Not sure what "two methods" you refer to, so I'll assume you're supposed to compute the line integral directly as well as with Green's theorem.
Direct computation:
It looks like the line integral is
[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy[/tex]
where C is the union of three line segment. We'll partition C and parameterize each component by
• C₁, the line segment from (0, 0) to (1, 0) : x(t) = t and y(t) = 0;
• C₂, from (1, 0) to (1, 4) : x(t) = 1 and y(t) = 4t;
• C₃, from (1, 4) to (0, 0) : x(t) = 1 - t and y(t) = 4 - 4t;
each with 0 ≤ t ≤ 1.
Compute the integrals over each component:
• Along C₁, we have y = 0, so this integral contributes nothing.
• Along C₂,
[tex]\displaystyle \int_0^1 4t \cdot 0 \, dt + (4t)^3 \cdot 4 \, dt = 256 \int_0^1 t^3 \, dt = 64[/tex]
• Along C₃,
[tex]\displaystyle \int_0^1 (1-t)(4-4t) \cdot (-dt) + (1-t)^2(4-4t)^3 \cdot (-4\, dt) \\\\ = \int_0^1 \left(-260 + 1288 t - 2564 t^2 + 2560 t^3 - 1280 t^4 + 256 t^5 \right) \, dt = -44[/tex]
So, the total line integral is
[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy = 0 + 64 - 44 = \boxed{20}[/tex]
Using Green's theorem:
The interior of C is the triangular region
[tex]D = \{(x, y) : 0 \le x \le 1 \text{ and } 0 \le y \le 4x\}[/tex]
and the integrand has no singularities either on C or within D. So by Green's theorem,
[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy = \iint_D \frac{\partial(x^2y^3)}{\partial x} - \frac{\partial(xy)}{\partial y} \, dx \, dy = \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx[/tex]
The remaining integral is trivial.
[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \int_0^1 x \int_0^{4x} (2y^3 - 1) \, dy \, dx[/tex]
[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \int_0^1 x \left(\frac12 (4x)^4 - 4x\right) \, dx[/tex]
[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \int_0^1 \left(128x^5 - 4x^2\right) \, dx[/tex]
[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \frac{64}3 - \frac43 = \boxed{20}[/tex]
Your 15-year-old brother comes home with the great news that he has decided to buy his first car and has just agreed to give $10,000 to someone on craig's list. He signed the contract and just needs to pay the seller and pick up the car. Your dad is upset and calls the seller to tell him your brother will not be buying the car. What can the seller do?.
Which shows the graph of the solution set of 6x + 4y < 12?.
Answer:
there no image
Explanation:
Answer:
3rd
Explanation:
Aria paid $75,000 for her house. Its property value increased by 2. 2% per year. When aria sold her house after eleven years, how much was it worth, to the nearest hundred dollars? a. $133,700 b. $95,400 c. $95,300 d. $93,100.
Answer:
$95,300. C
Explanation:
Answer:
answer is C
Explanation:
According to the hydrologic cycle, once precipitation has fallen on land, what paths might the water directly take?.
Answer:
What trajectories may precipitation travel after it falls on land? It either soaks into the earth through infiltration, pours over the surface as runoff, or evaporates instantly.
Explanation:
An equilibrium mixture contains 0. 600 mol of each of the products (carbon dioxide and hydrogen gas) and 0. 200 mol of each of the reactants (carbon monoxide and water vapor) in a 1. 00 l container. Co(g)+h2o(g)↽−−⇀co2(g)+h2(g) how many moles of carbon dioxide would have to be added at constant temperature and volume to increase the amount of carbon monoxide to 0. 300 mol once equilibrium has been reestablished?.
Answer:
thanks po
Explanation:
yes po thanks salamat kamsamhida arigato
Choose the best Spanish word to complete the sentence. Alan y Enrique __________ amigos. Es están son está.
Answer:
Son
Explanation:
Just got 100%, but further explanation: Es and esta are both easy to rule out, as neither of them refers to "they" (Alan y Enrique), and estan does not work because of the weird rules. Tbh I feel like you just have to memorize them except in some cases where one just clearly makes more sense than the other.
Answer: Pick answer C: "son"
Use stokes' theorem to evaluate s curl f · ds. F(x, y, z) = x2 sin(z)i + y2j + xyk, s is the part of the paraboloid z = 1 − x2 − y2 that lies above the xy-plane, oriented upward.
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]
What is the combined length of all the buttons longer.
