Evaluate the line integral, where c is the given curve. (x + 8y) dx + x2 dy, c c consists of line segments from (0, 0) to (8, 1) and from (8, 1) to (9, 0).

Answers

Answer 1

Parameterize the path from (0, 0) to (8, 1) by

• x(t) = 8t and y(t) = t

and the path from (8, 1) to (9, 0) by

• x(t) = 8 + t and y(t) = 1 - t

both with 0 ≤ t ≤ 1.

Over the first path, we have

[tex]\displaystyle \int_{C_1} (x+8y) \, dx + x^2 \, dy = \int_0^1 (8t + 8\cdot t) \cdot (8 \, dt) + (8t)^2 \cdot dt = \int_0^1 (128t + 64t^2) \, dt = \frac{256}3[/tex]

and over the second path,

[tex]\displaystyle \int_{C_2} (x+8y) \, dx + x^2 \, dy = \int_0^1 ((8 + t) + 8(1-t)) \cdot dt + (8+t)^2 \cdot (-dt) \\\\ = \int_0^1 (-48 - 23t - t^2) \, dt = -\frac{359}6[/tex]

and so the total line integral is

[tex]\displaystyle \int_C (x+8y) \, dx + x^2 \, dy = \frac{256}3 - \frac{359}6 = \boxed{\frac{51}2}[/tex]


Related Questions

Which is NOT an aspect of individual sports? A. Must recover quickly from mistakes B. Deeper skill set for the game C. Better cardiorespiratory fitness than team sports D. Good cooperation with others.

Answers

Answer:Option D on edge just took the quiz

Explanation:

Answer:

D, good cooperation with others

Explanation:

Have the day you deserve :)

The graph of ______________________ is called hyperbola.

Answers

Answer:

the mix of two parabolas is called graph of hyperbola

Once you identify a potential conflict of interest which questions should you ask yourself next.

Answers

Once you have identified a potential conflict of interest, the question you should ask yourself next is: Have I disclosed the matter to the appropriate parties?

A conflict of interest can be defined as a situation in which the aims, objectives, and concerns of two (2) or more parties do not align or are completely incompatible. Thus, a conflict of interest leads to an unreliable and compromised decision-making process.

The first step in the conflict of interest is identifying the purpose of the conflict and the last step is the management of this conflict by an appropriate party or authority.

Hence, after the identification of potential conflict of interest, the question you should ask yourself next is; have I disclosed the matter to the appropriate parties?

In conclusion, a potential conflict of interest should be disclosed to the appropriate parties as soon as it is identified.

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Answer:

Are threats to compliance with the code at an acceptable level?

Explanation:

According to AICPA Professional Code of Conduct: "When an actual conflict of interest has been identified, the member should evaluate the significance of the threat created by the conflict of interest to determine if the threat is at an acceptable level."

Is 5/16 bigger than 1/2.

Answers

No, half of 16 is 8 meaning that 1/2 is bigger than 5/16.

Answer: No

Explanation:

1/2|

8/16

So

8/16 is a larger than 5/16

Los verbos recíprocos solamente funcionan cuando hay por lo menos _____ personas que hacen la cosa a la otra.

Answers

Answer:

2

Explanation:

Answer: 2

Explanation:

just took test

Which method of choosing teams would be most hurtful to lower skilled players? A. Having team captains pick one player at a time B. Having people count off C. Having people team up according to birthdays D. Having people draw numbers.

Answers

Answer:

The answer has to be A

Explanation:

Cause that has to down grade one's skill

Answer:

Which method of choosing teams would be most hurtful to lower skilled players?

A. Having team captains pick one player at a time <<<------ Correct

B. Having people count off

C. Having people team up according to birthdays

D. Having people draw numbers.

Explanation:

Edge 2022 100% on unit test

You have a friend who lost 15 pounds of fat while on a diet. Where did the fat/mass go?.

Answers

It got converted into energy I guess

Which is a goal of the human genome project brainly.

Answers

Answer: the complete mapping and understanding of all the genes of human beings.

Find the measure of a negative angle coterminal with 95°.

Answers

The measure of a negative angle coterminal with 95° are for any integer n 95° – (1,080n)°. Thus, option (b) is correct.

What is coterminal?

