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]
Outline three Jewish beliefs about shekinah
Answer:
The three main beliefs at the center of Judaism are Monotheism, Identity, and covenant (an agreement between God and his people). The most important teachings of Judaism is that there is one God, who wants people to do what is just and compassionate.
Explanation:
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:
Bills new porch is rectangular with an area of 50 square feet.
Considering the whole question, the perimeter of the porch is 30 feet.
This is because the whole question is, "Bill's new porch is rectangular, with an area of 50 square feet. if the length of the porch is two times the width, what is the perimeter of the porch?"
Therefore to find the perimeter of the porch, here is the step by step:
Given that the length of the porch is two times the width.
Hence, assume that the width = X
Also, assume that the length = 2X
The general formula here:
50 = X × 2X
X × 2X50 = 2x²
2x²X² = 50 ÷2
50 ÷2X² = 25
25X = √25
√25X = 5
Hence, width = 5 feet.
Given that length of the porch is two times the width = 5 × 2 => 10 feet
Therefore Perimeter of a rectangle = 2 (Length + Breadth)
Put all the values in the formula
Perimeter of the porch = 2 × (5 + 10)
= 2 × (15)
= 30 feet.
Hence, in this case, it is concluded that the correct answer is 30 feet.
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bài bánh trôi nước được viết theo phương thức biểu đạt nào? Nếu thể thơ của bài thơ giải
Answer:
I dont understand what you are saying
Why does the reactivity of metals increase from right to left.
The outer electron shell of all of the noble gases (Neon, Argon, etc) have a complete octet (except helium which only has and only needs two electrons to complete its valence shell) which makes them very stable and nonreactive. The metals on the left (Na, Li, etc) all contain just one electron in their outer shell which makes them unstable and they tend to form ionic bonds.
Note that the column of elements just to the left of the noble gases (the rightmost column save one), the halogens, is also highly reactive, because the halogens all only need a single elecron to form the "stable octet" in the outer shell.
Solve for x. 9(x + 1) = 25 + x x = 2 x = 3 x = 4 x = 5.
Answer:
[tex]\boxed{\boxed{\sf x=2}}[/tex]
Explanation:
[tex]\sf 9(x + 1) = 25 + x[/tex]
*Apply Distributive property*
[tex]\leadsto\sf 9x+9=25+x[/tex]
Subtract 9 from both sides:
[tex]\leadsto\sf 9x+9-9=25+x-9[/tex]
[tex]\leadsto\sf 9x=x+16[/tex]
Subtract x from both sides:
[tex]\leadsto\sf 9x-x=x+16-x[/tex]
[tex]\leadsto\sf 8x=16[/tex]
Divide both sides by 8:
[tex]\leadsto\sf \cfrac{8x}{8}=\cfrac{16}{8}[/tex]
[tex]\leadsto\sf x=2[/tex]
_________________________________________
What is the equation for g, which is f(x) = 2x2 + 3x − 1 reflected across the y-axis?.
The answer to your question is:
Based on the diagram, can point d be the centroid of triangle acf? explain. Yes, point d is the point of intersection of segments drawn from all three vertices. Yes, de is three-quarters of the length of the full segment. No, de should be longer than ad. No, the ratio between ad and de is 3:1.
Answer:
A is the correct answer
Explanation:
EDGE
A centroid in a triangle, is the point where all the medians meet.
now a peculiar thing about the centroid is that, it cuts all medians in a 2:1 ratio. So, if that's true, then the median AE, is being cut in two segments AD and DE and AD : DE are on a 2 : 1 ratio.
What is centroid?In a triangle, the centroid is the point of intersection of the three medians, which are line segments joining each vertex to the midpoint of the opposite side.
The centroid divides each median into two segments, with the distance from the centroid to the vertex being twice the distance from the centroid to the midpoint of the opposite side.