Answer:
4 leght the button is 3 length
Explanation:
if you don't understand here's my link
https//com. ph
Complete the following equations (note that the equations are not balanced). Use the activity series if necessary. An activity series, listed as most reactive to least reactive: Upper L i, Upper K, Upper B a, Upper S r, Upper C a, Upper N a, Upper M g, Upper A l, Upper M n, Upper Z n, Upper C r, Upper F e, Upper C d, Upper C o, Upper N i, Upper S n, Upper P b, Upper H, Upper S b, Upper B i, Upper C u, Upper A g, Upper P d, Upper H g, Upper P t, Upper A u. Al AgCl Upper N a upper C l subscript 2 right arrow. ? AlAg3 Cl2 AlCl3 Ag no reaction AlCl Cl.
Answer :AlAg3 + Cl2
Explanation:
Al + AgCl Upper N a upper C l subscript 2 right arrow. ?
The complete chemical equation would be as follows:
[tex]AlAg_{3} + Cl_{2}[/tex]
Chemical equation is described as the representation or display of a chemical reaction in the form of chemical symbols or system.In the given equation, the subscript followed by AlAg3 by an upper C l subscript with 2. This will produce the reaction i.e. "[tex]AlAg_{3} + Cl_{2}[/tex]."
Thus, the complete equation would read as "[tex]AlAg_{3} + Cl_{2}[/tex]."
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Which detective seems to have more clues about solving the case? Bolsa Sancho.
Answer:
sancho
Explanation:
answers for the whole quiz -
1. true
2. false
3. a parrot
4. while he was hiding out
5. sancho
YOURE WELCOME
Sancho's detective seems to have more clues about solving the case. Thus option B is correct.
Who is a detective?Detectives are typically investigative people, which implies that they are extremely inquiring and curious people who enjoy spending time by themselves thinking. An investigator who works for a law enforcement agency is known as a detective.
Talking to witnesses and whistleblowers, gathering tangible evidence, reviewing databases, and interviewing sources are all common ways that investigators get information to solve crimes.
You've come to the right place if you're seeking for the Sancho from a Cervantes narrative crossword clue answers. Please double-check that you have the right answer or clue because it's common for crossword puzzles with similar clues to have disparate solutions. As a result, they are able to apprehend offenders and prosecute them at court. Therefore, option B is the correct option.
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Read the excerpt and answer the following question. What ideal of the american revolution did bolívar think would not work for south america? democracy individualism liberalism republicanism.
Answer:democracy
Explanation:
The idea of the American revolution did Bolivar think would not work for South America is democracy. The correct option is a.
What is the American revolution?Because of the American Revolution, true democratic politics became conceivable throughout the former colonies. In fact, the drafting of written state constitutions in 1776 and 1777 was the most important immediate result of America proclaiming independence.
The American Revolution ended in 1783, and the French Revolution began in 1789; however, the French Revolution was more complicated than the American Revolution.
The protest began in response to the British monarchy and Parliament levying taxes without regard for colonial representation.
Therefore, the correct option is a. democracy.
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Using the equations 2 sr(s) + o₂ (g) → 2 sro (s) ∆h° = -1184 kj/mol co₂ (g) → c (s) + o₂ (g) ∆h° = 394 kj/mol determine the molar enthalpy (in kj/mol) for the reaction c(s) + 2 sro(s) → co₂ (g) + 2 sr(s).
Considering the Hess's Law, the enthalpy change for the reaction is 790 kJ/mol.
Hess's Law indicates that the enthalpy change in a chemical reaction is the sum of the ∆H of each stage of the reaction will give us a value equal to the ∆H of the reaction when it occurs in a single stage.
In this case you want to calculate the enthalpy change of:
C(s) + 2 SrO(s) → CO₂ (g) + 2 Sr(s)
You know the following reactions, with their corresponding enthalpies:
Equation 1: 2 Sr (s) + O₂ (g) → 2 SrO (s) ∆H° = -1184 kJ/mol
Equation 2: CO₂ (g) → C (s) + O₂ (g) ∆H° = 394 kJ/mol
First stepIn this case, first, to obtain the enthalpy of the desired chemical reaction you need 1 mole of C (s) on reactant side and it is present in second equation. But since this equation has 1 mole of C (s) on the product side, it is necessary to locate this on the reactant side (invert the reaction). And when an equation is inverted, the sign of ΔH also changes.
Second stepNow, 2 moles of SrO (s) must be a reactant and is present in the first equation. Since this equation has 2 moles of Sr0 (s) on the product side, it is necessary to locate the O on the reactant side (invert the reaction) and the sign of ΔH changes.
SummaryIn summary, you know that two equations with their corresponding enthalpies are:
Equation 1: 2 SrO (s) → 2 Sr (s) + O₂ (g) ∆H° = 1184 kJ/mol
Equation 2: C (s) + O₂ (g) → CO₂ (g) ∆H° = -394 kJ/mol
Adding or canceling the reactants and products as appropriate, and adding the enthalpies algebraically, you obtain:
C(s) + 2 SrO(s) → CO₂ (g) + 2 Sr(s) ΔH= 790 kJ/mol
Finally, the enthalpy change for the reaction is 790 kJ/mol.
