Given that y = cos(x) makes up part of the boundary of C, I suspect you mean the given points to be (-π/2, 0) and (π/2, 0).
I also assume the given vector field is
[tex]\vec F(x,y) = \left\langle e^{-x} + y^2, e^{-y} + x^2 \right\rangle[/tex]
Since [tex]\vec F[/tex] has no singularities on C or in its interior, Green's theorem applies:
[tex]\displaystyle \int_C \vec F(x,y) \cdot d\vec r = \iiint_D \frac{\partial(e^{-y}+x^2)}{\partial x} - \frac{\partial(e^{-x}+y^2)}{\partial y} \, dA = 2 \iiint_D (x + y) \, dA[/tex]
where D is the interior of C, the region
[tex]D = \left\{ (x, y) : -\dfrac\pi2 \le x \le \dfrac\pi2 \text{ and } 0 \le y \le \cos(x) \right\}[/tex]
The integral then reduces to
[tex]\displaystyle 2 \iint_D (x + y) \, dA = 2 \int_{-\frac\pi2}^{\frac\pi2} \int_0^{\cos(x)} (x + y) \, dy \, dx[/tex]
[tex]\displaystyle 2 \iint_D (x + y) \, dA = 2 \int_{-\frac\pi2}^{\frac\pi2} \left( x\cos(x) + \frac12 \cos^2(x) \right) \, dx[/tex]
[tex]\displaystyle 2 \iint_D (x + y) \, dA = 2 \int_{-\frac\pi2}^{\frac\pi2} \left( x\cos(x) + \frac{1 + \cos(2x)}4 \right) \, dx[/tex]
[tex]\displaystyle 2 \iint_D (x + y) \, dA = \frac12 \int_{-\frac\pi2}^{\frac\pi2} \left( 4x\cos(x) + 1 + \cos(2x) \right) \, dx[/tex]
Since 4x cos(x) is an odd function over the symmetric interval [-π/2, π/2], its contribution to the integral is 0, and the remaining integral is trivial.
[tex]\displaystyle 2 \iint_D (x + y) \, dA = \frac12 \int_{-\frac\pi2}^{\frac\pi2} \left( 1 + \cos(2x) \right) \, dx = \boxed{\frac\pi2} [/tex]
When colleen first learned the word "ominous," she pictured a large, dark cloud to help her remember its meaning. Which term best describes this example?.
Answer:visual imagery
Explanation:
true or false
1. The computers of all the five generations have different properties.
Answer:
The answer to your question is true
How agriculture industry can provide job opportunities
Answer:
agriculture industry is also related with business in that if the business is huge or small it is considered as the business so, in a person doing business provides job opportunities to all people .yes, agriculture industry provides job opportunities such as farm worker, manager
purchasing agent ,grower, agriculture specialist,sale representative etc.
làm thế nào để xác định mình đã thích 1 người
which expression is equivalent to a+4a+8a+4a+8
Answer:
17a+8
Explanation:
combine like terms (all of the A's) and then the rest of the equation (8)
Answer:
17a+8
Explanation:
Ms. Sanchez’s students were asked how many hours they spend participating in organized sports each week. Each row of the table represents one sample from the class. Number of hours playing sports 5 5 3 0 6 2 2 4 5 2 3 4 3 0 1 4 0 4 3 6 what is the mean of the sample in the third row? 2. 2 2. 8 3. 0 3. 4.
The mean of a dataset is the average of the dataset.
The mean of the sample in the third row is 2.2
The dataset is given as:
5 5 3 0 6 2 2 4 5 2 3 4 3 0 1 4 0 4 3 6
From the complete question, the samples in the third row are:
Sample: 3 4 3 0 1
The mean of a dataset is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
Where:
n = 5 i.e. the number of samples
So, we have:
[tex]\bar x = \frac{3 + 4 + 3 + 0 + 1}{5}[/tex]
Add the expressions in the numerator
[tex]\bar x = \frac{11}{5}[/tex]
Divide 11 by 5
[tex]\bar x = 2.2[/tex]
Hence, the mean of the sample in the third row is 2.2
Read more about mean at:
https://brainly.com/question/11887128
David is a sophomore in high school and is studying for his united states history exam, in which he must recall all of the battles in the american revolutionary war. At first, he begins by just trying to group all of the facts associated with each battle into his memory. When he realizes he is forgetting some battles, he begins repeatedly associating the events that occurred in each battle with the place where the battle occurred. He finds he remembers the battles more readily this way, but he is still having a hard time remembering all the facts associated with each battle. Because he continues to think this is the best way to approach learning, he continues to study in this manner. After several bad grades, he realizes that his studying technique is not working, so he asks a friend who is doing better at remembering everything how she is studying. She said she is making up stories about each battle and how each battle is connected with other battles. David tries this method and finds it was much more effective for him.
