Not sure what "two methods" you refer to, so I'll assume you're supposed to compute the line integral directly as well as with Green's theorem.
Direct computation:
It looks like the line integral is
[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy[/tex]
where C is the union of three line segment. We'll partition C and parameterize each component by
• C₁, the line segment from (0, 0) to (1, 0) : x(t) = t and y(t) = 0;
• C₂, from (1, 0) to (1, 4) : x(t) = 1 and y(t) = 4t;
• C₃, from (1, 4) to (0, 0) : x(t) = 1 - t and y(t) = 4 - 4t;
each with 0 ≤ t ≤ 1.
Compute the integrals over each component:
• Along C₁, we have y = 0, so this integral contributes nothing.
• Along C₂,
[tex]\displaystyle \int_0^1 4t \cdot 0 \, dt + (4t)^3 \cdot 4 \, dt = 256 \int_0^1 t^3 \, dt = 64[/tex]
• Along C₃,
[tex]\displaystyle \int_0^1 (1-t)(4-4t) \cdot (-dt) + (1-t)^2(4-4t)^3 \cdot (-4\, dt) \\\\ = \int_0^1 \left(-260 + 1288 t - 2564 t^2 + 2560 t^3 - 1280 t^4 + 256 t^5 \right) \, dt = -44[/tex]
So, the total line integral is
[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy = 0 + 64 - 44 = \boxed{20}[/tex]
Using Green's theorem:
The interior of C is the triangular region
[tex]D = \{(x, y) : 0 \le x \le 1 \text{ and } 0 \le y \le 4x\}[/tex]
and the integrand has no singularities either on C or within D. So by Green's theorem,
[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy = \iint_D \frac{\partial(x^2y^3)}{\partial x} - \frac{\partial(xy)}{\partial y} \, dx \, dy = \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx[/tex]
The remaining integral is trivial.
[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \int_0^1 x \int_0^{4x} (2y^3 - 1) \, dy \, dx[/tex]
[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \int_0^1 x \left(\frac12 (4x)^4 - 4x\right) \, dx[/tex]
[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \int_0^1 \left(128x^5 - 4x^2\right) \, dx[/tex]
[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \frac{64}3 - \frac43 = \boxed{20}[/tex]
An astronaut takes what he measures to be a 10-min nap in a space station orbiting earth at 8000 m/s. A signal is sent from the station to earth at the instant he falls asleep, and a second signal is sent to earth the instant he wakes.
Answer:
The astronaut was asleep longer on earth then he was in space
Explanation:
calculate the boring stuff (speed, time) and it shows that he was asleep for a greater value in space
¿usted 1 of 1 en aquella tienda elegante los viernes? (trabajar).
Answer:
Huh? What question is that?Explanation:
Farhacker
Imsureeeeeeee123
What did it mean when foreign diplomats "kowtowed" to the Chinese emperor or his representatives? It meant that diplomats relinquished all their rights in the Forbidden City. It meant that diplomats recognized the superiority of the Chinese emperor. It meant that foreign missionaries could no longer visit China. It meant that diplomats had full trading rights equal to those of China.
Kowtowing is simply known to be the a form of paying respect. kowtowed to the Chinese emperor or his representatives simply meant that meant that diplomats recognized the superiority of the Chinese emperor.
Kowtow, is commonly said pronounced as kotow.
It is very common to traditional China as a form of respect or reverence. It is known as an act of supplication made by an inferior to his superior through the kneeling and knocking of head to the floor.It is a traditional forms of reverence. In many scenarios, the standing bow has displaced the kowtow.
Learn more from
https://brainly.com/question/3081933
Answer:
B edge 2021
Explanation:
The concept of having shared understanding in public speaking is most closely related to which dimension of source credibility?.
The concept of having shared understanding in public speaking is most closely related to this dimension of source credibility: common ground
Public speaking can be defined as an act of talking or speaking formally to an audience, in order to explain an idea, project, and product.
Source credibility is highly dependent on the level of delivery of a speaker who is speaking to an audience.
In public speaking, common ground is a dimension of source credibility which refers to the concept of having shared understanding between a public speaker and the audience.
In conclusion, a common ground exists when there is shared understanding between a public speaker and the audience.
Read more: https://brainly.com/question/20598367
A small fair charges an admission fee for children and adults. The cost for admission is $3 per adult and $2 per child. On a certain day, total admission fees were $900, and 350 people attended the fair. How many children attended the fair that day? 80 children 150 children 200 children 320 children.
150 children attended the fair for that day if $900, and 350 people attended the fair, hence option b is correct.
What is the number of children attended the fair?Detailed explanation:
Let's say there are x youngsters and y grownups.
350 persons in all visited the fair, thus.
So, x + y = 350.
In addition, fees per kid are $2 and fees per adult are $3.
