities associated with the purchase and payment business process includes buying products and services, receiving goods, recording payments to vendors, and verifying and approving invoices.

The sales of goods and services, on the other hand, are part of the sales process, not the purchase and payment process.

for such more question on business process

https://brainly.com/question/28436755

#SPJ11

using statistics helps us make decisions based on what kind of evidence?

Answers

Using statistics helps us make decisions based on empirical evidence, which is obtained through data analysis and inference.

Statistics provides us with a set of tools and methods to collect, analyze, and interpret data. By applying statistical techniques, we can make decisions based on evidence derived from empirical observations and measurements.

Statistics allows us to summarize and describe data, identify patterns and relationships, and draw conclusions from samples or populations. It helps us quantify uncertainty and assess the strength of evidence supporting different claims or hypotheses.

Decision-making based on statistics involves making inferences about a larger population based on the information available from a sample. By using probability theory and statistical models, we can estimate population parameters, test hypotheses, and make predictions about future events or outcomes.

Statistics provides a systematic and rigorous framework for evaluating evidence and reducing bias in decision-making. It allows us to objectively assess the reliability and validity of information, making decisions that are informed by data-driven analysis rather than intuition or anecdotal evidence.

In summary, statistics helps us make decisions based on evidence obtained through data analysis, enabling us to draw reliable conclusions, quantify uncertainty, and make informed choices in various fields such as business, medicine, social sciences, and more.

Learn more about parameters here:

https://brainly.com/question/29911057

#SPJ11

Sally has 14 diamonds and she puts 6 in the ground how many more diamonds does sally have?

Answers

Answer:

Sally would have 8 diamonds left

Need help on both pleaseeee then I will be finished and need the someone to explain what the words define

 Need help on both pleaseeee then I will be finished and need the someone to explain what the words define

Answers

Answer:

Linear pair angles

Step-by-step explanation:

Angle 5 and six are linear because they are both on the same line.

HI
I WANT AN ANSWER THAT
HOW WILL I MAKE r the subject of the formula
A= ½πr2,

Answers

Answer:

r = √(A/π)

Step-by-step explanation:

HI

I WANT AN ANSWER THAT

HOW WILL I MAKE r the subject of the formula

A= ½πr²,

inverse formula

r = √(A/π)

6g + 1, for g = 0 i need it in a sentence

Answers

Answer:

6*0 +1 = 1

Step-by-step explanation:

if g equals 0 the answer is 1

An isosceles triangle has a perimeter of 46 inches. The base is 6 less than twice each of the congruent legs. What is the sum of the lengths of the two congruent legs?

Answers

Answer: 26 inches

Step-by-step explanation:

An isosceles triangle has two congruent legs.

1) Set up the equations

P = b + 2L

b = 2L-6

2) Substitute for variables

46 = (2L - 6) + 2L

3) Solve the equation

46 = 4L - 6

52 = 4L

13 = L

4) Solve the problem

It asks for what is the sum of the two congruent legs

13 + 13 = Ans

26 = Ans

Can anyone help me on this math test real quick here is one of the questions!!

Can anyone help me on this math test real quick here is one of the questions!!

Answers

Answer:

D. 9/16

Step-by-step explanation:

3/4*3/4=9/16

Answer:

9/16

Hope this helped you!

V₁=13L
P₁ = 8 atm
V₂=7L
P₂= ?? atm

Answers

Answer:

14.85

Step-by-step explanation:

P₁V₁ = P₂V₂

13 x 8 = P₂ x 7

P₂ = (13 x 8)/7

  = 104/7

P₂ = 14.85 atm

Find value of x and y

Find value of x and y

Answers

3x=6
3/3. 6/3
X=2

(2) +2=y-1
4=y-1
+1. +1
5=y

hi i need help on question 20! pls

hi i need help on question 20! pls

Answers

Answer:

the answer is 3

Step-by-step explanation:

the formula gives the length of the side, s, of a cube with a surface area, sa. how much longer is the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters?

Answers

As per the formula of surface area of cube, the length of the cube is 5.45 meters.

The general formula to calculate the surface area of the cube is calculated as,

=> SA = 6a²

here a represents the length of cube.