People are often influenced by different things that affect their behavior. The concepts that relates to this scenario is explained below.
Metacognition is known to be the act of thinking about one's own thought and learning. David first use a method to remember the battles in the American Revolutionary war, and later on uses an alternative method. He asked a friend when he saw his errors. This shows that David understood his thought process and is trying too control it.
Method of loci is known as a strategy of memory enhancement that uses visualizations to boast e recall of information. David uses this to link the events that happened in each battle with the place where the battle took place.
Deep processing is known as a step taken in processing spectrum of mental recall via examining of language used. David's friend uses stories for each battle and connects it with other battles. David then uses deep processing via examining the battles too.
Rehearsal often uses repetition to remember things. David always practicing boast his remembrance of the battles in the American Revolutionary War.
Elaboration is used to enhance total remembrance. By making up stories about each battle and relates it to other battles, it aid David in learning.
Chunking is known as the act of taking different pieces of information and placing them into larger units. David friends sees each battle as a single unit and then they often link up the different events together.
Mental set is known as the ability of the brain to stick with the most familiar solution to a problem and ignore others. David uses the friends method and apply as it aid remembrance more.
See the other part of the question
Explain how each of the following concepts relates to this scenario.
Metacognition
Method of loci
Deep processing
Rehearsal
Elaboration
Chunking
Mental set
Learn more about these scenarios above from
https://brainly.com/question/16017972
Carrying a load of 100 pounds can reduce your cars fuel efficiency by ?
Answer: 1%
Explanation:
"According to the Environmental Protection Agency, each additional 100 pounds on a vehicle can reduce its fuel efficiency by 1%. Carrying open cargo (i.e., on flatbeds) is also less fuel-efficient than carrying cargo inside a closed truck."
One of the five reasons young drivers, age 16 to 20 are involved in more
collisions than older drivers is _______
pressure.
A. peer
B. school
C. night
Answer:
A
Explanation:
because their friends can be drinking in the car and says to the driver will u like to drink and persuading which will lead to him being drunk
What is the opportunity cost in this scenario?
Mikael has saved $4,000 for his to trip to Brazil. He has calculated that his total transportation expenses will be $1,000. The hotel will cost him
another $1,500. He will spend about $500 on food. He plans on spending the remaining $1,000 for sightseeing and buying souvenirs.
While booking his plane ticket, he realizes that the price has gone up. His total transportation expenses will go up by $200. He realizes that he
cannot cancel his hotel reservation. He also doesn't want to go cheap on food. Finally, he decides to give up visiting the popular Ouro Preto
during his stay in Brazil.
The opportunity cost in this scenario is Sightseeing.
The Opportunity Cost in this scenario will be the amount of $1,000 that has been made available for sightseeing and buying souvenirs.
Opportunity Cost is an alternative forgone which a person or an individual give up or forgone in order to choose other available alternative when making a decision which inturn may result in the loss of gain that would have been derived if the alternative forgone was choosing.
Example of opportunity cost is giving up
on buying movies tickets for a textbook.
Therefore the opportunity cost in this scenario is Sightseeing.
Learn more about Opportunity cost here:
https://brainly.com/question/13036997
Which model best shows the movement of oxygen during photosynthesis?
Plant
Ò A. Atmosphere
O B. Soil - Plant
C. Plant - Soil
D. Plant - Atmosphere
What should the food worker do to safely thaw the pork.
Answer:
if the pork is in a bag, you can thaw it in a sink, or if it is not in a bag, put the pork in a bag before thawing it in said sink.
Which statement correctly describes a property of white light.
[tex] \\ [/tex]
It contains different wavelengths of visible light.
How do you grow rice
Answer:
put some rice in a pot
Then mix it up with some sauce
pour in some dirt
and you'll get some sweet plant
Explanation:
Ideally, you need at least 40 continuous days of warm temps over 70 F. (21 C.) to grow rice.
