Stokes' theorem says that the surface integral of the curl of the vector field F across the surface S is equal to the line integral of F along the boundary of S.
In this case, the boundary is a circle in the x,y-plane with radius 2. (To see this, set z = 0 and rearrange the equation for the paraboloid as x² + y² = 4.)
Then
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_{\partial S} \vec F \cdot d\vec r[/tex]
where
[tex]\vec r = 2\cos(t) \,\vec\imath + 2\sin(t) \,\vec\jmath[/tex]
parameterizes the circular boundary of S with 0 ≤ t ≤ 2π. Then
[tex]d\vec r = \dfrac{d\vec r}{dt}\,\dt = (-2\sin(t)\,\vec\imath + 2\cos(t)\,\vec\jmath)\,dt[/tex]
and the integral becomes
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_{\partial S} \vec F \cdot d\vec r[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} \vec F(\vec r(t)) \cdot \frac{d\vec r}{dt}\,dt[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s \\= \int_0^{2\pi} ((2\cos(t))^2 \sin(0)\,\vec\imath + (2\sin(t))^2\,\vec\jmath + (2\cos(t))(2\sin(t))\,\vec k) \cdot(-2\sin(t)\,\vec\imath + 2\cos(t)\,\vec\jmath)\,dt[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} 8\sin^2(t)\cos(t) \, dt[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} 8\sin^2(t) \, d(\sin(t))[/tex]
[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \frac83 (\sin^3(2\pi)-\sin^3(0)) = \boxed{0}[/tex]
Adam by hugh cook meaning.
the poem focuses on Adam, the first person in Heaven, who had eaten the forbidden fruit. so the message is do what god tells you and if he tells you not to do something don't do it
On a position vs. Time graph, which feature would represent motion in the negative direction over time?.
A time graph reveals specific information on the velocity (change in position with respect to a change in time).
So, on a position - time graph, the feature representing motion in the negative direction over time is a downward sloping line segment.
A slope in a position time graph depicts the velocity also called the slope in this type of graph as it the change in position over time.
So, a downward sloping line segment feature in a time graph indicates that the motion of the object is in the negative direction. While a positive sloping line segment indicates otherwise.
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Answer:
a downward-sloping line segment
Explanation:
Oscar started freaking out about the test formal brainly.
Answer:
?
Explanation:
Answer:
y lol
Explanation:
Which of the following is true of the capital requirement? check all that apply.
Answer:
Its intended goal is to protect the interests of those who hold equity in the bank.
The amount of capital required depends on the type of assets the bank holds.
Explanation:
edge!!
Sino gusto sumali sa meet ko
ito code:-
zcn-mqti-ssh
UwU
Answer:
hmm...I don't understand
Did you go to the swim meet.
Answer:
what?
Explanation:
Multiple-choice questions on advanced placement exams have five options: a, b, c, d, and e. A random sample of the correct choice on multiple-choice questions on a variety of ap exams1 shows that b was the most common correct choice, with of the questions having b as the answer. Does this provide evidence that b is more likely to be the correct choice than would be expected if all five options were equally likely? show all details of the test. The data are available in apmultiplechoice.
Answer:
the answer would be a
Explanation:
What is the potential energy of a rock that weighs 5 kg and sits on top of a 10- meter high hill?.
Answer:
490 Joule
Explanation:
Solution:
Given,
Mass (m) = 5 kgAcceleration due to gravity= 9.8 m/sHeight (h)= 10 mHere,
Potential Energy (P.E.)= mgh
=5×9.8×10
= 490 Joule
Points b c and d lie on a straight line.
Answer:
Explanation:
continuation?
5006+6
this is the hardest question on Earth i KEEP GETTING IT WRONG PLEASE help me
Answer:
5012
Explanation:
5006 + 6 equals 5012
if the natural market forces are left to their own devices, will tourism result in income redistribution that works in favor of the poorer segments of the population?
Answer:
No
Explanation:
No, companies will most likely reduce benefits/wages to increase profit margins and increase revenue, resulting in increased share value and happier shareholders.
Which of the following is a difference between phase i and phase ii of meiosis?(1 point).