Here we know that  the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.

When we apply the value on the formula, then we get the expression like the following,

=> 180 = 6a²

where a refers the length of the cube.

=> a² = 30

=> a = 5.45

To know more about Surface area here.

https://brainly.com/question/29298005

#SPJ4

Write an expression having only 2 terms that is equivalent to 2x - 3. Explain how you wrote the expression amd how you can check that it is equivalent.​

Answers

Answer:

2x -3 =2x + 3

Step-by-step explanation:

Addition is commutative so as subtraction so 2x-3=2x+3



Given f (x)=9-14/x, find all c in the interval [2, 7] that satisfy the Mean Value Theorem

Answers

The value of c is √14 in the interval [2, 7], which satisfies the Mean Value Theorem.

By definition, the mean value theorem is

f'(c) = [f(b) - f(a)]/b - a

So, in this case, we know that a = 2 and b = 7.

Now, we need to find f(2) and f(7) by replacing those values with the given function

f(x) = 9 - 14/x

f(7) = 9 - 14/7 = 9 - 2 = 7

So, f(b) = f(7) = 7.

f(x) = 9 - 14/x

f(2) = 9 - 14/2 = 9 - 7 = 2

So, f(a) = f(2) = 2

Then, we replace all values,

f'(c) = [f(b) - f(a)]/b - a

= (7 - 2)/(7 - 2)

= 5/5

= 1

Now, calculate the derivative of the function, which has to be equal to 1,

f(x) = = 9 - 14/x

f'(x) = 14/x² = 1

Now, we solve the equation to calculate the value of c,

14/x² = 1

x² = 14

x = √14

Therefore, c = √14 is the value inside the given interval that satisfies the mean value theorem.

To know more about Mean Value Theorem, here

https://brainly.com/question/29107557

#SPJ4

Shade 3/4 on the grid

Answers

What grid????? There’s no grid
shade 3 spots and leave one open

Help me thank you so much

Help me thank you so much

Answers

\(\huge\text{Hey there!}\)


\(\maths{\sqrt{90}\)

\(\mathsf{{= \sqrt[3]{10}}}\)

\(\mathsf{= \sqrt{3^2\times10}}\)

\(\mathsf{= \sqrt{3\times 3 \times10}}\)

\(\mathsf{= \sqrt{9\times10}}\)

\(\mathsf{= \sqrt{90}}\)

\(\mathsf{= 9.48683298051}\)

\(\mathsf{\approx 9.48683298}\)

\(\mathsf{\approx 9.5}\)


\(\large\textsf{Thus, it is a little over 9 but not quite 10 yet..}\)


\(\huge\text{Therefore, your answer should be: \boxed{\mathsf{Option\ A. \ W}}}\huge\checkmark\)


\(\huge\text{Good luck on your assignment \& enjoy your day!}\)


~\(\frak{Amphitrite1040:)}\)

Question 6
In the diagram of the flower bed below, are the triangles congruent by the AAS
Congruence Theorem?
yes
No

Answers

Yes, the flower bed below, are the triangles congruent by the AAS Congruence Theorem.

We have to given that,

In the diagram of the flower bed below are the triangles.

Now, By the given diagram,

Two triangle are shown.

Here, One side are common.

In both triangle, Measure of one angle is 90 degree

And , By definition of alternate angle one pair of angle is equal.

Hence, By ASA congruency theorem given triangles are congruent.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Question 6In the diagram of the flower bed below, are the triangles congruent by the AASCongruence Theorem?yesNo

A cyclist rides a distance of 36 km at an average speed of 16 km/h.

Calculate the time taken to complete this ride. Give your answer in hours and minutes.

Please Help!

Answers

Answer:

2.25 hours, or 2 hours and 15 minutes.

Step-by-step explanation:

All we do is 36/16 which is 2.25. 0.25 or 1/4 of an hour is 15 minutes. So, your answer is 2 hours and 15 minutes.

It takes 2 hour and 12 minutes for the cyclist to complete the ride of 36km distance.