Let M be the midpoint of side AB, N be the midpoint of side AC, and P be the midpoint of side BC. Then, we have:
CD = 2DP
CE = 2DN
We are also given that DE = 15. Since D is the centroid, we have:
AD = BD = CD/3
AE = CE/3
DC + DP = PC
CE + DN = NE
AD + AE = DE
Using these relationships, we can find CD and CE:
CD = 2DP = 2(PC - DC) = 2((AD + DP) - (AD/3)) = 2(2AD/3) = 4AD/3
CE = 2DN = 2(NE - CE) = 2((AE + DN) - (AE/3)) = 2(2AE/3) = 4AE/3
To find AD and AE, we can use the fact that AD + AE = DE and AD = BD:
AD + BD = DE
AD + (2AD/3) = 15
5AD/3 = 15
AD = 9
AE = DE - AD = 15 - 9 = 6
Substituting these values into the equations for CD and CE, we get:
CD = 4AD/3 = 4(9)/3 = 12
CE = 4AE/3 = 4(6)/3 = 8
Therefore, CD = 12 and CE = 8.
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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
Solve for n. 11(n – 1) + 35 = 3n n = –6 n = –3 n = 3 n = 6.
Answer:
[tex]n = - 3[/tex]
is answer
What is the acceleration of a 32 kg object if a 6. 75 n force is applied to it? 0. 21 m/s2 4. 74 m/s2 21. 09 m/s2 216. 00 m/s2.
The acceleration of the object is 4.74 m/s²
From the question given above, the following data were obtained:
Mass (m) = 32 Kg
Force (F) = 6.75 N
Acceleration (a) =?The acceleration of the object can be obtained as follow:
[tex]a = \frac{f}{m} \\ \\ a \: = \frac{32}{6.75} \\ \\ [/tex]
a = 4.74 m/s²Therefore, the acceleration of the object is 4.74 m/s²
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What is a polynomial function in standard form with zeros 1 –1 2 and 4.
The polynomial function obtained from the Zeros given, written in standard form is x⁴ - 6x³ + 7x² + 6x - 8
Hope it helps!
Answer:
x⁴ - 6x³ + 7x² + 6x - 8
Explanation:
Write the linear factor for each zero.
[tex]g(x) = (x - 1) (x + 1) (x - 2) (x - 4)[/tex]
Multiply the first two, then the second two.
[tex]g(x) = (x^{2} + x - x -1) = (x^{2} - 1) then (x^{2} - 4x - 2x + 8)[/tex]
Use the Distributive Property.
[tex](x^{2} - 1) (x^{2} - 6x + 8) = (x^{4} - 6x^3 + 8x^{2} - x^{2} + 6x - 8)[/tex]
Simplify.
[tex]x^{4} - 6x^{3} + 7x^{2} + 6x - 8[/tex]
Evaluate the line integral, where c is the given curve. C (x/y) ds, c: x = t3, y = t4, 1 ≤ t ≤ 4.
We have
x = t³ ===> dx/dt = 3t²
y = t⁴ ===> dy/dt = 4t³
Then with the given parameteriztion, the line integral along C of x/y is
[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac{t^3}{t^4} \sqrt{(3t^2)^2 + (4t^3)^2} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac1t \sqrt{9t^4 + 16t^6} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac{\sqrt{t^4}}t \sqrt{9 + 16t^2} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 \frac{t^2}t \sqrt{9 + 16t^2} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \int_1^4 t \sqrt{9 + 16t^2} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \frac1{32} \int_1^4 32t \sqrt{9 + 16t^2} \, dt[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \frac1{32} \int_1^4 \sqrt{9 + 16t^2} \, d\left(9+16t^2\right)[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \frac1{32} \cdot \frac23 \left(9+16t^2\right)^{\frac32}\bigg|_1^4[/tex]
[tex]\displaystyle \int_C \frac xy \, ds = \frac1{48} \left(265^{\frac32} - 25^{\frac32}\right) = \boxed{\frac{265\sqrt{265}-125}{48}}[/tex]
The line integral will be "[tex]\frac{265\sqrt{265} - 125 }{48}[/tex]". To understand the calculation, check below.
