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

How does groundwater become polluted? a. Pollutants mixed with water pass through permeable layers above the aquifer. B. Factories dump their waste directly into aquifers. C. Refuse infiltrates the water table when garbage is dumped. D. All of the above Please select the best answer from the choices provided A B C D.

Answers

Answer:

A

Explanation:

Pollutants mixed with water pass through permeable layers above the aquifer.

What is Groundwater?

Water that is found underground in saturated regions beneath the surface of the earth is known as groundwater. The water table is the term for the saturated zone's upper surface.

Contrary to popular perception, underground rivers are not created by groundwater. Similar to how water fills a sponge, it fills the pores and cracks in subterranean materials like sand, gravel, and other rock.

Rock materials are referred to as aquifers if groundwater flows naturally out of them or if it can be pumped out of them. One of the most significant natural resources for the country is groundwater, which is found in aquifers beneath the Earth's surface.

Therefore, Pollutants mixed with water pass through permeable layers above the aquifer.

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How can you turn conflict into a positive experience brainly.

Answers

by learning from past mistakes

Energy released by the electron transport chain is used to pump h+ into which location in eukaryotic cells?.

Answers

Answer:

Energy released by the electron transport chain is used to pump H+ into the mitochondrial intermembrane space - Option D-.

Explanation:

There exist three proteinic complexes immersed in the internal mitochondrial membrane. These complexes have the electron transporters and the enzymes necessary to catalyze the electron transference from one transporter to the other. In complexes, I and III released energy by electrons provokes changes in membrane transport protein conformation. These changes make possible the protons transport against their concentration gradient, going from the mitochondrial matrix toward the intermembrane space. The protons concentrations difference between the matrix and the intermembrane space represents released energy.

Select the items that are needs from your credit card statement.

Answers

Answer:

A summary and detailed list of payments, credits, purchases, balance transfers, cash advances, fees, interest, and other transactions.

One common attention getter used in a speech introduction is.

Answers

Answer:

Asking a question that you want the audience to answer or consider

Explanation:

Please mark as brainliest if this helped you

Who was the U. S. President when Texas became part of the United States?.

Answers

Answer:

president James K. Polk

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

This excerpt best illustrates Kurt Vonnegut’s message that everyone in a society should have equal talent and beauty. Advances in technology should be closely monitored. Television viewing limits individual thought and creativity. Absolute equality prevents personal freedoms of expression.

Answers

Answer:d

Explanation: I did it

Answer:

The answer is D

Explanation:

The oblique pyramid has a square base. An oblique pyramid has a square base with a base edge length of 2 centimeters. The vertical height of the pyramid is 3. 75 centimeters. What is the volume of the pyramid? 2. 5 cm3 5 cm3 6 cm3 7. 5 cm3.

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Answer:

What brought an end to efforts during the late thirteenth century to form an alliance of European states and the il-khanate of Persia aimed at crushing Islamic forces in the eastern Mediterranean

Explanation:

Answer:

58One-third cm3

Explanation:

E2020

At stp which gas will diffuse more rapidly than ne.

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Answer:

neon

Explanation:

The graph of ______________________ is called hyperbola.

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Answer:

the mix of two parabolas is called graph of hyperbola

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

Dwayne is making a cladogram using a diagonal line. Where should he place the least primitive organism? E A B D.

Answers

Answer:

E

Explanation:

Answer: E

Explanation: edge 2022

After years of maintaining a steady population of 32,000, the population of a town begins to grow exponentially. After 1 year and an increase of 8% per year, the population is 34,560. Which equation can be used to predict, y, the number of people living in the town after x years? (Round population values to the nearest whole number. ) y = 32,000(1. 08)x y = 32,000(0. 08)x y = 34,560(1. 08)x y = 34,560(0. 08)x.

Answers

Answer:

A: y=32,000(1.08x)

Explanation:

correct on edge <3

Which of the following would not be considered a characteristic of communism.

Answers

All citizens fall into one of three social classes

A city's population is represented by the function P=25,000(1. 0095)t , where t is time in years. How could the function be rewritten to identify the daily growth rate of the population? What is the approximate daily growth rate? Drag and drop the choices into the boxes to correctly complete the table. If a value does not match, do not drag it to the table. Function Daily growth rate.

Answers

Answer:

The yearly growth rate is 0.95%. For the daily growth rate, change t, to t/365/

Explanation:

Scan some articles for words formed by affixes.

Answers

Remember, affixes simply refers to words that are attached to a word (add the beginning or end of the word) to form a new word or word form.
Find five examples of such words in a sentence are:
"Because of the temperature, the pot was untouchable." We notice here that the word was formed from the word touch; by adding 'un' at the beginning and 'able' to the end we form the word 'untouchable'.
"They were unbeatable for the whole season." We can notice here that the word was formed from the word beat; by adding 'un' at the beginning and 'able' to the end we form the word 'unbeatable'.
"There is a lot of misinformation about the pandemic." We observe here that the word was formed from the word information; by adding 'mis' at the beginning we form the word 'misinformation'.
"I successfully wrote my exams." We also observe here that the word was formed from the word success; by adding 'fully' at the end which forms the word 'successfully'.
"He feels joyful today." We observe that the word was formed from the word joy; by adding 'ful' at the end which forms the word 'joyful

Read the excerpt from "Harlem. " Does it stink like rotten meat? Or crust and sugar over- like a syrupy sweet? Read the excerpt from "The Weary Blues. " Droning a drowsy syncopated tune Rocking back and forth to a mellow croon In both poems, Hughes uses the imagery to establish tone. Offer background information. Convey a criticism. Conjure pleasant memories.