What is unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Total distance covered by cyclist= 36km

Average speed of the cyclist = 16km/hr

Therefore, using unitary method:

                16 km distance takes time = 1hr

Therefore, 1 km distance takes time =(1/16)hr

Therefore, 36 km distance takes time = (1/16)×36 hr

                                                     =(1/4)×9 hr

                                                     =9/4 hr

                                                     =2.25 hr

                                                      =(2+0.25)hr

                                                      =2hr+0.25hr

                                                      =2hr+0.25×60minutes

                                                      =2hr and 15 minutes.

Hence, it takes 2hr and 15 minutes for the cyclist to complete 36 km rides.

To learn more about unitary method click here:

https://brainly.com/question/21179768

#SPJ3

7. Eight centimeters on the map represent two kilometers in reality. Determine the scale of this​

Answers

Answer:

8 centimeters : 2 kilometers =

1 centimeter : 1/4 kilometer

A random sample of voters from three cities is asked to indicate political party affiliation. The results are given in the table. City Political Party Affiliation Democrat Independent Republican Miami 211 57 132 Austin 126 84 190 Detroit 158 96 146 To test whether the proportion of party affiliations for each city is the same, which inference procedure is appropriate to use?

Answers

The appropriate inference procedure to use when testing whether the proportion of party affiliations for each city is the same is the Chi-Square Test for Independence.

The Chi-Square Test for Independence is appropriate in this case because it allows you to test the relationship between two categorical variables (in this case, city and political party affiliation) using a contingency table (like the one provided). The test helps determine whether there is a significant association between the variables or if the observed frequencies are due to chance.

To perform the Chi-Square Test for Independence, follow these steps:

1. Create a contingency table with the observed frequencies of each combination of city and political party affiliation.

2. Calculate the expected frequencies for each cell of the table, assuming there is no association between the variables.

3. Calculate the chi-square test statistic, which is the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies.

4. Determine the degrees of freedom, which is equal to (number of rows - 1) * (number of columns - 1).

5. Compare the calculated test statistic to the critical value from a chi-square distribution with the determined degrees of freedom and an appropriate significance level (typically 0.05).

6. If the test statistic is greater than the critical value, reject the null hypothesis that there is no association between the variables, and conclude that the proportion of party affiliations for each city is not the same.

In your case, you would apply this procedure using the given data for the three cities and their political party affiliations.

Learn more about Chi-Square Test:

https://brainly.com/question/4543358

#SPJ11

List the coordinates of FOUR vertices that create the feasible region on the graph. Submit your answer in the form of FOUR ordered Pairs (x, y)

List the coordinates of FOUR vertices that create the feasible region on the graph. Submit your answer

Answers

Answer:

see below

Step-by-step explanation:

The feasible region is the shaded area. We just need to find the coordinates of its vertices. These are (200, 200), (300, 0), (500,0) and (300, 200).

what is the next number in the sequence? 9….16….24….33…

Answers

The given sequence is 9, 16, 24, 33. To find the next number, let's look for a pattern in the differences between the terms.

The difference between 16 and 9 is 7, between 24 and 16 is 8, and between 33 and 24 is 9.

The pattern in the differences is that they are increasing by 1 each time. So, the next difference would be 10.

To find the next number, we add the next difference to the last term in the sequence. Adding 10 to 33 gives us 43.

Therefore, the next number in the sequence is 43.

To find the next number in the given sequence, we looked for a pattern in the differences between the terms. We observed that the differences were increasing by 1 each time. Using this pattern, we added the next difference to the last term in the sequence to find the next number.

The next number in the sequence 9, 16, 24, 33 is 43.

To know more about   sequence   visit

https://brainly.com/question/30262438

#SPJ11

MATH
Use the Law of Detachment to draw a conclusion from the two given statements.
If not possible, write not possible.
1) If a person went to the concert, then they had a ticket to get in to the show.
2) Nadia went to the concert.
Start

Answers

It is possible yea it is

Rob has 40 coins, all dimes and quarters, worth $7.60. How many dimes
and how many quarters does he have?
... please solve this using if systems of equations

Answers

seen you with ur ex

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. f(x)=2(x 2
+3)(x+1) 2
−3, multiplicity 1 , crosses the x-axis; −1, multiplicity 2 , crosses the x-axis None −1, multiplicity 2 , touches the x-axis and turns around -3, multiplicity 1 , crosses the x-axis; −1, multiplicity 2 , touches the x-axis and turns around. −1, multiplicity 2 , crosses the x-axis

Answers

The polynomial function \(\(f(x) = 2(x^2+3)(x+1)^2\)\) has zeros at -3 with multiplicity 1, and -1 with multiplicity 2. The graph of the function crosses the x-axis at -3 and -1.

