The boundary of S is the unit circle C in the (x, y) plane with equation x² + y² = 1, which we can parameterize by
r(t) = x(t) i + y(t) j + z(t) k
with 0 ≤ t ≤ 2π, where
x(t) = cos(t)
y(t) = sin(t)
z(t) = 0
so that
dr = (dx/dt i + dy/dt j + dz/dt k) dt = (sin(t) i - cos(t) j) dt
By Stokes' theorem, the surface integral of the curl of F across S is equal to the line integral of F along C :
[tex]\displaystyle \iint_S \mathrm{curl} F \cdot d\vec s = \int_C \vec F \cdot d\vec r[/tex]
We have
[tex]\vec F(x(t), y(t), z(t)) = \sin^2(t) \, \vec\jmath + \sin(t) \cos(t) \, \vec k[/tex]
[tex]\implies \vec F \cdot d\vec r = -\sin^2(t)\cos(t) \, dt[/tex]
so the line integral is
[tex]\displaystyle \int_C \vec F \cdot d\vec r = - \int_0^{2\pi} \sin^2(t) \cos(t) \, dt[/tex]
Substitute u = sin(t) and du = cos(t) dt :
[tex]\displaystyle \int_C \vec F \cdot d\vec r = - \int_0^0 u^2 \, du = \boxed{0}[/tex]
Bernie is an aspiring video game developer. Learning which of the following software would benefit him the most?.
Since Bernie aspires to become a video game developer, learning a 3-D animation software would benefit him the most: C. 3-D animation software.
A software developer refers to a creative individual that develops a concept and writes a set of executable instructions (codes), in order to create a software applications (programs) that proffers a solution to a particular problem by applying various engineering principles.
In Computer programming, software applications (programs) are typically categorized into the following groups:
Computer-aided design softwareSampling softwareSystem software3-D animation softwareA 3-D animation software is a graphic design software that is designed and developed for rendering animated or graphic images in three (3) dimensions.
Hence, a software developer that is interested in becoming a video game developer should learn how to use a 3-D animation software effectively and efficiently.
Read more on software here: https://brainly.com/question/25703767
Your question is lacking the necessary answer options, so I will be adding them here:
A) Computer-aided design software
B) Sampling software
C) 3-D animation software
D) System software
A cart accelerates at 2 m/s2 when a force of 60 N is applied. What is the mass of the cart? (Formula: F=ma) 0. 03 kg 30 kg 62 kg 120 kg.
Answer:
30 kg
Explanation:
From F=ma
60 N = m*2m/s^2
m = 30 kg
Which of the following sentences contains the correct usage for virtuosity? a. The virtuosity of the animals was expressed in their gait. B. The musicians showed extreme virtuosity in their range. C. The virtuosity of the figures in the painting gave it a heavenly appearance. Please select the best answer from the choices provided A B C.
Answer:
The answer would be B.
Explanation:
Answer:
B. The musicians showed extreme virtuosity in their range.
Explanation:
E2020!
One of the lady spartans was falling to the ground.
What is the best choice for the equation of the line of best fit shown? Note that this estimate would be a strong prediction since it is an interpolation (between data points) and the graph shows fairly strong negative correlation.
Answer: b. Y= -1.5x + 23
Explanation: got it right on edge
Answer:
first one is y= -1.5x+23
second one is 11
Explanation:
What did robert sternberg believe about intelligence? (site 1).
Answer:
Robert Sternberg argued practical intelligence, a person's ability to react and adapt to the world around them.
Explanation:
E2020
Robert Sternberg argued practical intelligence, a person's ability to react and adapt to the world around them did robert sternberg believe about intelligence.
What is Robert Sternberg's theory?According to the view of psychologist Robert Sternberg, there are three different levels of love: intimacy, passion, and commitment. It is critical to understand that a relationship built on one aspect has a lower chance of success than one built on two or more.
Another theory of intelligence was created by Robert Sternberg. He called it the triarchic theory of intelligence since it divides intelligence into three categories: practical, creative, and analytical intelligence.
One of the most significant psychologists of the 20th century, Robert J. Sternberg is best known for his ground-breaking studies on creativity, love, intellect, and cognitive styles.
Thus, Robert Sternberg argued practical intelligence, a person's ability to react,
For more information about Robert Sternberg's theory, click here:
https://brainly.com/question/29729895
#SPJ5
What is a common element to many Garafuna treats and foods? meat corn coconut.
Answer:
The answer is "Coconut"
Explanation:
Have a great day!
The common element to many Garifuna treats and foods is coconut. The correct option is c.
What is Garifuna treat?Coconut is a common ingredient in Garifuna food, along with other fundamental components like roots and tubers, including yams and sweet and bitter yucca, as well as bananas and sweet potatoes, among others.
Additionally, coconut is a common ingredient in many of the main courses, snacks, and desserts. This essential component is widespread throughout the Caribbean Sea region.
This style of characteristic food, which is rich in combinations and variants, is a result of the customs of the Garifuna people's forefathers, who were primarily indigenous African, Carib, and Arawak people.