AnswerHowever, Meiosis I begins with one diploid parent cell and ends with two haploid daughter cells, halving the number of chromosomes in each cell. Meiosis II starts with two haploid parent cells and ends with four haploid daughter cells, maintaining the number of chromosomes in each cell.:
Explanation:
According to john green, why was luther successful with his rebellion when others before him had failed?.
Answer:
As indicated by John Green, Luther's prosperity with the insubordination originated from his capacity to, at first, cause his lessons to resound with laborers and adolescents. Be that as it may, this reverberation didn't keep going long. Luther before long turned his lessons against the workers for the lords and sovereigns.
Explanation:
Thus according to John Green, Luther's capacity to originally made his beliefs appealing to workers and teenagers contributed to the rebellion's success.
Who is Luther?The Renaissance, which resulted in Protestantism becoming the fourth main force in Christendom after Catholic Faith was sparked in part by Martin Luther's convictions.
According to John Green, Luther's success with inappropriate behavior stemmed from his ability to initially make his lectures resonate with workers and teenagers. Whatever the case, this reverberation lasted only a short time.
The workers serving the princes and sovereign states were the target of Luther's teaching soon after. However, this echo was brief. The teachings of Luther soon shifted away from the peasants and toward the kings.
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A force acts on a particle that undergoes a displacement.
Answer:
An F Vector Force
Example:
The work done by the force on the particle is 1 J.
The angle between the force and the displacement is 81.87⁰.
The given parameters;
F = (4i - 3j)
displacement of the particle, s = (i + j)
The work done by the force on the particle is calculated as follows;
The angle between the force and the displacement is calculated as follows;
If five times a number increased by six, the result is at least 26. What is the least possible number that satisfies these condition ?.
The least possible number that satisfies the condition is 4
Let the number be a.
Thus,
Five (5) times the number = 5 × a = 5a
From the question given above, we were told that five (5) times the number when increased by 6 is 26. This can be written as:
5a + 6 = 26Finally, we shall determine the value of a. This can be obtained as follow:
5a + 6 = 26
Collect like terms
5a = 26 – 6
5a = 20
Divide both side by 5
a = 20 / 5
a = 4Therefore, the least possible number that satisfies the condition is 4
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What does it mean to be ‘other oriented’?
Answer:
Putting others needs before your own
Answer:
thinking, caring and acting in accordance with the interests of others is a common relational style
Explanation:
egd
If 1=15 and 6=20 what is 3.
if 1 = 15 and 6=20 what is 3
=
25
West corp. Issued 25-year bonds two years ago at a coupon rate of 5. 3 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is the ytm?.
Answer:
america
Explanation:
because im black
A story with multiple narrators will usually have a(n) ____________ plot.
Answer:
nonlinear
Explanation:
It has become increasingly popular in young adult novels to have
multiple narrators. Often, this is done through alternating
chapters. One chapter is told from one perspective, while the
next chapter is told from another. This can be done with either
first person or third person limited.
Multiple Narrators
This will likely mean that the plot is nonlinear in such a novel. The
reader will jump from one character and event to another (and
sometimes even see the same event twice, but from different
perspectives).
This is also sometimes called "alternating point of view".
Stories could either have a single or multiple narrator(s). Hence, stories having multiple narrators would usually have a non-linear plot.
Multiple narrators in a story means that characters in the story are numerous, hence, acts and scenes would have to be passed on to these characters from time to time. As for single narrator, this is not the case as the number of actors are very limited.Hence, because multiple narrators often hinders a story to be chronologically ordered, then it would result in a non-linear plot.
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My mom suggested keep the surroundings clean and green.
This is the correct sentence:
My mom suggested keeping the surroundings clean and green.It's correct to say keeping and not keep because you have to form the sentence using suggest + the verb with ing (keep + ing: keeping).
I was able to find the instructions to complete the exercise online: Write sentences using suggest + V-ing or suggest + clause with should.
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Use the formula for annual compound interest. A = P (1 StartFraction r Over n EndFraction)nt Remember, A refers to the total amount owed. Calculate the total amount that Tom would repay. $10,337 $11,337 $12,337 $13,337.