To find the zeros and their multiplicities, we set \(\(f(x)\)\) equal to zero and solve for \(\(x\).\)

Setting \(\(f(x) = 0\),\) we have:

\(\[2(x^2+3)(x+1)^2 = 0\]\)

Since the product of two factors is zero, at least one of the factors must be zero. Thus, we solve for \(\(x\)\) in each factor separately:

1. \(\(x^2 + 3 = 0\):\)

  This equation does not have real solutions since the square of a real number is always non-negative. Therefore, this factor does not contribute any real zeros.

2. \(\(x + 1 = 0\):\)

  Solving for \(\(x\), we find \(x = -1\).\) This gives us a zero at -1 with multiplicity 1.

Since the factor \(\((x+1)^2\)\) is squared, the zero -1 has a multiplicity of 2.

Therefore, the zeros for the polynomial function are -3 with multiplicity 1 and -1 with multiplicity 2. The graph of the function crosses the x-axis at both zeros.


To learn more about polynomial function click here: brainly.com/question/29054660

#SPJ11

What is the value of y=10x+2 when x=4

Answers

Answer:

y = 42

Step-by-step explanation:

Given

y = 10x + 2 ← substitute x = 4

y = 10(4) + 2 = 40 + 2 = 42

Answer:

=42

Step-by-step explanation:

y=10(4)+2

10 x 4 = 40

40 + 2 = 42

y=42

The measures of two angles are (4x + 39) and (16x - 12). What is the value of x that will make the two
angles congruent?
А
4.25
B
2.55
с
1.35
D
2.25

Answers

Answer:

A= 4.25

Step-by-step explanation:

4x+39−16x=16x−12−16x

−12x+39=−12

−12x+39−39=−12−39

−12x=−51

-12x/-12 = -51/-12

x=17/4

17/4= 4.25

The value of x that will make these two angles congruent is A. 4.25.

What is congruency?

When angles are of equal measure we say that they are congruent to each other similar is for the sides of a figure when the corresponding sides of a similar figure are of the same length we say that the sides are congruent to each other.

We know two angles are congruent when they are of equal measure, Therefore we have to equate these two angles with each other.

So, (4x + 39) = (16x - 12).

4x + 39 = 16x - 12.

4x - 16x = -12 - 39.

-12x = -51.

12x = 51.

x = 51/12.

x = 4.25.

learn more about congruency here :

https://brainly.com/question/7888063

#SPJ5

Divide 500 among aryl,joy and kenneth such that arlyn's share is 2/3 of joy's share ang joy's share is 2/3 of Kenneth's share how much will each get?

Answers

The amount that each will get from the given fraction of amount is :

Kenneth's share = $236.842

Joy's share = 2/3 x = $157.895

Arlyn's share = 4/9 x = $105.263

Given that,

Total amount = 500

Let the fraction of amount of money Kenneth gets = x

The fraction of amount of money Joy gets = 2/3 of Kenneth's share

                                                                       = 2/3 x

The fraction of amount of money Arlyn gets = 2/3 of joy's share

                                                                         = 2/3 (2/3 x)

                                                                         = 4/9 x

Now,

x + 2/3x + 4/9 x = 500

(9x + 6x + 4x) / 9 = 500

9x + 6x + 4x = 4500

19x = 4500

x = 236.842

Kenneth's share = $236.842

Joy's share = 2/3 x = $157.895

Arlyn's share = 4/9 x = $105.263

Hence each will get $236.842, $157.895 and $105.263.

Learn more about Fractions here :

https://brainly.com/question/30423291

#SPJ1

The volume of a cylinder, V, in terms of radius, r,
and height, h, is given by V = πr 2
h. If a cylinder has
a height of 6 meters, express the radius as a function
of V and find the radius of a cylinder with volume of
300 cubic meters.