Therefore, the correct option is c, coconut.
To learn more about Garifuna treat, refer to the link:
https://brainly.com/question/6108333
#SPJ5
A popular low-cost airline, budget airways, has gone out of business. Although the service and price provided by the airline was what customers wanted, the larger airlines were able to drive the low-cost airline out of business through an aggressive price war. Which component of the competitive environment does this illustrate?.
Answer:
threat of competitor rivalry
Explanation:
Which detail best supports the central idea that the animals felt pride in growing and supplying their own food?.
Answer:c
Explanation:
The detail that best supports the central idea of animals feeling pride in growing and supplying their own food is their happiness and the positive pleasure they derived from consuming it, now that it was genuinely self-produced.
How did the animals' attitude towards their food change, reflecting their newfound sense of accomplishment and ownership?The animals' happiness and acute positive pleasure in consuming the food highlights their pride and satisfaction in growing and supplying their own sustenance, a departure from the times when they were dependent on their masters for meager rations.
This transformation underscores their sense of achievement and autonomy. Therefore the detail that best supports the central idea of animals feeling pride in growing and supplying their own food is their happiness and the positive pleasure they derived from consuming it, now that it was genuinely self-produced.
Read more about central idea
brainly.com/question/1914190
#SPJ2
A vector makes an angle, θ, with the horizontal. The horizontal and vertical components of the vector will be equal in magnitude if θ is.
A vector has horizontal and vertical components.
The value of [tex]\mathbf{\theta }[/tex] is 45 degrees, when the horizontal and vertical components are equal
Let the magnitude of the vector be H.
So, the horizontal (h) and the vertical components (v) of the vector would be:
[tex]\mathbf{v = Hcos(\theta)}[/tex] --- vertical
[tex]\mathbf{h = Hsin(\theta)}[/tex]
Equate both expressions
[tex]\mathbf{h = v}[/tex]
Substitute values for h and v
[tex]\mathbf{Hcos(\theta) = Hsin(\theta)}[/tex]
Divide both sides by H
[tex]\mathbf{cos(\theta) = sin(\theta)}[/tex]
When [tex]\mathbf{cos(\theta) = sin(\alpha)}[/tex], then
[tex]\mathbf{\theta + \alpha = 90^o}[/tex]
So, we have:
[tex]\mathbf{\theta + \theta = 90^o}[/tex]
[tex]\mathbf{2\theta = 90^o}[/tex]
Divide both sides by 2
[tex]\mathbf{\theta = 45^o}[/tex]
Hence, the value of [tex]\mathbf{\theta }[/tex] is 45 degrees
Read more about vectors at:
https://brainly.com/question/18660017
The function h(x) is defined as shown. H(x) = StartLayout Enlarged left-brace 1st row 1st column x 2, 2nd column x less-than 3 2nd row 1st column negative x 8, 2nd column x greater-than-or-equal-to 3 EndLayout What is the range of h(x)? –[infinity] < h(x) < [infinity] h(x) ≤ 5 h(x) ≥ 5 h(x) ≥ 3.
Answer:
The correct answer would be the third choice. (B)
Explanation:
The range of h(x) as per the given data will be h(x) ≤ 5. The correct option is B.
What is a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.
The function is continuous and has a maximum value of 5 in the specified condition. The range of it is h(x) ≤ 5.
Thus, the correct option is B.
For more details regarding function, visit:
https://brainly.com/question/29633660
#SPJ5
In the interior of the earth can be classified as primordial and radiogenic heat brainly.
The Core is in the interior of the earth can be classified as primordial and radiogenic heat
Expain 5 factors that can slow down
the growth of democracy in Nigeria
Answer:
hmm I think is Salam or lukira
What is collaboration? a. Working successfully with other people b. Struggling when working with other people c. Telling other people how they can work best d. Choosing to work alone instead of with other people.
Answer: A) Working successfully with other people
Explanation:
Meaning: the action of working with someone to produce or create something.
Answer:
A. working successfully with other people
y = 4(x - 2)(x + 4)
In the quadratic equation above, a is a nonzero
constant. The graph of the equation in the xy-plane
is a parabola with vertex (c,d). Which of the
following is equal to d ?
A) -90
//
B) -8a
©) -5a
D) -2a
Answer-A
Explanation:
White shapes and black shapes.
Answer:
9/32
Explanation:
Hopefully it’s relevant to the question.
Which of the following statements is true about the 1920s?.
Answer: a
Explanation:
Answer:
B
Explanation:
What are three advantages of digital x-rays over film.
Answer:
Digital x-rays require less time, reduce radiation, and are cheaper.
:)
Please select the word from the list that best fits the definition A democratic system in which the named "ruler" is a symbolic head of state, and power rests in the hands of elected officials. Democracy monarchy constitutional monarchy democratic socialism.
Answer:
Constitutional Monarchy
Explanation:
just did it
A democratic system in which the named “ruler” is a symbolic head of state, and power rests in the hands of elected officials is the constitutional monarchy.