First, you need to find one or several plastic containers without holes. One or several depends upon how many miniature pseudo rice paddies you want to create. Next, either purchase rice seed from a gardening supplier or buy long grain brown rice from a bulk foods store or in a bag. Organically grown rice is best and it can’t be white rice, which has been processed.
Fill the bucket or plastic container with 6 inches (15 cm.) of dirt or potting soil. Add water up to 2 inches (5 cm.) over the soil level. Add a handful of the long grain rice to the bucket. The rice will sink to the dirt. Keep the bucket in a warm, sunny area and move it to a warm place at night.
Rice plants don’t need too much care from here on out. Keep the water level at 2 inches (5 cm.) or so above the dirt. When the rice plants are 5-6 inches (12.5-15 cm.) tall, increase the water depth to 4 inches (10 cm.). Then, allow the water level to lower on its own over a period of time. Ideally, by the time you harvest them, the plants should no longer be in standing water.
If all goes well, rice is ready to harvest in its fourth month. The stalks will go from green to gold to indicate it is time to harvest. Harvesting rice means cutting and gathering the panicles attached to the stalks. To harvest the rice, cut the stalks and allow them to dry, wrapped in a newspaper, for two to three weeks in a warm, dry place.
Once the rice stalks have dried, roast in a very low heat oven (under 200 F./93 C.) for around an hour, then remove the hulls by hand. That’s it; you can now cook with your very own home grown, long grain brown rice.
Which of the following situations can best be used to illustrate the meaning of prosperity? a. Manuel has lots of friends, a loyal dog, a well-paying job, and savings in the bank. B. Toshiko likes mashed potatoes, crisp apples, dark chocolate, and peaches. C. Caleb skis down the mountain every day to get to his job in the village. D. Janna designs costumes for all the musicals and plays at school.
Answer: A because he successful and that's what prosperity means.
Manuel has lots of friends, a loyal dog, a well-paying job, and savings in the bank can best be used to illustrate the meaning of prosperity. Thus, option A is correct.
What is prosperity?The blossoming, prospering, luck, and great social status are all characteristics of prosperity. Pleasure and happiness are two other variables that can be abundantly affluent in all proportions and are frequently produced by prosperity.
As Manuel help lots of friends as well as the dog. And paying job and savings post office suggest that he is having prosperity. Having all the good things in their life and living at that point of time with a backup plan is termed as prosperity that the person is having.
Therefore, option A is the correct option.
Learn more about prosperity, here:
https://brainly.com/question/12644777
#SPJ5
To describe a sequence of transformations that maps triangle.
Answer:
daaam I wish I could help but im struggling in the same thing
Explanation:
how many chapters are there in the Bible?
there are 66 chapters in Bible
Which of the following non-renewable resources of energy has the smallest amount of fuel left on earth?.
Answer:
Their is no answer choices but Nonrenewable energy resources include coal, natural gas, oil, and nuclear energy.
Explanation:
You select cell a1, hover the pointer over the cell border to reveal the move icon, then drag.
A spreadsheet is used to make the organization of data in a tabular form through a computer application software which can also perform mathematical operations.
With this in mind, we can see that the data is arranged in rows and columns as they can be used to record data for business invoices, expenditures, etc.
Some popular spreadsheets includes:
Micros0ft ExcelLibre0ffice, etcA cell border can be added, resized and moved, along with the contents to another location.
Please note that your question is incomplete so I gave you a general overview to help you better understand the concept.
Read more about spreadsheets here:
https://brainly.com/question/4965119
Managers at eller manufacturing are considering purchasing a new refrigerated delivery truck that will produce equal annual cash flows of $36,000 for 6 years. The truck’s net present value is $12,780, its cost is $144,000, its useful life is 6 years, and its annual depreciation expense (no salvage value) is $24,000. What is the discount rate used by eller to evaluate this project?.
It should be noted that the discount rate that was used by Eller to evaluate this project is 10%.
