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]
In the sale of a business, if the requirements of the uniform commercial code are not followed, who would most likely suffer the greatest injury?.
If the requirements of the uniform commercial code (UCC) are not followed, then the BUYER would most likely suffer the greatest injury. A buyer is an individual who buys something.
The Uniform Commercial Code (UCC) is a set of regulations that govern commercial transactions in the USA.
This code (UCC) was first published in 1952 after approval from the American Law Institute.
The major goal of the UCC is the improvement of the principles that govern commercial transactions in the USA.
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Jim and sue were going to be married and were very much in love. Before the wedding date, they went out for coffee and orally agreed to how the marital assets would be split if they divorced. Four years later they divorced. Jim attempted to enforce their oral prenuptial agreement. What will be the result?.
Answer:Before the wedding date, they went out for coffee and orally agreed to how the marital assets would be split if they divorced. Four years later they divorced.
Explanation:
Which of the following is a key strategy for nutrition coaching?.
Answer:
Add-on sessions for individual nutrition coaching. It's time to become certified in nutrition if you already have fitness clients. …
Provide nutrition coaching for small groups. Nutritional coaching for small groups is similar to personal training. …
Organize a nutrition challenge. You will not only retain more coaching clients when you offer nutrition challenges, but they will also help your clients reach their goals.
Provide nutrition-only coaching. If you're a coach, you know there will always be people asking you questions about nutrition in the gym.
Engage in corporate group work. Coaching corporate groups is one area that coaches simply don't take advantage of enough.
I Hope This Helps You :)
What is the approximate tangential speed of an object orbiting earth with a radius of 1. 8 × 108 m and a period of 2. 2 × 104 s? 7. 7 × 10–4 m/s 5. 1 × 104 m/s 7. 7 × 104 m/s 5. 1 × 105 m/s.
Answer: the period is 2.2 x 104 s, then the rotational speed is:
1 / 2.2x104 = 4.55x10-5 rad/s
We can solve for the tangential speed using the formula:
v = ωr
where ω is the rotational speed
v is the linear or tangential speed
r is the radius
So,
v = 4.55x10-5(1.8x108)
v = 5.1 x 104 m/s
Explanation:
The approximate tangential speed of an object orbiting earth with a radius of 1. 8 × 108 m is 5.1 x 104 m/s.
What is tangential speed?Any item moving along a circular path has a linear component to its speed called tangential velocity.
An object's velocity is always pointed tangentially when it travels in a circle at a distance r from the center. Tangential velocity is the name given to this.
The period is 2.2 x 104 s, then the rotational speed is:
1 / 2.2 x 104 = 4.55 x 10⁻⁵ rad/s
We can solve for the tangential speed using the formula:
v = ωr
where ω is the rotational speed
v is the linear or tangential speed
r is the radius
So,
v = 4.55 x 10⁻⁵ (1.8 x 108)
v = 5.1 x 104 m/s
Therefore, the tangential velocity is 5.1 x 104 m/s.
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What contributed to poor working conditions for factory workers in the late 1800s? choose three answers.
Emerson’s remarks in the excerpt most directly reflected which of the following developments during the early nineteenth century?.
Answer:
A the emergence of a nation culture
Explanation:
The reflected development during the early age of Emerson remarks was the even of emergence of a nation culture.
I hope this helps!
Emerson’s remarks in the excerpt most directly reflected the emergence of a national culture. Therefore option A is correct.
What is Nation Culture?The norms, behaviors, beliefs, practices, and values that the people of a sovereign nation share are referred to as national culture (e.g., a Chinese or Canadian national culture). It alludes to particular traits like language, religion, ethnicity, and racial identity, as well as cultural history and customs.
According to the study, organizational values may be categorized into four categories: power distance, individuality vs collectivism, masculinity against femininity, and uncertainty avoidance.
National cultural values are societally accepted conceptions of what is admirable, proper, and desirable. A national society's preferences for addressing problems with internal integration and exterior adaptation pose a threat to its existence.
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Ken is not satisfied with his thesis statement in sentence 3. Which of the following should replace sentence 3 to provide a more effective thesis statement?.
Discuss 3 questions you should ask yourself when assessing your fitness and explain how your answers determine your fitness to drive.
The seasonal product team needs a vendor who can quickly adjust to changes in product demand. The planning team has sent over a table comparing how the four available vendors have been performing. Can you identify which vendor to recommend?.
There are different kinds of vendors. The best that I can identify and recommend is Vendor V in the diagram attached.