Answer:
11,337
Explanation:
Answer:
$11,337
Explanation:
Some numbers are formed with closed paths.
Answer:
what is the question
Explanation:
Which of the following most directly contributed to the change over time depicted on the two maps?.
Locations are often shown on a map. The option that directly contributed to the change over time depicted on the two maps is the The building of canals and roads.
In 1800, U.S. citizens and immigrants to the country often traveled majorly by horseback or on the rivers.
As time went by, crude roads and canals were made. It was later on that railroads was made which was used to move people and goods with greater efficiency.Conclusively, A map is shows the visual representation of a location and the various part that is found in that specific location.
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Which of the following most directly
contributed to the change over time depicted on
the two maps?
(A) The construction of a national highway
system
(B) The establishment of different time zones
across the country
(C) The building of canals and roads
(D) The use of diesel engines
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Which of the following is a way to buy stocks.
Answer:
Through Hiring a Stockbroker
Answer:
Online through a brokerage Web site
Explanation:
Help plz lol………………………….
Answer:
105/330
Explanation:
drama:
25 students
both:
60 students
sports:
140 students
total:
225 students
330-225=105
In the diagram, ce=12 units and be=5 units. Based on the given information, what is ae? 2 units 7 units 12 units 17 units.
Answer:
C. 12 units.
Right on edge
In the diagram, ce=12 units and be=5 units. Based on the given information. So, the answer will be 7 units. Thus, option B is correct.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In the diagram,
⇒ CE = 12 units
⇒ BE = 5 units
Now,
Since, Triangle CBE is an right triangle.
And, We have;
⇒ CB = AB
⇒ ∠DBC = 90°
⇒ ∠ABE = ∠DBC = 90° (opposite angles formed by the intersection of AC and DE.)
As, ∠CBE and ∠ABE are supplementary angles and form a straight line.
So, We get;
⇒ ∠CBE + ∠ABE =180°
⇒∠CBE = 180° - ∠ABE
= 180°- 90°
= 90°
And, Between triangle ΔCBE & ΔABE;
⇒ ∠CBE = ∠ABE = 90°
⇒ CB = AB (given)
⇒ BE = BE (common side)
Hence, The triangles Δ CBE & ΔABE are congruent.
⇒ Δ CBE ≅ ΔABE( by S-A-S Congruency)
⇒ CE = AE ( as triangle Δ CBE & ΔABE are congruent then the sides are same.)
⇒ AE = 12 units
Thus, The length of AE = 12 units
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A student uses the apparatus to determine the concentration of a solution of hydrofluoric acid. Which component will the student put in the burette?.
Answer: Titrant
Explanation: make me brainlets
The lawmaking responsibility of the members of the house is to.
Answer:
The lawmaking responsibility of the members of the House is to 1) discuss pending bills with their constituents. 2) make sure their supporters approve of a bill. 3) propose, amend, and vote on bills and resolutions
Explanation:
The lawmaking responsibility of the members of the House is to
discuss pending bills with their constituents.
make sure their supporters approve of a bill.
propose, amend, and vote on bills and resolutions.
gather public support for their bills.
Francis has the standard plan offered by his employer and is making an office visit to an in-network doctor to treat his flu-like symptoms. How much would francis be asked to pay by the office manager in the doctor's office?.
There are different kinds of healthcare plans. Francis will not pay (Option one) if he be asked to pay by the office manager in the doctor's office.
There is a standard of minimum coverage that is applicable to employment based health plans.
A health plan must meets the minimum required value standard if;
a. It was designed to pay at least 60% of the total cost of medical services for a standard population.
b. Does the employer offer a health plan that meets the minimum value standard.
Francis is already covered in his his standard plan and therefore will not be expected to pay the money. But in cases of only some percentage of the plan is covered, then the individual can cover the rest expenses.
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Francis has the Standard Plan offered by his employer and is making an Office Visit to an in-network
doctor to treat his flu-like symptoms. How much would Francis be asked to pay by the office manager in
the doctor’s office?
a. $0
b. $15
C. $25
d $40
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Answer: C
Explanation:
Solve for x in the equation x^2-8x+41=0.