Learn more:
brainly.com/question/5976752?referrer=searchResults brainly.com/question/13707449?referrer=searchResults brainly.com/question/13707449?referrer=searchResults brainly.com/question/6263007?referrer=searchResults brainly.com/question/14641878?referrer=searchResults brainly.com/question/2912965?referrer=searchResultsLike strain theory, control theory explains deviance as a natural occurrence. Please select the best answer from the choices provided T F.
Answer:
True
Explanation:
Answer:
True
Explanation:
As on Edu 2022
Which of the following is a definition of reduction?.
Answer:
The reduction means ???
Explanation:
What to say
Consider the two male oryx that are shown below. Mc005-1. Jpg Which of Charles Darwin’s main points is depicted in the image? Organisms within a population compete with each other to survive. Over time, beneficial variations will be passed on to future generations. More offspring are produced than can be supported by an environment. All organisms within a population have an equal chance for survival.
Answer:
option B
Explanation:
Answer:
B
Explanation: is the best answer
I hosted a birthday party last sunday and the guests ______ havoc on my house!.
Answer:
I hosted a birthday party last sunday and the guests wreaked hovoc on my house!
What is the main purpose of the concluding paragraph.
Answer:
to summarize, wrap up and put a end to a text or essay.
Explanation:
The tiger's whisker questions and answers.
Answer:
Explanation:
The folktale "The Tiger´s Whisker" originates from Korea, and it is used mostly as a child´s tale. It narrates the story of Yun Ok, whose husband has changed drastically from a loving, and gentle man, to an irrascible one, thanks to the wars. In desperation, Yun Ok, goes to a hermit and asks for a potion. The man tells her that in order to do so, she must bring a whisker from a live tiger. Yun Ok does as she is told, and patiently gains the trust of a tiger, and gets the needed whisker. In the end, she finds out that the lesson the hermit wanted her to learn was that to regain her husband, she needed to apply the same technique she used on the tiger, and not a potion. Given this background, the answers would be thus:
1. A folktale is defined precisely as: A story that is often passed along by word of mouth from one generation to another. This is the correct answer.
2. In this question, the answer is: Her husband has become very distant since he returned from war. This is what is narrated in the story as the reason for Yun Ok´s husband´s estrangement.
3. The correct answer here is: He laughs at Yun Ok´s idea because he thinks she is foolish to believe that solving the problem with her husband could be so simple. Though not directly stated, the hermit does laugh in a way when he says to Yun Ok that healing her husband with a potion is not like taking care of an ear infection. And he makes her feel somewhat foolish for her request. But she insists and he gives in.
4. The answer to this question is: She decides that reconnecting with her husband is worth the risk. This is stated in the story when Yun, although afraid, still continues persistently to go after the tiger, always keeping in mind that all is for the benefit of herself and her husband.
5. The answer here is: She learns that through patience, she can win her husband´s trust and heart like she earned the trust of the tiger. This is the lesson she learns when the hermit burns the whisker and makes her reflect on how she was able to get it from a wild tiger, saying that a man cannot be fiercer, or more difficult, than a tiger.
6. The answer here is: She is patient and demonstrates perseverance by spending six long months, slowly getting the tiger to trust her before she plucks out his whisker. This is exactly what she does in the story. She spends every day of those six months, carefully gaining the tiger´s trust, until he allows her near, and then allows her to take his whisker.
Consider the equilibrium describing the endothermic dissolution of a solid in water. Z n ( o h ) 2 ( s ) − ⇀ ↽ − z n 2 + ( a q ) + 2 o h − ( a q ) if you have a saturated solution at equilibrium, what changes could you make to increase the solubility of the compound?.
To drive this equilibrium in the forward direction, for a saturated solution, the temperature of the system must be increased.
We have been told that the reaction; Zn(OH)2 ( s ) ⇄ Zn2+(aq) + 2OH − (aq), is an endothermic reaction. Recall that in an endothermic reaction, energy is absorbed and the energy of the products is greater than that of the reactants.
In order to drive this equilibrium in the forward direction, for a saturated solution, we can Increase the temperature of the solution. More Zn(OH)2 will dissolve in the solution.
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An astronaut takes what he measures to be a 10-min nap in a space station orbiting earth at 8000 m/s. A signal is sent from the station to earth at the instant he falls asleep, and a second signal is sent to earth the instant he wakes.
Answer:
The astronaut was asleep longer on earth then he was in space
Explanation:
calculate the boring stuff (speed, time) and it shows that he was asleep for a greater value in space
Which graph represents the solution set y > – x + 2?.
Look at the graph
___________
A hemisphere of radius 8 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the center of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the cylinder of maximum volume.