Answers

Answer: establish tone

Explanation: ed 2021

There are different kinds of tones. Hughes uses the imagery to establish tone.

What does establishing tone implies?

For one to establish a tone means to set a kind of  quality, feeling, etc., by the approach one use in  speaking or writing.

Tone is known to be an author's attitude toward a specific subject. The tone can be seen by looking at word choices and phrases that is used by the author or looking at the language used.

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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

Distinguish the various types of landforms formed by wind.

Answers

Answer:

Wind Eroded Arid Landforms – Deflation basins, Mushroom rocks, Inselbergs, Demoiselles, Demoiselles, Zeugen , Wind bridges and windows. Depositional Arid Landforms – Ripple Marks, Sand dunes, Longitudinal dunes, Transverse dunes, Barchans, Parabolic dunes, Star dunes and Loess.

Answer:

Fixed Sand Sheets. Fixed sand sheets are undulating sandy hills that are found. ...

Ventifacts. Ventifacts are stones of various sizes that have been faceted by abrasion. ...

Ripples. Ripples are small sand waves with wavelengths of about one meter. ...

Yardangs. ...

Sand Dunes.

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What is the combined length of all the buttons longer.

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Answer:

4 leght the button is 3 length

Explanation:

if you don't understand here's my link

https//com. ph

why do people catfish people for

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The person uses catfishing in order to appear as a better version of themselves by using a fake identity.

Which of the following is not a traditional food found in Uruguay?.

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Answer:

Gnocchi is not a traditional food found in Uruguay.

Explanation:

Identify the true statements about surface tension.

Answers

Answer:

surface tansion increases as the temperature of the liquid rises

This natural resource was once very abundant in Western Europe and helped power the Industrial Revolution. Question 4 options: Iron Coal Oil Water.

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Answer: Its Coal

Explanation: I did the K12 quiz

Use the completed profile: american reformer sheet for this lesson to answer the following question. Please enter the letter of the choice in the blank. Which reformer did you choose? a. Robert owen b. John noyes c. Lyman beecher d. Horace mann e. Dorothea dix.

Answers

Answer:

I know 100% that Lyman Beecher = Temperance (I took the test)

I believe

Dorothea Dix = education

Horace mann= prisons/asylums

John Noyes = utopian society

No clue which one goes with Robert Owen

Hope this helps :)

Consider the two male oryx that are shown below. Mc005-1. Jpg Which of Charles Darwin’s main points is depicted in the image? Organisms within a population compete with each other to survive. Over time, beneficial variations will be passed on to future generations. More offspring are produced than can be supported by an environment. All organisms within a population have an equal chance for survival.

Answers

Answer:

option B

Explanation:

Answer:

B

Explanation: is the best answer

If two populations are merged, each with different frequencies of an allele at a locus, and random mating occurs immediately, how long will it take to achieve a hardy–weinberg equilibrium in the new population?.

Answers

If two populations with different frequencies of an allele at a locus randomly mate, then only ONE generation will take to achieve Hardy–Weinberg equilibrium. This principle is used in population genetics.

The Hardy–Weinberg equilibrium is a principle used in population genetics to calculate allele and genotype frequencies in a population.

The Hardy-Weinberg equilibrium states that allele and genotype frequencies in a population will remain constant from one generation to the next in absence of different evolutionary forces.

The evolutionary forces that may alter the Hardy-Weinberg equilibrium include natural selection, mutations, nonrandom mating, genetic drift, and gene flow.

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A tube is being stretched while maintaining its cylindrical shape.

Answers

Answer:

This question is incomplete, the complete question is;

A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the rate of 2 millimeters per second. At the instant that the radius of the tube is 6 millimeters, the volume is increasing at the rate of 96π cubic millimeters per second. Which of the following statements about the surface area of the tube is true at this instant? (The volume V of a cylinder with radius r and height h is V=πr2h. The surface area Sof a cylinder, not including the top and bottom of the cylinder, is S=2πrh.)

A) The surface area is increasing at the rate of 28pi square mm per second.

B) The surface area is decreasing at the rate of 28pi square mm per second.

C) The surface area is increasing at the rate if 32pi square mm per second.

D) The surface area is decreasing at the rate of 32pi square mm per second.

Answer:

Surface Area is increasing at the rate of 28π mm²/sec  ( Option A )

Explanation:

Given the data in the question;

let r be the radius and h be the height of the tube

so volume V = πr²h

dv/dt = πr² dh/dt + 2nrh dr/dt

⇒ 96n = π × 36 × 2 + 2π × 6h dr/dt

⇒ 24π = 12nh dr/dt ⇒ h.dr/dt = 2

Area Surface S = 2nrh

ds/dt = 2π ( r.dh/dt + h.dr/dt )

= 2π ( 6×2 + 2)

= 2π (14)

= 28π

therefore Surface Area is increasing at the rate of 28π mm²/sec ( Option A )

What is the best definition of the underlined word as it is used in the sentence? unlucky or unfortunate; pitiable unknown or unfamiliar; mysterious without intelligence; foolish without tenderness; harsh.

Answers

Answer: A- unlucky or unfortunate; pitiable

Explanation: The words around it help me figure out the meaning!

Answer:

i believe the correct answer is A.

Explanation:

its correct on EDGE2021

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