From the information given, the following can be depicted:
Annual cash inflows = $36,000 Period of cash inflows = 6 years Cash outlay (initial investment) = $144,000 Depreciation expense = $24,000 Estimated useful of trucks = 6 years Net present value = $12,780It should be noted that the Present Value Annuity Factor at 10% for 6 years is given as 4.355
Therefore, the Present Value of Annuity cash inflows will be
= ($36,000 x 4.355) = $156,780
Less initial investment cash outlay = $144,000
Net present value = $12,780
Learn more about discounts on:
https://brainly.com/question/13999687
[tex]-2xy^2(x^3y-2x^2y^2+5xy^3[/tex]
[tex]\boxed{\sf a(b+c+d)=ab+ac+ad}[/tex]
[tex]\\ \sf\longmapsto -2xy^2(x^3y-2x^2y^2+5xy^3)[/tex]
[tex]\\ \sf\longmapsto -2x^4y^3+4x^3y^4-10x^2y^5[/tex]
Hope it helps
What is an equation of the line that passes through the points (-6, -3) and
(-3,-5)?
Answer:
Y= -2/3X - 7
Explanation:
Why do you believe the concerns around smartphones were identified as responsibilities and not dilemmas?
Which group represents external customers of an organization
Chinese companies are able to charge lower prices since in most cases, their government would support them by paying for their fixed costs. Such companies are able to apply …………………. This means the company would set price to cover only overheads. Select one: a. Incremental pricing b. Rigid cost-plus pricing c. Skimming pricing d. Flexible cost-plus pricing
Answer:
Flexible cost plus pricing
Shira wants to do well on her next test so her grade in the class does not fall. This is an example of which type of motivation?.
It is an example of intrinsic motivation.
Motivation can be described as the factors that drive a person to act in a certain manner. These factors can be material, cognitive, emotional or social. Motivation can lead to either positive or negative outcomes. For example, a person motivated to succeed would spend hours studying while a person whose aim is to make quick profit can be motivated to engage in crime.
Intrinsic motivation is a type of motivation in which the driving force to carry out an activity is due to internal factors. Shira's desire to do well is not externally motivated. It is due to her desire to succeed.
To learn more about intrinsic motivation, please check: https://brainly.com/question/8774416
Answer:
the answer is extrinsic
Explanation:
ED 2022
Depth perception is not important in determining proper following distance.
A. True
B. False
Depth perception is not important in determining proper following distance is the false statement.
What is lack of depth perception?The brain is able to integrate both images into a single 3-D image in a process called stereopsis. With the help of this information, it is possible to calculate both the distance between the items and their distance from one another.
Thus, the statement is not true.
For more details about lack of depth perception, click here:
https://brainly.com/question/13601773
#SPJ2
What number is 4 times as many as 25.
Answer:
100
Explanation:
multiply them..... .... . .. . . . . . . . . . . I had to reach the character limit
What is the value of the expression
x² + 2x - 2xy – 2y + y^2 when x - y = 50 ?
x ² + 2x - 2xy - 2y + y ² = (x ² - 2xy + y ²) + 2 (x - y)
… = (x - y)² + 2 (x - y)
… = 50² + 2 × 50
… = 2600
The Escobar family went on a car trip. They drove 100 miles on country roads and 240 miles on the highway. They drove 50% faster on the highway than on the country roads. Let r represent their rate on country roads in miles per hour. a. Write and simplify an expression that represents the number of hours it took the Escobar family to complete their trip in terms of r. (Hint: 50% faster means 150% of the original rate.) b. Find their total travel time if they drove the posted speed limit.
Answer: Hey I'm sorry I didn't get to answer your question it's just that I need the points because I don't have enough to get help with my question. I hope you get the answer that you need for you question. Good Luck :)..
Explanation:
The expression that represents the number of hours it took the Escobar family to complete their trip in terms of r is 260/r
The expression for the total time of travel?Let r represent their rate on country road and R represent their rate on highway.
So, we have:
R = (100% + 50%) * r
Evaluate
R = 1.5r
Rate is calculated using:
Rate = Distance/Time
So, we have:
r = 100/t and R = 240/T
Make T and t the subject
t = 100/r and T = 240/R
The total time of travel is:
Total = t + T
So, we have:
Total = 100/r + 240/R
Substitute R = 1.5r
Total = 100/r + 240/1.5r
Simplify
Total = 100/r + 160/r
Evaluate the sum
Total = 260/r
The total time of travelThe speed limit is 40mph
This means that:
r = 40
In (a), we have:
Total = 260/r
Substitute 40 for r
Total = 260/40
Evaluate
Total = 6.5
Hence, their total time of travel is 6.5hours
Read more about rate and distance at:
https://brainly.com/question/4931057
#SPJ2