Since, $900 is assumed to represent the entire sales.
So, 2x + 3y = 900
Consequently, we have the equation system,
2x + 3y = 900
x + y = 350
Now let's resolve the equations.
x + y = 350 ⇒ y = 350 - x
The result is that 2x + 3y = 900 2x + 3(350 -x) = 900 2x + 1050 - 3x = 900 -x = -150 x = 150.
The result is that y = 350 - x y = 350 - 150 y = 200.
Therefore, As a result, 150 children and 200 adults, respectively, visited the fair.
Learn more about children, here:
https://brainly.com/question/6461117
#SPJ5
why did the mushroom go to the party
uh I don't know why? tell me im really clueless
Antimony (sb) has two stable isotopes with isotopic masses of 120. 9038 u and 122. 9042 u. What is the natural abundance of the heavier isotope?.
Answer:
average Atomic mass of thallium = 204.38
let heavier isotope is x%
204.3833 (100) = x(204.9744) + (100-x) 202.9723
20438.33 = 2.0021x + 20297.23
x= 70.476
correct answer is 70.3%
Explanation:
check the pic
Max is a brand-new father who can’t wait to document his twins’ achievements in their baby books. From earliest to latest, what order should max place these motor development milestones in his twins’ baby books?.
There are different stages of motor learning. They are the cognitive phase, the associative phase, and
the autonomous phase. From earliest to latest, the order that Max should place these motor development milestones in his twins’ baby books are:
Rolling over Sitting without support Crawling on hands and knees Standing well aloneBabies often start to develop motor skills from the center of the body outward and from head to tail.
They often learn to hold their head and neck before they learn to move their arms.
They also learn to move their arms in different directions before they learn to manipulate their fingers.
Motor development can also be known to have in seven stages throughout an individual's life.
Learn more from
https://brainly.com/question/25445912
The diagram shows the intersections of several straight roads. The avenues run parallel to each other. First Avenue and Second Avenue are parallel. Oak goes through both streets at point A and B. Main goes diagonally down through both streets and intersects with Oak Street. The distance from First to Second on Main is 280 feet. The distance from Second to the intersection of Oak is 140 feet. The distance from Point B to the intersection of Main is 113 feet. Amana walks along Oak from point A to B. To the nearest foot, how far does she walk? 75 ft 226 ft 307 ft 347 ft.
Answer:
answer is B 226 ft
Explanation:
because I got it right
Answer:
The above answer is correct - option B. 226 is your answer :D
Explanation:
Here's a screenshot for proof :)
If a dam is installed across a river, what effect will this have on the coastline?.
Answer:
The effects of dams on rivers can have dramatic consequences both upstream and downstream as the natural flow and drainage of the land is altered. One of the most obvious of these effects is a profound altering of the natural sediment load carried by the waters of the previously free-flowing river.
Explanation:
For which pairs of functions is (f circle g) (x)?.
Answer:
Option B is correct. The required composite function where f(g(x)) is x is f (x) = StartFraction 2 Over x EndFraction and g (x) = StartFraction 2 Over x EndFraction
Explanation:
Sierra left $4. 50 as a tip for a waiter. This was 18% of the bill before the tip. How much was her total bill before the tip? Enter your answer in the box.
Answer:
Total amount is: $25
Explanation:
Which graph represents the function f(x)=−|x−3|+1 ?.
Answer: (-1,1) and (3,-3)
Americium-241 is widely used in smoke detectors. Calculate the amount of americium-241 consumed in a smoke detector (initially containing 5. 00 µg of am) that has been used for one year if the half-life is 433 years.
0.008 μg of americium-241 was consumed in a smoke detector
The half life of a substance is:
[tex]N=N_o(\frac{1}{2} )^\frac{t}{t_\frac{1}{2} } \\\\Where\ N\ is\ the \ amount \ of\ substance\ remaining\ after\ t\ years,\\N_o\ is\ the\ original\ amount, t_\frac{1}{2} \ is\ half\ life.\\\\\\Given\ N_o=5\ \mu g,t=1\ year,t_\frac{1}{2} =433\ years. Hence:\\\\N=5*10^{-6}(\frac{1}{2} )^\frac{1}{433} =4.992\ \mu g[/tex]
The amount consumed = 5 - 4.992 = 0.008 μg
0.008 μg of americium-241 was consumed in a smoke detector.
Find out more at: https://brainly.com/question/4483570
A chamber contains equal molar amounts of c₂h₂, ch₄, and h₂. If the total chamber pressure is 5. 00 atm, then the partial pressure of c₂h₂ is:.
Answer:
I don't know answer what
The partial pressure of c₂h₂ is25 atm.
What is partial pressure?When more than one gas is present in a container, each gas exerts pressure, which is known as partial pressure. Its partial pressure refers to the pressure of any gas inside the container.