Angles in common position (angles with the starting side on the positive x-axis) that have a shared terminal side are referred to as coterminal angles. It's as easy as subtracting or adding 360° or 2 to each inclination, depending on whether it's measured in degrees or trigonometric functions. There are an endless amount of coterminal angles to be discovered.

The measure of a negative angle coterminal with 95°

Ф + 360 n

n is any integer (negative or positive)

Ф = 95°,

- 3n is an integer,

The co-terminal angles of 95° are,

= 95° + 360° (-3n)

= 95° - (1080 n)° ; for any integer n.

As a result, the measure of a negative angle coterminal with 95° are for any integer n 95° – (1,080n)°. Therefore, option (b) is correct.

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Your question is incomplete, but most probably the full question was.

for any integer n 95° – (1,450n)°, for any integer n 95° – (1,080n)°, for any integer n 95° – (780n)°, for any integer n 95° – (340n)°,

Albert einstein (1)______ born in germany in 1879. In 1895, he (2)______to school in switzerland. After college, he (3)______ in switzerland for 28 years, and then he (4)______ to the us in 1933. He (5)______ in 1955 in the us.

Answers

Answer:

1) was

2) went

3) move to the

4) will be

5) is

Explanation:

I hope it will help u

Albert Einstein WAS born in Germany in 1879. In 1895, he WENT to school in Switzerland. After college, he LIVED in Switzerland for 28 years, and then he MOVED to the US in 1933. He DIED in 1955 in the US.

Albert Einstein was a German physicist who developed the theory of relativity.

Albert Einstein is popularly known due to his huge intelligence, and he won the Nobel Prize (1921).

Einstein's work is today very important to understand the origin of the Universe.

In conclusion, Albert Einstein WAS born in Germany in 1879. In 1895, he WENT to school in Switzerland. After college, he LIVED in Switzerland for 28 years, and then he MOVED to the US in 1933. He DIED in 1955 in the US.

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Parallel lines cut by a transversal coloring activity.

Answers

Answer:

this is the answer

Explanation:

hope it will help you

An apple ipad sells for $699. 00 on ebay. The markup is 30% on cost. What is the total cost of the ipad sold on ebay?.

Answers

Answer:

$ 537.75

Explanation:

How is a poem's rhyme scheme marked and identified? upper or lowercase letters, such as "ABAB" Roman numerals, such as "I, II, I, II" Arabic numerals, such as "1212" punctuation symbols, such as "!?!?".

Answers

Answer:

A is the correct answer

Explanation:

took the test         yahoot

A poem's rhyme scheme is marked and identified as: upper or lowercase letters, such as "ABAB"

What is a poem?

A poem can be defined as a literary work which is made up of written or spoken words that are chosen and arranged carefully in separate lines, based on their sound (diction), meaning, and rhythm.

The types of poems.

In English literature, there are different types of poems and these includes:

Free verseSonnetOdeElegiesFixed verse

Generally, a poem's rhyme scheme is marked and identified as upper or lowercase letters, such as "ABAB."

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Which statements accurately describe satellite motion? check all that apply.

Answers

What are the options?

Your 15-year-old brother comes home with the great news that he has decided to buy his first car and has just agreed to give $10,000 to someone on craig's list. He signed the contract and just needs to pay the seller and pick up the car. Your dad is upset and calls the seller to tell him your brother will not be buying the car. What can the seller do?.

Answers

The seller can’t do anything. The brother is 15 years old and underage, therefore, he had no say if his legal guardian says no. The seller going behind the back h guy of the father would be a crime.

Alicia refused to take that job so that she had more time on her studies.

Answers

In order for Alicia to prepare for the meeting with her boss, it's important that she should plan to discuss the ways attending college is helping her to be better at her job.

From the complete information, Alicia is going to college and working. Her employer wants to give her more roles. An effective way to communicate with her employer is to prepare a list of suggestions on how her workload might be reassigned.

She can also sign a contract to stay with the company for a period of time in order to show her commitment and thereby reach a mutually agreeable resolution.

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The office supply superstore sells pens for 60 cents.

Answers

Is there suppose to be a picture or more to the question?

Global competition accelerated product development by competitors.

Answers

Answer:

its b

Explanation:

What is the combined length of all the buttons longer.

Answers

Answer:

4 leght the button is 3 length

Explanation:

if you don't understand here's my link

https//com. ph

What is the total kinetic energy of a 0. 15 kg hockey puck sliding at 0. 5 m/s and rotating about its center at 8. 4 rad/s? the diameter of the hockey puck is 0. 076 m.

Answers

The mass of the puck is

m = 0.15 kg.

The diameter of the puck is 0.076 m, therefore its radius  is

r = 0.076/2 = 0.038 m

The sliding speed is

v = 0.5 m/s

The angular velocity is

ω = 8.4 rad/s

The rotational moment of inertia of the puck is

I = (mr²)/2

 = 0.5*(0.15 kg)*(0.038 m)²

 = 1.083 x 10⁻⁴ kg-m²

The kinetic energy of the puck is the sum of the translational and rotational kinetic energy.

The translational KE is

KE₁ = (1/2)*m*v²

      = 0.5*(0.15 kg)*(0.5 m/s)²

      = 0.0187 j

The rotational KE is

KE₂ = (1/2)*I*ω²

      = 0.5*(1.083 x 10⁻⁴ kg-m²)*(8.4 rad/s)²

      = 0.0038 J

The total KE is

KE = 0.0187 + 0.0038 = 0.0226 J

Answer: 0.0226 J

Which equation is equivalent to StartRoot x EndRoot 11 = 15? x 11 = 225 x 121 = 225 StartRoot x EndRoot = 15 11 StartRoot x EndRoot = 15 minus 11.

Answers

Answer:

Answer is shown in the image! (D)

Explanation:

What is the following product? Assume x greater-than-or-equal-to 0 (4 x StartRoot 5 x squared EndRoot 2 x squared StartRoot 6 EndRoot) squared 80 x Superscript 4 Baseline 8 x Superscript 4 Baseline StartRoot 30 x EndRoot 24 x Superscript 4 80 x Superscript 6 Baseline 8 x Superscript 5 Baseline 8 x Superscript 5 Baseline StartRoot 30 EndRoot 24 x Superscript 4 104 x Superscript 4 104 x Superscript 4 16 x Superscript 4 Baseline StartRoot 30 EndRoot.

Answers

Answer:

1

Explanation:

Answer:

D

Explanation:

you just gotta trust me

A company is selling used office equipment for 12000.

Answers

Answer:

So?what do u need to know or work ou in this question

Explanation:explanation is

Two uniform solid balls are rolling without slipping at a constant speed.

Answers

wha t is the question ?

Which of the following is considered one of the most famous pieces of art of the Renaissance? a. Gates of Glory b. Gates of Paradise c. Gates of Gold d. Gates of Purgatory Please select the best answer from the choices provided A B C D.

Answers

Answer:B Gates of Paradise

Explanation: I got it right and cuz I said soooo

Gates of Paradise, is considered one of the most famous pieces of art from the Renaissance. Therefore option B is correct.

It refers to a set of gilded bronze doors created by the renowned Italian sculptor Lorenzo Ghiberti. These doors are part of the Baptistery of San Giovanni in Florence, Italy.

Ghiberti spent over two decades working on these doors, completing them in 1452. The intricate relief sculptures on the doors depict various scenes from the Bible, showcasing Ghiberti's mastery of perspective and naturalistic representation.

The name "Gates of Paradise" was given by Michelangelo, highlighting the exceptional artistic quality of the doors.

They are celebrated for their beauty, artistic innovation, and significant contribution to the Renaissance art movement.

Therefore option B is correct.

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Nationalism resulted in a powder keg on the Balkan Peninsula in 1914, and all that was needed was a spark to set it off. What provided this spark and set in motion the events that led to the Great War? Question 4 options: the mobilization of forces by Serbia and Bosnia-Herzegovina the visit of Otto von Bismarck to the Bosnian capital of Sarajevo the assassination of Archduke Franz Ferdinand of Austria the assassination of Kaiser Wilhelm II of Germany.

Answers

Answer:

the assassination of Archduke Franz Ferdinand of Austria

Explanation:

took the test

Answer:

the  Assassination of Franz Ferdinand

Explanation: took the k12 test lol

Meiosis is a type of cell division that is specific to(1 point).