Answers

Answer:

See explanation

Step-by-step explanation:

Volume of a cylinder = πr²h

Solve for r

V = π * r² * h

r² = V/πh

Find the square root of both sides

r = √V/πh

If height = 6 meters and volume = 300 cubic meters. Find r

r = √V/πh

= √(300/3.14*6)

= √(300/18.84)

= √15.923566878980

r = 3.9904344223381

Approximately,

r = 4 meters

Other Questions
CSE310 Asymptotic notation true false WITH EXPLANATION(i) If f(n) E O(n) and g(n) S(n), then f(n)+g(n) E e(n) G) If f(n) E O(n), then n2 x f(n) E O(n3 (k) If f(n) E O(n) and g(n) E O(n2), then f(n) x g(n) E O(n3 (1) If f(n) (n log n), then f(n) n e o(n2 log n). (m) If f(n) (n logn) and g(n) (n logn), then (1). (n) If f(nje 0(n) and 9(nje O(n2), then lim. -0 (o) If f(n) E (n) and g(n) E (n), then g(n) g(n) 91 g(n If 1 droplet of water falls from a pipe every 10 seconds. How many droplets of water would have fallen from the pipe in 10 minutes The sum of terms of an arithmetic progression is . andthe common difference is . Find the first term of the series Which type of insurance does a person need if they wish to continue to receive apaycheck while they are out of work due to an injury? Select the processes that are used by cells to strip electrons off of the c-h bonds of a glucose molecule. A man on a 135-ft vertical cliff looks down at an angle of 1613' and sees his friend. a) How far away is the man from his friend?b) How far is the friend from the base of the cliff? EMS providers arrive at an unsafe scene. What should they do? What was the change in mass of the contents of the crucible? compare the mass after heating to the mass before heating. In(22n)+12no Consider the sequence 40n+sin(n) In=1 Answer the following questions: () Does the sequence converge? Answer: Click for List (ii) What is the limit of the sequence? The limit of the sequence is Why do most large companies have outside directors on their boards? what is a function of the minaret on an islamic mosque? Read the passage from "Should We Be Banning Plastic Shopping Bags?Shoppers like plastic bags because they are convenient and lightweight. Individual bags keep fruits and vegetables clean and separate from other items in a shopping cart. They keep frozen foods from getting other groceries wet on the way home. Also, they keep purchases like bug spray from accidentally contaminating food. Which best summarizes the authors agenda in this passage?ResponsesA: The author's agenda is for shoppers to be able to continue using plastic bags.B: The author's agenda is to get people to store fruits and vegetables in plastic bags.C: The author's agenda is to educate people on how to use plastic bags to keep frozen food dry.D: The author's agenda is to stop food contamination by getting shoppers to use plastic bags. How many pennies are on the nth square? 2n 2n 1 2n + 1 2n 1 2n + 1 how would you prepare 10ml of a 0.050m sucrose solution from the 0.10m solution? (hint: this is a dilution problem, use m1v1 = m2v2) Is the answer I choose right and if not please tell me what it is Nd Please tell me how to show the work also ! which of the following is likely to be associated with deserts? a) complete absence of vegetation b) complete absence of precipitation c) basins of internal drainage d) prevalence of soil creep e) lack of trees other than palms The Chess Club is having a bake sale to raisemoney for a tournament. The club must raise atleast three times what they raised at the lastbake sale. What is the minimum amount theymust raise if the last bake sale raised $45?A $15B $45C $90D $135 You will edit and revise your argumentative essay then submit an improved final draft. You will also submit a reflection paragraph to discuss three changes you have made and how they improved your essay.View the grading rubric for the assessment.Make edits and revisions based on written feedback, your DBA, and reminders in this lesson.Write a reflection paragraph discussing three changes you made to your essay. Explain how each change strengthened your argument.Save the final draft and your reflection paragraph to your computer or drive.Submit your complete final draft and your reflection paragraph in 06.09 Perfect Your Final Draft. Which of the following equations shows a slope of 5 for the line the equation represents _________________ are people who flee their homeland to avoid the dangers of war.