Partial pressures can be calculated in one of two ways:
To determine the individual pressure of each gas in a mixture, use PV = nRT. Determine the proportion of pressure from the total pressure that may be assigned to each individual gas by using the mole fraction of each gas.When there is a combination of two or more gases in a given volume, the pressure created by each individual gas in the mixture is expressed using the phrase partial pressure.
The partial pressures of the individual gases make up the total pressure of the gas combination. P1 + P2 + P3 = Ptot = Pi
Learn more about partial pressure, here
https://brainly.com/question/13199169
#SPJ5
Before writing a composition it is best to blank it first.
Answer: Before you start writing, remind yourself of the basic composition composition. Almost all articles have three parts: introduction, body of information and conclusion. The five-paragraph text is a common repetition of this and includes an introductory paragraph, three body paragraphs, and a conclusion paragraph.
Explanation:
Which theme is revealed by orwell’s use of situational irony in this excerpt? leaders should not be trusted. Ideals can become mocked in practice. Naïve citizens allow corrupt governments. Equality applies to all social classes.
Answer:
C
Explanation:
Edge 2021
The theme revealed by Orwell’s use of situational irony in the excerpt is naïve citizens allow corrupt governments. Hence option c is correct.
What is irony?Irony is defined as the comparison of what appears to be true on the surface with what is true or what is expected; this is a crucial rhetorical and literary tactic. The use of a mocking tone by the character is verbal irony and shows sarcasm.
The other animals were kept under the tyranny of the pigs enough to allow them to maybe realize that they had been duped by the false principles of the uprising. In the end, Napoleon uses the animals' gullibility to reinforce his dictatorship, in which the pigs can live comfortably at the expense of the other creatures.
Thus, the theme revealed by Orwell’s use of situational irony in the excerpt is naïve citizens allow corrupt governments. Hence option c is correct.
To learn more about irony, refer to the link below:
https://brainly.com/question/1695719
#SPJ2
Julissa is printing out copies for a work training. It takes 4 minutes to print a color copy, and it takes 2 minutes to print a grayscale copy. She needs to print no fewer than 8 copies within 25 minutes. Which system of inequalities represents the number of color copies, x, and grayscale copies, y, that Julissa can print to meet her goal?.
The system of inequalities for Julissa can be given as 4x + 2y ≤ 25
and x + y ≥ 8.
What is a system of inequalities?
The system of inequalities is given with the use of the more than inequalities for the correspondence to one variable.
In the given system, the inequalities lies with the grayscale copies, and color copies with the time limit of 25 minutes and minimum number of 8 copies.
Let the number of color copies = x
The time taken to print each color copy = 4 minutes
Thus, the time taken to print x color copies = 4x
Let the number of gray scale copies = y
The time taken to print each gray scale copy = 2 minutes
Thus, the time taken to print y gray scale copy = 2y
Total copies printed = x + y
Maximum time taken to print x color copies and y grayscale copies = 25 minutes
So,
4x + 2y ≤ 25
and x + y ≥ 8
Learn more about system of inequalities, here:
https://brainly.com/question/19526736
#SPJ2
A manager records the number of hours, x, each employee works on his or her shift and develops the probability distribution below. Fifty people work for the manager. How many people work 4 hours per shift? probability distribution hours worked: x probability: p(x) 3 0. 1 4 ? 5 0. 14 6 0. 3 7 2000. 36 8 0. 06 0 1 2 4.
Answer:
c
Explanation:
i took the test rn
From the data that we have here the total number of people that are known to work for 4 hours per shift is 2.
How to solve for the workersThe sum of all of these probabilities would be equal to 1. Hence we would have:
0.1+x+0.14+0.36+0.3+0,06 = 1
x + 0.96 = 1
x = 1 - 0.96
x = 0.04
The total number of people that is said to work for this manager is said to be 50.
50 x 0.04
= 2
Therefore the total number that work at 4 hours per shift is 2.
Read more on probability here: https://brainly.com/question/25870256
#SPJ2
According to the beginning of wisdom which of the following is not consistent with the old testament.
Answer:
I don't know answer what is
In a school 2/3 of the students study a language.
Which of the following are primate characteristics? check all that apply.
Answer:
Primates are a diverse group of animals that vary from humans to lemurs and have a variety of characteristics that distinguish them from other mammals. All primates have eyes in the front region of the skull, a big brain compared to body size, a variety of tooth forms and sizes, a high level of intellect, reasonably dexterous hands, and many other traits.
Explanation:
One common attention getter used in a speech introduction is.
Answer:
Asking a question that you want the audience to answer or consider
Explanation:
Please mark as brainliest if this helped you
A hemisphere of radius 8 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the center of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the cylinder of maximum volume.
The dimensions of the cylinder that has the maximum volume can be
found be finding the maximum value of the volume function.