The seasonal product team should consider taking or using Vendor V. This is because of their performance. When you look at the diagram, you will see that their performance is better in all parameter given in the table (Diagram attached).
Vendor V is in all parameters improving the performance of all the four elements and it can easily adjust to any seasonal changes.
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How do you do this ??.?.?.?.??.??.?.?
Answer: I.D.K MAN SORRYExplanation:
Maximize the objective function p = 5x + 3y for the given constraints. X ≥ 0 y ≥ 0 3x + 6y ≤ 48 2x + 8y ≤ 56.
The maximized value of the objective function is 38
The objective function is given as:
Max P = 5x + 3y
The constraints are given as:
3x + 6y ≤ 48 2x + 8y ≤ 56x ≥ 0 y ≥ 0To do this, we make use of the graphical method.
See attachment for the graph of the constraints.
From the graph, we have the following feasible point
[tex](x,y) = (4,6)[/tex]
Substitute 4 for x and 6 for y in the objective function.
[tex]Max\ P = 5x + 3y[/tex]
So, we have:
[tex]P = 5 \times 4 + 3 \times 6[/tex]
[tex]P = 20 + 18[/tex]
[tex]P = 38[/tex]
Hence, the maximized value of the objective function is 38
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Answer:
Explanation:
If an objective function has a maximum value, it will occur at one of the vertices of the feasible region (i.e., the solution region for the system of inequalities). The feasible region's vertices occur at (0, 0), (0, 7), (4, 6), and (16, 0).
Use the x- and y-value from each vertex to evaluate the objective function P = 5x + 3y.
(x, y) 5x + 3y P
(0, 0) 5(0) + 3(0) 0
(0, 7) 5(0) + 3(7) 21
(4, 6) 5(4) + 3(6) 38
(16, 0) 5(16) + 3(0) 80
Therefore, the maximum of the objective function is 80.
James bennett also allocates wealth between youth and old age. He has no cash currently (in his youth), but will inherit $3000 in his old age. He can lend and borrow at the bank at 18% (that is, lending $1 in youth will give him $1. 18 in old age). He has an investment opportunity that costs $12,000 now in his youth and has a payoff of $15,000 in his old age. This is the only investment opportunity available to him. What is the most he can consume in his youth?.
The present value (PV) of $15,254.24 is the most James bennett can consume in his youth.
Given the following data:
Inheritance = $3000Interest rate = 18%Investment opportunity (youth) = $12,000Investment opportunity (old age) = $15,000To calculate the most James bennett can consume in his youth:
First of all, we would determine the future value of James bennett from his investment and inheritance as follows:
[tex]FV = 15000 + 3000[/tex]
FV = $18000
Mathematically, the most James bennett can consume in his youth is given by this formula:
[tex]PV = \frac{FV}{(1+i)^n}[/tex]
Substituting the given parameters into the formula, we have;
[tex]PV = \frac{18000}{(1+0.18)^1}\\\\PV = \frac{18000}{1.18}[/tex]
PV = $15,254.24
Therefore, the present value (PV) of $15,254.24 is the most James bennett can consume in his youth.
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Hillary glued three rectangular pieces of cardboard together to create a house for her lizard in the shape of a triangular prism. The dimensions are shown in the image below.
Even though the process is endothermic, snow can sublime. Which tendency in nature accounts for this phase change?.
Answer:
Explanation:
.
They allow us. On our choice of the elective subjects in school and your hobbies.
Elective subject simply means an optional subject because it's not compulsory and one can choose the subject that he or she wants
An elective subject simply means an optional subject. Such subjects are not compulsory. The compulsory subjects are the core subjects.
One has a choice to the elective subjects that can be chosen in college. There are list of options that are in the study plan where one can choose an elective.
In conclusion, my hobbies are reading and playing football with my friends during leisure.
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When you stifle a sneeze, you can damage delicate tissues because the pressure of the air that is not allowed to escape may rise by up to 45 kpa.
so if i keep holding in my sneezes could i die
How does your power output in climbing the stairs compared to the power output of a 100 watt.
Answer:
the power output is the amount of gravitational potential energy being carried out by releasing electricity
If cell a3 contains the text the death of chivalry what will the function.
Based on the information given, The function =PROPER(A3) will be The Death Of Chivalry.
It should be noted that in excel, the "PROPER" function is a function that is used in converting the first character to upper case and the rest converted to lower case.
Since we are told that the cell A3 contains the text '' the death of chivalry'' , the "PROPER" function in excel means that each of the first letters of each word will be in upper case.
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Which of the following describes a neutral atom of oxygen.