Line integralAccording to the question,
Curves, x = t³ or,
[tex]\frac{dx}{dt}[/tex] = 3t²
y = t⁴ or,
[tex]\frac{dx}{dt}[/tex] = 4t³
Now, the line integral along C will be:
→ [tex]\int\limits_C {\frac{x}{y} } \, ds[/tex] = [tex]\int\limits^4_1 {\frac{t^3}{t^4} }[/tex] √(3t²)² + (4t³)² dt
= [tex]\int\limits^4_1 {\frac{1}{t} }[/tex] √9t⁴ + 16t⁶ dt
= [tex]\int\limits^4_1 {\frac{t^4}{t} }[/tex] √9 + 16t² dt
= [tex]\int\limits^4_1 {\frac{t^2}{t} }[/tex] √9 + 16t² dt
= [tex]\int\limits^4_1[/tex] t√9 + 16t² dt
= [tex]\frac{1}{32}[/tex] [tex]\int\limits^4_1[/tex] √9 + 16t² d (9 + 16t²)
= [tex]\frac{1}{32}\times \frac{2}{3}[/tex] [tex](9+16t^2)^{\frac{3}{2} } |_1^4[/tex]
= [tex]\frac{1}{48}[/tex] ([tex]265^{\frac{3}{2}} - 25^{\frac{3}{2}[/tex])
= [tex]\frac{265 \sqrt{265 } -125 }{48}[/tex]
Thus the above approach is correct.
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What was the role of muslim religious leaders in africa.
Answer: In most cases, the Muslim religious leaders serve also as community leaders and have broad political influence; their visit will contribute to strengthening the diplomatic ties between Israel and Africa.
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Which word in the passage helps the reader determine the meaning of the word miscarriage? What is the best definition of the word miscarriage as it is used in this passage?.
The word in the passage helps the reader determine the meaning of the word miscarriage is disgraced. The best definition of the word miscarriage as it is used in this passage is a failure.
What is Inference?
Inference in any literature piece refers to achieving the conclusion of any subject with the support of facts and evidence present in the particular piece of literature.
According to the dictionary, the synonym meaning of the word miscarriage is a failure, ruin, or something that is not achieved or spoiled by something. Most of the time this word is used with Pregnancy when an individual loses their baby.
In this passage, it is used with context as "to be exposed to censure, without hope of praise; to be disgraced by miscarriage, or punished for neglect," where the word miscarriage which means failure is supported by disgraced to determine the meaning.
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The complete question is Probably
It is the fate of those who toil at the lower employments of life, to be rather driven by the fear of evil, than attracted by the prospect of good; to be exposed to censure, without hope of praise; to be disgraced by miscarriage, or punished for neglect, where success would have been without applause, and diligence without reward.
-Preface to A Dictionary of the EnglishLanguage,Samuel Johnson
Answer:
First is Disgraced, Second is failure
Explanation:
No prob :D
A family has two cats named gordo and flaco. Gordo weighs 15 pounds and flaco weighs 8 pounds. A cat’s weight is classified as unhealthy if the weight is located in the top 5% or bottom 5% of all cat weights. The distribution of cat weights is approximately normal with mean 9. 5 pounds and standard deviation 1. 5 pounds. Which of the following is the best description of gordos and flacos weights?.
How did fossils help and teach scientists about the history of the earth brainly.
Answer:
Fossils helped teach scientist by giving information of the species that lived back then.
Explanation:
The fossils have clues on them help identify what they are.
How does the author unfold the details of the text painter of light.
The author unfolds the details of the "Painter of Light" text when presenting Kinkade's life chronology.
We can arrive at this answer because:
"Painter of Light" is a text with a chronological structure, which presents a series of events that occurred in a timeline.In this text, this kind of structure is used for Kinkade's life chronology, showing the most important events in his life and how that made him relevant to introduce to readers.It is important to point out that textual structure is the way a text is organized to present information to the reader.
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Answer: The answer is A
Explanation:
Based on the context, what is the best definition of shrewdly as it is used in these lines? thoughtfully quickly cleverly sharply.
Answer:
Its D
Explanation:
From the excerpt of Hamlet, the meaning of the word shrewdly is sharp. Thus, option d is accurate.
What is shrewd?Shrewdly is the word that defines the piercing and strong which is used in reference to the wind or the air. In the text, Hamlet tells Horatio that the wind was cold and sharp.
It is used in the text to show how the wind was strong, and piercing making the environment cold around them. The word does not describe quickness, thoughtfulness, and clever nature as these words do not define wind.
Therefore, option d. sharp is the correct option.
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How many positive integers are there between 100 and 999.
Answer:
be the positive integers between 100 and 999 inclusive. contains 900 integers, while we are interested in integers divisible by 7. Thus 128 integers are divisible by 7.
Explanation:
hope this helps
Answer:
Let be the set of positive integers between 100 and 999. The set contains 900 integers, and the integers are divisible by 7. By division rule, where is the finite set with union of pairwise disjoint subsets with elements.