[tex]\mathrm{The \ \underline{height \ of \ the \ cylinder \ of \ maximum \ volume \ is \ \dfrac{8}{\sqrt{3} }}}[/tex][tex]\mathrm{The \ \underline{radius \ of \ the \ cylinder \ of \ maximum \ volume \ is \ \dfrac{8 \cdot \sqrt{6} }{3}}}[/tex]Reasons:
The known parameter of the hemisphere are;
The radius of the hemisphere = 8
Required;
The radius and height of the maximum volume of the inscribed cylinder.
Solution:
Let h represent the height of the cylinder, and let r represent the radius of
the cylinder, we have;
r² + h² = 8²
Therefore;
r² = 8² - h² = 64 - h²
r² = 64 - h²
The volume of the cylinder, V = π·r²·h = π·(64 - h²)·h
V(h) = π·(64·h - h³)
At the maximum volume, we have;
[tex]\dfrac{dV(h)}{dh} = \dfrac{d}{dh} \left(\pi \cdot \left(64 \cdot h - h^3 \right) \right) = \pi \cdot \left(64 - 3 \cdot h^2 \right) = 0[/tex]
64 - 3·h² = 0
64 = 3·h²
[tex]h =\sqrt{\dfrac{64}{3} } = \dfrac{8}{\sqrt{3} }[/tex]
[tex]\underline{\mathrm{The \ height \ of \ the \ cylinder, \ h} = \dfrac{8}{\sqrt{3} }}[/tex]
[tex]r^2 = 64 - \dfrac{64}{3} = \dfrac{128}{3}[/tex]
[tex]r =\sqrt{\dfrac{128}{3}} = \dfrac{8 \cdot \sqrt{6} }{3}[/tex]
[tex]\underline{\mathrm{The \ radius \ of \ the \ cylinder, \ } r = \dfrac{8 \cdot \sqrt{6} }{3}}[/tex]
Learn more here:
https://brainly.com/question/14104351
Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Predictable) Education investment fund $10 Other (Predictable) Retirement investment fund $40 Other (Predictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings? a. $40 b. $60 c. $74 d. $55.
Answer:
C. 74
Explanation:
Answer:
Explanation:
C 74
In which situations have you participated in a group discussion at school? Check any that apply. To plan an event to solve a problem to debate an issue to complete a project to present a theory or solution to discuss a book or other reading.
Answer:
all of them are correct
Explanation:
Edge 2021
These situations have a person participated in a group discussion at school are:
to plan an event.to solve a problem.to debate an issue.to present a theory or solution.What is group?
The term group refers to the two or more people are the involved on the particular activity. A group is an involved of the person are the based on the informal group. It was the people are to enjoy the person to the another person company.
A group discussion or focused group is usually the format of an informal discussion group. It was the plan at the school event. It was to resolve the issue and the problem. The discussion of the specific issue. There was either a theory or a solution.
As a result, the situations have a person participated in a group discussion at school.
Learn more about on group, here:
https://brainly.com/question/15560909
#SPJ2
This natural resource was once very abundant in Western Europe and helped power the Industrial Revolution. Question 4 options: Iron Coal Oil Water.
Answer: Its Coal
Explanation: I did the K12 quiz
Involving others in meaningful tasks is an example of which positive leadership quality.
An example of positive leadership quality that typically requires a leader involving others in meaningful tasks is: Delegation.
Leadership can be defined as a strategic process that involves the act of motivating, encouraging and inspiring a group of people (followers or employees) that are under you to become innovative, create positive changes that fosters growth and development, and significantly enhance the success of your business firm or company in the future.
Basically, there are five (5) main types of leadership style and these include:
Transactional leadershipAuthoritarian leadershipParticipative leadershipTransformational leadershipDelegative leadershipA delegative leadership style is also referred to as laissez-faire leadership and it typically involves a leader assigning roles, meaningful tasks or decision-making responsibility to a highly qualified and competent subordinate. Thus, it is a leadership style that assess the unique talent and qualities possessed by each member of a team while involving them in meaningful tasks.
In conclusion, delegation is an example of positive leadership quality that typically requires a leader involving others in meaningful tasks.
Read more: https://brainly.com/question/14751566
A radioactive substance has a continuous decay rate of 0. 064 per minute. How many grams of a 150 gram sample will remain radioactive after 45 minutes? round the answer to the nearest tenth of a gram, and do not include the unit in your answer.
Answer:
147.1
Explanation:
150 - 0.064(45)
150 - 2.88 = 147.12
Aria paid $75,000 for her house. Its property value increased by 2. 2% per year. When aria sold her house after eleven years, how much was it worth, to the nearest hundred dollars? a. $133,700 b. $95,400 c. $95,300 d. $93,100.
Answer:
$95,300. C
Explanation:
Answer:
answer is C
Explanation: