Consider the following line integral. C xy dx + x2y3 dy, c is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 4).

Answers

Answer 1

It looks like the integral is

[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy[/tex]

Let's close the loop by adding a line integral over the line segment joining (1, 4) to (0, 0). Then the closed loop is the triangular region

T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x}

Since the integrand has no singularities over or on the boundary of T, we have by Green's theorem

[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy = \iint_T \left(\frac{\partial(x^2y^3)}{\partial x} - \frac{\partial(xy)}{\partial y}\right) \, dx \, dy = \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx[/tex]

Compute the double integral:

[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \int_0^1 \int_0^{4x} \left(128x^5 - 4x^2\right) \, dx = \frac{60}3[/tex]

From this result, we subtract the line integral over the extra line segment we added. Parameterize this path by

C' : {(1 - t, 4 - 4t) : 0 ≤ t ≤ 1}

The line integral over C' is

[tex]\displaystyle \int_{C'} xy \, dx + x^2y^3 \, dy = \int_0^1 (1-t)(4-4t)(-dt) + (1-t)^2(4-4t)^3(-4\,dt)[/tex]

[tex]\displaystyle \int_{C'} xy \, dx + x^2y^3 \, dy = \int_0^1 \left(256 t^5-1280 t^4+2560 t^3-2564 t^2+1288 t-260 \right) \, dt = -44[/tex]

so that the line integral over C alone is 60/3 - (-44) = 64.


Related Questions

Which of the following distinguishes prophase 1 of meiosis from prophase of mitosis?.

Answers

Based on a scientific study, the difference between prophase 1 of meiosis from prophase of mitosis is "homologous chromosomes pair up."

prophase 1 of meiosis vs. prophase of mitosis

Prophase 1 of meiosis is the first stage of meiosis which involves recombination and alleles crossing over genetic material to form non-identical haploid chromatids.

In Contrast, the prophase of mitosis is also the first stage of mitosis which splits the duplicated genetic fabric present in the nucleus of a parent cell to form new identical daughter cells.

However, one of the significant differences between prophase 1 of meiosis and prophase of mitosis in appearance is " homologous chromosomes pair up."

Hence, in this case, it is concluded that the correct answer is "homologous chromosomes pair up."

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Which description from "sugihara" best indicates that several hours have passed?.

Answers

Answer:

its A

Explanation:

hope this helps, pls lmk if its wrong

Promoters and enhancers are dna sequences both bound directly by ____________.

Answers

Answer:

Transcription factors

How does the author unfold the details of the text painter of light.

Answers

The author unfolds the details of the "Painter of Light" text when presenting Kinkade's life chronology.

We can arrive at this answer because:

"Painter of Light" is a text with a chronological structure, which presents a series of events that occurred in a timeline.In this text, this kind of structure is used for Kinkade's life chronology, showing the most important events in his life and how that made him relevant to introduce to readers.

It is important to point out that textual structure is the way a text is organized to present information to the reader.

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Answer: The answer is A

Explanation:

Which provides evidence of universe expansion that supports the big bang theory.

Answers

Answer:

Hubble's discovery in the 1920s of a relationship between a galaxy's distance from Earth and its speed

The link between a galaxy's speed and distance from Earth was discovered by Hubble in the 1920s.

What is Big Bang theory?

Big Bang theory is defined as the physical theory that explains how the universe expanded from an initial state of high density and temperature. The early evolution of the universe is explained by the Big Bang theory. In accordance with this idea, the Universe began in a very small, very hot, and very dense state. It has since grown, gotten less dense, and gotten cooler.

The Big Bang theory is backed up by two significant scientific discoveries: the link between a galaxy's speed and distance from Earth, discovered by Hubble in the 1920s. In the 1960s, the cosmic microwave background radiation was discovered.

Thus, the link between a galaxy's speed and distance from Earth was discovered by Hubble in the 1920s.

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A spherical balloon is inflating with helium at a rate of. How fast is the​ balloon's radius increasing at the instant the radius is ​ft? how fast is the surface area​ increasing?.