Answers

Answer:

The answers are:

1.Sex cells

2.Can compare similarities found in reference sequences to determine any potential relations

3.Somatic cell mutations are not passed to the next generation.

4.They are both forms of cell division.

5.They both can pass on genetic variations that can be inherited.

Explanation:

Meiosis is a type of cell division that is specific to germ cells. The correct option is C.

What are germ cells?

Germ cells differentiate to create male along with female gametes, sperm, and unfertilized eggs (oocytes or ova), and then meiosis occurs to generate a haploid set of chromosomes.

After that, haploid gametes combine to form a diploid zygote, which develops into a new individual.

The eggs and sperm that reproducing organisms use to pass on their genomes from generation to generation are referred to as germ lines (parents to offspring).

Germ cells are egg and sperm cells, as opposed to somatic cells, which are all other cells in the body.

Meiosis is a type of cell division that produces four gamete cells while reducing the number of chromosomes in the parent cell by half. This process is necessary for the production of egg and sperm cells for reproduction.

Thus, the correct option is C.

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Your question seems incomplete, the missing options are:

A. daughter cells

B. sperm cells

C. germ cells

D. egg cells

Ann works in a supermarket for $10. 00 per hour. If her pay is increased to $12. 00, then what is her percent increase in pay?.

Answers

Her pay has increased by 20%

(12-10)100/10 = 20

Which research paper would this article best support? ""Discovering Filmmaking in the Twenty-First Century"" ""A Discussion of Filmmaking in the Modern Film Industry"" ""The Realities of Filmmaking in the Twenty-First Century"" ""Tracking the Intricacies of the Modern Filmmaking Process"".

Answers

There are a lot of research paper constantly been written everyday.  The research paper that this article best support tracking the intricacies of the modern filmmaking process.

A research paper is simply known to be a piece of academic writing that gives a detailed analysis, interpretation, and argument based on thorough independent research.

Writing a research paper often demands the individual to show a good knowledge of your topic, engage with a variety of sources, and make a good contribution to the debate.

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Answer:

Explanation:

its d tracking...

Using the equations 2 sr(s) + o₂ (g) → 2 sro (s) ∆h° = -1184 kj/mol co₂ (g) → c (s) + o₂ (g) ∆h° = 394 kj/mol determine the molar enthalpy (in kj/mol) for the reaction c(s) + 2 sro(s) → co₂ (g) + 2 sr(s).

Answers

Considering the Hess's Law, the enthalpy change for the reaction is 790 kJ/mol.

Hess's Law indicates that the enthalpy change in a chemical reaction is the sum of the ∆H of each stage of the reaction will give us a value equal to the ∆H of the reaction when it occurs in a single stage.

In this case you want to calculate the enthalpy change of:

C(s) + 2 SrO(s) → CO₂ (g) + 2 Sr(s)

You know the following reactions, with their corresponding enthalpies:

Equation 1: 2 Sr (s) + O₂ (g) → 2 SrO (s) ∆H° = -1184 kJ/mol

Equation 2: CO₂ (g) → C (s) + O₂ (g) ∆H° = 394 kJ/mol  

First step

In this case, first, to obtain the enthalpy of the desired chemical reaction you need 1 mole of C (s) on reactant side and it is present in second equation. But since this equation has 1 mole of C (s) on the product side, it is necessary to locate this on the reactant side (invert the reaction). And when an equation is inverted, the sign of ΔH also changes.  

Second step

Now, 2 moles of SrO (s) must be a reactant and is present in the first equation. Since this equation has 2 moles of Sr0 (s) on the product side, it is necessary to locate the O on the reactant side (invert the reaction) and the sign of ΔH changes.

Summary

In summary, you know that two equations with their corresponding enthalpies are:

Equation 1:  2 SrO (s) → 2 Sr (s) + O₂ (g)     ∆H° = 1184 kJ/mol

Equation 2: C (s) + O₂ (g) → CO₂ (g)     ∆H° = -394 kJ/mol

Adding or canceling the reactants and products as appropriate, and adding the enthalpies algebraically, you obtain:

C(s) + 2 SrO(s) → CO₂ (g) + 2 Sr(s)     ΔH= 790 kJ/mol

Finally, the enthalpy change for the reaction is 790 kJ/mol.

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