What is Constitutional monarchy?Constitutional monarchy is a form of state in which there is separation of powers, where the monarch holds the Executive Power appointing the government, while the Legislative Power, is exercised by an assembly or parliament, usually elected by citizens.
In opposition to absolute monarchy, political science distinguishes between constitutional monarchy and parliamentary monarchy. In the constitutional monarchies, the king retains the Executive Power. On the other hand, in the parliamentary monarchies, the Executive Power comes from the Legislative, which is elected by the citizens, the monarch being an essentially symbolic figure.
Therefore, A democratic system in which the named “ruler” is a symbolic head of state, and power rests in the hands of elected officials is the constitutional monarchy.
Learn more about democratic system on:
https://brainly.com/question/19515894
#SPJ7
You meet a new person at a party who tells you that she is a counseling psychologist. You correctly believe that she.
Answer: counsels people with adjustment and life stress problems.
Explanation:
i believe that the asnwer is D.councils people with adjustment and life stress problems counseling psychological speciality. ranging from career development,stress management, mental disorders prevention, personal development, attitude adjustments supervision and training, developing hobbies and interests, etc.
Miranda purchased 425 shares of Dagofi Radar stock at $14. 15 apiece. She earns $374. 00 in dividends every year. What is the yield on Miranda’s Dagofi Radar stock? a. 0. 0622 b. 6. 22 c. 26. 4 d. 0. 264.
Answer:
A) 0.0622
Explanation:
Energy released by the electron transport chain is used to pump h+ into which location in eukaryotic cells?.
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.
Marcia has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. The table below shows the information about the two credit cards Marcia currently uses. Card A Card B Amount $1,879. 58 $861. 00 APR 14% 10% Monthly Payment $43. 73 $18. 29 After 5 years, how much will Marcia have saved in interest by consolidating the two balances? a. $1,526. 40 b. $2,422. 80 c. $105. 00 d. $227. 40.
Answer:
Explanation:
The answer is D. $227.40. I took the exam and got it right.
What is the similarities of prehistoric and egyptian.
Answer:
prehistoric cave paintings, traditional rules :)
Explanation:
did this Question last week with my class 3rd period !
How does soto build a central idea of his story in the excerpt? by showing how carolyn’s family lives in a way that is strange to him, soto supports the idea that culture causes conflict between people. By showing how carolyn’s family lives in a way that is boring to him, soto supports the idea that people from different cultures do not share interests. By showing how carolyn’s family lives in a way that is familiar to him, soto supports the idea that people from different cultures can also share a culture. By showing how carolyn’s family lives in a way that is similar to him, soto supports the idea that there are very few differences among cultures.
Answer:
d
Explanation:
Soto build a central idea by showing how Carolyn's family lives in a way that is familiar to him. Soto supports the idea that people from other cultures can also share a culture.
What is the central idea of a story?Theme is regarded as the key or main idea of any form of literary work. It is known to be that idea that unifies all the element of a story.
Conclusively, By showing how Carolyn's family lives in a way that is familiar to him, Soto supports the idea that people from different cultures can also share a culture, Soto was able to show the main idea of the story.
Learn more about central idea from
https://brainly.com/question/2684713
Wwwusuaayayshsshahhsiw jejeuuerye
Answer:
thank you
Explanation:
........
A gas occupies 22. 4 l at stp and 23. 0 l at 100°c and 1. 25 atm pressure. How many moles of gas did the system gain or lose?.
Answer:
Use photo math its a good choice if your having hard time with math
Choose the best Spanish word to complete the sentence. ¿Dónde __________ Claudia? está es somos soy.
Answer: es
Explanation:
Answer:
Esta
Explanation:
Trust
If the weight of an object on earth is 245 n, what must be the mass of the object?.
Answer:
128
Explanation:
Check all statements that are correct about the nervous system control of blood flow.
The human body is made up of a nervous system. The statements that are correct about the nervous system control of blood flow are;
B. A decrease in vasomotor tone causes blood vessels to dilate and blood pressure to decrease.
C. Nervous control of blood vessels causes blood to be shunted from one large area of the body to another.
D. In skeletal and cardiac muscle tissue, epinephrine and norepinephrine released by the sympathetic nervous system cause the blood vessels to dilate, increasing blood flow.
Nervous control of the circulation is said to be of a more global functions such as they help in resupply blood flow to different areas of the body, regulating the pumping activity of the heart, and giving quick control of blood pressure.
See full question below
Check all statements that are correct about the nervous system control of blood flow. Check Al That Apply
An increase in vasomotor tone chutes blood vessels to dilate further and blood pressure to decrease
A decreto in vnamoror tone cautet blood vessels to dilate and blood pressure to decroma.
Nervous control of blood vessels causes blood to be shunted from one large area of the body to another.
in skeletal and cardiac muscle tissue opinephrine and norepinephrine released by the sympathetic nervous system cause the blood vessels to dilate, Increasing blood flow.
Learn more from
https://brainly.com/question/19457033
https://brainly.com/question/16164895