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Using implicit differentiation, and considering that the inflation rate is of 200 cubic feet per minute and the radius is of 5 feet, it is found that:

The radius is increasing at a rate of 0.6366 feet per minute.The surface area is changing at a rate of 80 feet squared per minute.

The volume of an sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

Applying implicit differentiation, the rate of change is given by:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

For this problem:

Inflation rate of 200 cubic feet per minute, hence [tex]\frac{dV}{dt} = 200[/tex]Radius is of 5 feet, hence [tex]r = 5[/tex]

Then:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

[tex]200 = 4\pi (5)^2\frac{dr}{dt}[/tex]

[tex]\frac{dr}{dt} = \frac{200}{100\pi}[/tex]

[tex]\frac{dr}{dt} = 0.6366[/tex]

The radius is increasing at a rate of 0.6366 feet per minute.

The surface area is:

[tex]S = 4\pi r^2[/tex]

Hence, the rate of change is:

[tex]\frac{dS}{dt} = 8\pi r\frac{dr}{dt}[/tex]

Hence:

[tex]\frac{dS}{dt} = 8\pi (5)(0.6366) = 80[/tex]

The surface area is changing at a rate of 80 feet squared per minute.

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A 400-kg box is lifted vertically upward with constant velocity by means of two cables pulling at 40. 0° on either side of the vertical direction. What is the tension in each cable?.

Answers

Answer:

2558 N.

Explanation:Each rope takes half, so the vertical component of the force on each rope is half of this, or 1960 N.. But they are pulling at a 40 degree angle, so if t is the tension then t*cos(40) = 1960. This gives t = 2558 N.

A researcher claims that the epinephrine signaling pathway controls a catabolic process in muscle cells. Which of the following statements best helps justify the researcher’s claim?.

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Catabolism is simply refered to asthe process or sequences of enzyme-catalyzed reactions. Ths statements that best helps justify the researcher’s claim is that Glycogen phosphorylase catalyzes the conversion of glycogen to glucose-1-phosphate.

Catabolism is the process through which a good number of big molecules in living cells are degraded.or broken down into smaller pieces.

Some of the chemical energy released during catabolic processes is conserved in the form of energy-rich compounds such as adenosine triphosphate [ATP].

When anabolic and catabolic processes are in balance state, tissue remains intact and in good shape.

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The comparative financial statements of marshall inc. Are as follows. The market price of marshall common stock was $82. 60 on december 31, 20y2.

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It should be noted that the working capital will be $1584000, the current ratio is 2.80 while the quick ratio is 2.20.

From the complete information, the working capital is calculated thus:

= Current asset - Current liabilities

= 2464000 - 880000

= 1584000

The current ratio will be:

= Total current asset / Total current liabilities

= 2464000 / 880000

= 2.80

The quick ratio will be calculated thus:

Total current asset = 2464000

Less: Inventory = 420000

Less: Prepaid expenses = 108000.

Total quick assets = 1936000

Total current liabilities = 8800000

Quick ratio = 2.20

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Outline three Jewish beliefs about shekinah

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Answer:

The three main beliefs at the center of Judaism are Monotheism, Identity, and covenant (an agreement between God and his people). The most important teachings of Judaism is that there is one God, who wants people to do what is just and compassionate.

Explanation:

Brainly. Com answers.

Answers

Answer:

what is this

Explanation:

tell right questions

What um im not sure if your looking for an answer or whatever

9. ¿Qué quiere decir Yanez cuando
dice que es de cáscara amarga"?
Ayuda please

Answers

Es muy probable que Yañez se haya referido a una persona amargada, de temperamento difícil y ocasionalmente atravesado.

El vocablo "ser de la cáscara amarga" es un término despectivo para referirse a personas amargadas, de temperamento difícil y ocasionalmente atravesado, el cual ha sido el significado más difundido.

Históricamente, ha cambiado de sentido durante varios siglos, en el siglo XVIII se empleaba para referirse a personas pendencieras y traviesas, en el siglo XIX por conservadores para referirse despectivamente de liberales y socialistas y en el siglo XX por socialistas para denominar despectivamente a conservadores y reaccionarios.

En síntesis, es muy probable que Yañez se haya referido a una persona amargada, de temperamento difícil y ocasionalmente atravesado.

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Based on the graph, what conclusion can be drawn about trade between the United States and China? The United States has a trade surplus with China. China’s economy is declining, which has harmed trade. The United States has a trade deficit with China. China’s economy is improving, which has helped trade.

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The conclusion that can be drawn is that the United states has a trade deficit with China.

What is a trade deficit?

This trade deficit is known to often takes place only when the value of a country's imports is said to be more than the value of their  exports in terms of physical goods and services.

Note a trade deficit implies that a country such as United States is buying more goods and services than they are actually selling and as such, the conclusion that can be drawn from the graph is that the United states has a trade deficit with China.

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Answer:

The United states has a trade deficit with China.

Explanation:

Its correct

You have a 20 year annuity with a present value of $575,000. If the apr is 6%, what is the monthly yield?.

Answers

Annuities allow us to measure the cost of making payments over a period of time. Given the entries in the question given, the monthly yield will be;

$4119.48

Since the interest will be compounded monthly, the number of periods will be 12. To determine the monthly payment from a payout annuity, use the formula;

Present value = Monthly yield (1 - (1 + APR/12)^-12 × n

                                             APR/12

Fixing the above into the equation;

$575,000 = PMT (1 - (1 + 0.06/12)^-12 × 20

                              0.06/12

$575,000 = PMT 139.6

Making PMT the subject of the formula,

PMT = 575,000/139.6

PMT = $4118.911

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I often relate to the following groups early childhood brainly.

Answers

whaaaaat ???????????

La probabilidad de que un caballo viva 20 años es 2/3 y la de que una vaca viva 20 años es 3/5, ¿cuál es la probabilidad de que tanto el caballo, como la vaca vivan 20 años?.

Answers

Por definición de probabilidad, la probabilidad de que tanto el caballo, como la vaca vivan 20 años es [tex]\frac{2}{5}[/tex].

En primer lugar, debes saber que la Probabilidad es la mayor o menor posibilidad de que ocurra un determinado suceso.

En otras palabras, la probabilidad establece una relación entre el número de sucesos favorables y el número total de sucesos posibles.

En este caso, se llama suceso A al evento de que un caballo viva 20 años, mientras que el suceso B será el evento de que una vaca viva 20 años.

La intersección de sucesos es una operación cuyo resultado está compuesto por los sucesos no repetidos y comunes de dos o más conjuntos.

Esto es, la intersección de sucesos {A∩B} es el suceso formado por todos los elementos que son, a la vez, de {A} y {B}.  De esta manera, el suceso {A∩B} se verifica cuando ocurren simultáneamente {A} y {B}.

Entonces, se debe calcular la probabilidad de que ocurra A y B al mismo tiempo, considerando que la probabilidad de la intersección de sucesos independientes (la probabilidad de cada uno de ellos no está influida porque el otro suceso ocurra o no, es decir, cuando ambos sucesos no están relacionados):

P(A∩B)= P(A)×P(B)

En este caso, la probabilidad de que ocurra A es [tex]\frac{2}{3}[/tex] y la probabilidad de que ocurra B es [tex]\frac{3}{5}[/tex]. Entonces:

P(A∩B)= [tex]\frac{2}{3}[/tex]×[tex]\frac{3}{5}[/tex]

P(A∩B)=[tex]\frac{2}{5}[/tex]

Finalmente, la probabilidad de que tanto el caballo, como la vaca vivan 20 años es [tex]\frac{2}{5}[/tex].

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Who intended to write an epic poem 12 books long? Question 3 options: Francis Drake Sir Walter Raleigh Edmund Spenser William Shakespeare.

Answers

Answer:

emund spencer

Explanation:

k12 test got it right have a great day xD

What is the equation of the translated function, g(x), if f(x) = x2? g(x) = (x – 4)2 6 g(x) = (x 6)2 – 4 g(x) = (x – 6)2 – 4 g(x) = (x 4)2 6.

Answers

Answer:

d

Explanation: just took the test on edge

Imagine that you are a writer for a leading newspaper company in the philippines brainly.

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If I was a writer, the implementation of a 24-hour curfew for minors in time of pandemic is vital in order to keep them safe.

This is an incomplete question. The question is about the implementation of a 24-hour curfew for minors in time of pandemic. A pandemic is an epidemic of an infectious disease which has spread over large regions and has affected several individuals.

During a pandemic, there's an outbreak of diseases that can be transmitted from person-to-person contact. Therefore, it's important for people to be safe.

To address this issue, there should be an implementation of a 24-hour curfew for minors in the time of pandemics. This is vital to keep them safe.

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How does the first amendment protect religious freedom for american citizens? choose exactly two answers that are correct.

Answers

Answer:

It lets people practice their faith in their own way and

It prevents the government from establishing a national religion.

Explanation:

A family has two cats named gordo and flaco. Gordo weighs 15 pounds and flaco weighs 8 pounds. A cat’s weight is classified as unhealthy if the weight is located in the top 5% or bottom 5% of all cat weights. The distribution of cat weights is approximately normal with mean 9. 5 pounds and standard deviation 1. 5 pounds. Which of the following is the best description of gordos and flacos weights?.

Answers

Yea I’m going home with you and I don’t have to go to do homework and I’m done ✔️ go to bed early

Help plz lol………………………….

Answers

Answer:

105/330

Explanation:

drama:

25 students

both:

60 students

sports:

140 students

total:

225 students

330-225=105

Which correctly applies the distributive property to show an equivalent expression to (8. 6)(–2. 5)? (8)(2) – (0. 6)(0. 5) (8)(–2) – (0. 6)(–0. 5) (8. 6)(2) – (8. 6)(0. 5) (8. 6)(–2) + (8. 6)(–0. 5).

Answers

Answer:

the answer is D or the forth answer or (8.6)(–2) + (8.6)(–0.5)

Explanation:

I know because I am doing the test right now

Pain does all of the following things except.

Answers

Answer:

A. indicate potential danger in environment

Explanation:

Klaus invested $8,000 in a savings account. If the interest rate is 3. 45%, how much will be in the account in 15 years by compounding continuously? round to the nearest cent.

Answers

Answer:13,422.62

Explanation:

Write an informative essay explaining what has caused the english spoken today to be different.

Answers

Answer:

fortnit

Explanation:rr

Some of the main influences on the evolution of languages include:

The movement of people across countries and continents, for example migration and, in previous centuries, colonisation. For example, English speakers today would probably be comfortable using the Spanish word “loco” to describe someone who is “crazy”.
Speakers of one language coming into contact with those who speak a different one. No two individuals speak identically: people from different geographical places clearly speak differently and even within the same community there are variations according to a speaker’s age, gender, ethnicity and social and educational background. For example, the word “courting” has become “dating”.
New vocabulary required for inventions such as transport, domestic appliances and industrial equipment, or for sporting, entertainment, cultural and leisure reasons. For example, the original late 19th-century term “wireless” has become today’s “radio”.
Due to these influences, a language always embraces new words, expressions and pronunciations as people come across new words and phrases in their day-to-day lives and integrate them into their own speech

What is created when rocks bend due to the compression of tectonic plates? Question 1 options: Faulting Subduction Folding Whipping.

Answers

Answer:

Third option: Folding

Explanation:

When the movement of tectonic plates causes stress and pressure on a rock, and it bends, it is called folding.

Hope this helps :)

are there other universes?

Answers

Answer:

no

Explanation:

If you believe that you have a water sample that is contaminated with barium, what could you add to it to test it?.

Answers

Answer: potassium sulfate

Explanation:

Which of the following most directly contributed to the change over time depicted on the two maps?.

Answers

Locations are often shown on a map. The option that directly contributed to the change over time depicted on the two maps is the The building of canals and roads.

In 1800, U.S. citizens and immigrants to the country often traveled majorly by horseback or on the rivers.

As time went by, crude roads and canals were made. It was later on that railroads was made which was used to move people and goods with greater efficiency.

Conclusively,  A map is shows the visual representation of a location and the various part that is found in that specific location.

See full question below

Which of the following most directly

contributed to the change over time depicted on

the two maps?

(A) The construction of a national highway

system

(B) The establishment of different time zones

across the country

(C) The building of canals and roads

(D) The use of diesel engines

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