Explanation:
can i get brainliest
The half-life of protactinium-226 is 2 minutes. If you started with 20 grams of pa-226, how much do you have after 8 minutes?.
Answer:
28.25
Explanation:
Your automatic payment option pays bills of $23. 17, $55. 67, $2,345. 15, $575. 25 and $1. 15. How much was the mean payment?.
You work in a company that has begun selling annual subscriptions to its new online magazine. During december, the company sold the first subscriptions, receiving $600,000, which represents one-fifth of its revenues from all sources for the year. The entire amount has been collected in cash. As the end of the the year approaches, you notice that the company recorded the entire $600,000 to revenue and there is no plan to make an adjusting entry.
Answer:
a.cademics.helper
Explanation:
IG reach out get the answer from here
The accounting error that was committed and how it affected the financial accounts will be stated in the note.
What are financial accounts?Financial accounts are defined as the process of documenting, compiling, and disclosing a company's financial statement transactions. The preparation of financial reports for external audiences like investors, creditors, and tax authorities to learn more about a company's performance is the primary goal of financial accounting.
The $600,000 that was raised from the sale of the new online magazine's annual subscription is the amount that will be raised for the upcoming 12-month period that will begin in December of the current year. Of the total, only $50000 will be noted for the year. Therefore, $550000 in related services for the following eleven months should be recorded as unearned income.
Thus, the accounting error that was committed and how it affected the financial accounts will be stated in the note.
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Your question is incomplete, but probably your complete question was
You work in a company that has begun selling annual subscriptions to its new online magazine. During December, the company sold the first subscriptions, receiving $600,000, which represents one-fifth of its revenues from all sources for the year. The entire amount has been collected in cash. As the end of the the year approaches, you notice that the company recorded the entire $600,000 to revenue and there is no plan to make an adjusting entry.
Draft a memo around two paragraphs in length to your supervisor, which explains the following:
The accounting error that has been made
The effect this error will have on the financial statements dated at the end of December
The problems that might result
The importance of fixing the error and what needs to be done to fix the error
Make sure to include proper grammar, spelling, etc.
In the cycle shown is mantle made of silicate rocks why.
Answer:
The rocks that make up Earth's mantle are mostly silicates—a wide variety of compounds that share a silicon and oxygen structure. Common silicates found in the mantle include olivine, garnet, and pyroxene.
Explanation:
who likes food should tell me
Explanation:
Whooo doesn't like food
apparition
enchanted
ghost
ghostly
ghoulish
goblin
haunted house
haunting
Use the drop-down menus to complete the statements below to answer this question: can you determine whether a system of linear equations has a solution just by looking at the graph of the equations?.
Answer:
The coordinates of a point satisfies the equation of a line if the point lies on the line
If a single point satisfies the equations of two lines, the point is on both lines, so the lines will intersect at that point.
This means that each point where the two lines touch is a solution to the system of equations
This means that if you substitute the x and y values of the point for x and y in the equations, both equations will be true
Explanation:
Answer:
on the line
on both lines, intersect
intersect, solution
true
Explanation:
I did it on Imagine Math.
Which of the following factors best supports the argument in the excerpt?.
Answer:
probaly awnser C
Explanation:
or B or a
A boy exerts an average force of 65n when he lifts a box 1. 2m. How much work does he do?.
Answer:
78 Nm
You can multiply force (N) and distance (m).
Which of the following people worked with government in the 1960s to get laws passed to help noncitizens and farm workers? Huey Newton Bobby Seale Stokely Carmichael Dolores Huerta.
Government often makes laws that aim for the betterment of its people. Cesar Chavez worked with government in the 1960s to get laws passed to help noncitizens and farm workers.
Cesar was known to be a man who use nonviolent means as used by Mahatma Gandhi and Martin Luther King Jr. in all his works.
He was known to be the founder of the National Farm Workers Association (later the United Farm Workers of America)
He won a lot of significant victories so as the pay and improve working conditions for farm workers is improve in the late 1960s and 1970s
See full question below
Which of the following people worked with government in the 1960s to get laws passed to help noncitizens and farm workers?
Huey Newton
Bobby Seale
Cesar Chavez
Dolores Huerta
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Answer:
Explanation:
Dolores huerta