Answer: You don give any of the options but an atom of oxygen can be written as O
Explanation:
Which of the following is not a characteristics of african music.
Answer:
A vast number of dances
Explanation:
Mark as Brainliest Answer
List down all the foods and drinks.
The list of foods we have for breakfast are:
Milk, bread, eggs, corn, and fruits.Food is any substance we put in our mouth that is edible, digestible, and nourishes the body to make us grow.
Drinks are food substances in form of liquid that is ingested for the purposes of facilitating digestion and replenishing the lost water from the body.
Breakfasts are foods and drinks we eat in the morning and examples of them are:
Milk, bread, eggs, corn, and fruits.Learn more about Food substances here:
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Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. Jpg degrees. Es004-1. Jpg degrees.
The reference angle is the smallest angle between the terminal side and the x-axis.
[tex](1)\ \theta = 300^o[/tex]
300 degrees is in the 4th quadrant.
So, the reference angle is
[tex]\alpha = 360 - \theta[/tex]
[tex]\alpha = 360 - 300[/tex]
[tex]\alpha = 60^o[/tex]
Hence, the reference angle of 300 degrees is 60 degrees
[tex](2)\ \theta = 225^o[/tex]
225 degrees is in the 3rd quadrant.
So, the reference angle is
[tex]\alpha = \theta - 180[/tex]
[tex]\alpha = 225 - 180[/tex]
[tex]\alpha = 45^o[/tex]
Hence, the reference angle of 225 degrees is 45 degrees
[tex](3)\ \theta = 480^o[/tex]
480 degrees is in the 2nd quadrant (i.e. 480 - 360 = 120)
So, the reference angle is
[tex]\alpha = 180 - \theta[/tex]
[tex]\alpha = 180 - 120[/tex]
[tex]\alpha = 60^o[/tex]
Hence, the reference angle of 480 degrees is 60 degrees
[tex](2)\ \theta = -210^o[/tex]
-210 degrees is in the 2nd quadrant (i.e. 360 - 210 = 150)
So, the reference angle is
[tex]\alpha = 180 - \theta[/tex]
[tex]\alpha = 180 - 150[/tex]
[tex]\alpha = 30^o[/tex]
Hence, the reference angle of -210 degrees is 30 degrees
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Answer:
i
Explanation:
the second one is -1
Select the correct answer. Read the description and select the course described. Es lo que primero se ofrece en el menú. Son pequeñas porciones de snacks acompañadas por una bebida. A. Plato de fondo b. Aperitivo c. Bajativo d. Entrada.
The correct option for the statement in Spanish 'es lo que primero se ofrece en el menú' is 'aperitivo'. The word 'aperitivo' in English means appetizer.
An appetizer is a small dish containing food or a small drink served before a meal in order to stimulate appetite.
In consequence, an appetizer can be a light snack taken before the main meal.
Some examples of well-known appetizers include, among others, Chicken Enchilada Dip, Cowboy Caviar, Scallion, Caramelized Onion Dip, etc.
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Answer: B. aperitivo
What can you learn from the heading of a court case?.
Answer:
we learn from court case law is blind. alaways take way of law never do any criminal activities
Answer:
Which court decided the case
Explanation:
Consider the triangle shown. Which shows the sides in order from longest to shortest?.
All of the following are characteristics of the blue crab except.
Answer:
A. Blue Crab Doesn't Hav Teeth
B.
If angle acb is 34 degrees what is the measure of angle adb.
Answer:
34 because the shape is split.
Explanation:
1.Jun _______ France for 4 months.
A. have learnt
B. learnt
C. learns
D. has learnt
Answer:
has learnt
Explanation:
i think France is supposed to be French
The cost of 8 pens is $2. 50. How much will 2 dozen cost?.
Answer:
$ 7.5
Explanation:
1. Common way:
if one pen costs $ x
8x=2.5
x=0.3125
2 dozen = 24
24*0.3125=7.5
2. shortcut:
2 dozen = 24 = 3 times of 8
because 8 pens cost $2.5, 2 dozen pens cost 3 times of $2.5, thus, $7.5
Jordan has a jar of quarters. When he has 60 quarters in the jar, the jar weighs 52 ounces. When there are 125 quarters in the jar, the jar weighs 65 ounces. What is the weight of the empty jar? 39 ounces 40 ounces 44 ounces 60 ounces.
Answer:
40
Explanation:
X=quarters
Y=weight if empty jar
Y+125X=65
Y+60X=52
subracting the equations you get
65X=13/65=1/5
Y+25=65
Y=40
Answer:
40
Explanation:
just took the test and got a hundred :)