The dimensions of the cylinder that has the maximum volume can be
found be finding the maximum value of the volume function.
[tex]\mathrm{The \ \underline{height \ of \ the \ cylinder \ of \ maximum \ volume \ is \ \dfrac{8}{\sqrt{3} }}}[/tex][tex]\mathrm{The \ \underline{radius \ of \ the \ cylinder \ of \ maximum \ volume \ is \ \dfrac{8 \cdot \sqrt{6} }{3}}}[/tex]Reasons:
The known parameter of the hemisphere are;
The radius of the hemisphere = 8
Required;
The radius and height of the maximum volume of the inscribed cylinder.
Solution:
Let h represent the height of the cylinder, and let r represent the radius of
the cylinder, we have;
r² + h² = 8²
Therefore;
r² = 8² - h² = 64 - h²
r² = 64 - h²
The volume of the cylinder, V = π·r²·h = π·(64 - h²)·h
V(h) = π·(64·h - h³)
At the maximum volume, we have;
[tex]\dfrac{dV(h)}{dh} = \dfrac{d}{dh} \left(\pi \cdot \left(64 \cdot h - h^3 \right) \right) = \pi \cdot \left(64 - 3 \cdot h^2 \right) = 0[/tex]
64 - 3·h² = 0
64 = 3·h²
[tex]h =\sqrt{\dfrac{64}{3} } = \dfrac{8}{\sqrt{3} }[/tex]
[tex]\underline{\mathrm{The \ height \ of \ the \ cylinder, \ h} = \dfrac{8}{\sqrt{3} }}[/tex]
[tex]r^2 = 64 - \dfrac{64}{3} = \dfrac{128}{3}[/tex]
[tex]r =\sqrt{\dfrac{128}{3}} = \dfrac{8 \cdot \sqrt{6} }{3}[/tex]
[tex]\underline{\mathrm{The \ radius \ of \ the \ cylinder, \ } r = \dfrac{8 \cdot \sqrt{6} }{3}}[/tex]
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Two uniform solid balls are rolling without slipping at a constant speed.
A probe orbiting venus exerts a gravitational force of 2. 58 × 103 n on venus. Venus has a mass of 4. 87 × 1024 kg. The mass of the probe is 655 kilograms. The gravitational constant is 6. 67 × 10-11 n*m2/kg2. To three significant digits, the probe is × 106 m from the center of venus.
Answer:
[tex]\mathrm{9.08 \times 10^6 \:km}[/tex]
Explanation:
To solve for the distance between the probe and the center of Venus, use the formula:
[tex]\mathrm{F = \frac{G\: m1 \:m2}{r^2}}[/tex]
Plugin the values:
G =
[tex]6.67\times10^{-11} \mathrm{\frac{m3}{kg\: s2}}[/tex]
[tex]\mathrm{F} =2.58 \times 10^3\mathrm{N}[/tex]
[tex]\mathrm{m1 = 4.87 \times 10^{24}\:kg}[/tex]
[tex]\mathrm{m2 = 655\: kg}[/tex]
Hence:
[tex]\mathrm{F = \frac{G\: m1 \:m2}{r^2}}[/tex]
[tex]2.58 \times 10^{23} = 6.67 \times 10^{-11} (4.87 \times 10^{24})[/tex]
[tex]\frac{(655)}{r^2}[/tex]
[tex]\mathrm{r = 9.08 \times 10^6 \:km}[/tex]
A tube is being stretched while maintaining its cylindrical shape.
Answer:
This question is incomplete, the complete question is;
A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the rate of 2 millimeters per second. At the instant that the radius of the tube is 6 millimeters, the volume is increasing at the rate of 96π cubic millimeters per second. Which of the following statements about the surface area of the tube is true at this instant? (The volume V of a cylinder with radius r and height h is V=πr2h. The surface area Sof a cylinder, not including the top and bottom of the cylinder, is S=2πrh.)
A) The surface area is increasing at the rate of 28pi square mm per second.
B) The surface area is decreasing at the rate of 28pi square mm per second.
C) The surface area is increasing at the rate if 32pi square mm per second.
D) The surface area is decreasing at the rate of 32pi square mm per second.
Answer:
Surface Area is increasing at the rate of 28π mm²/sec ( Option A )
Explanation:
Given the data in the question;
let r be the radius and h be the height of the tube
so volume V = πr²h
dv/dt = πr² dh/dt + 2nrh dr/dt
⇒ 96n = π × 36 × 2 + 2π × 6h dr/dt
⇒ 24π = 12nh dr/dt ⇒ h.dr/dt = 2
Area Surface S = 2nrh
ds/dt = 2π ( r.dh/dt + h.dr/dt )
= 2π ( 6×2 + 2)
= 2π (14)
= 28π
therefore Surface Area is increasing at the rate of 28π mm²/sec ( Option A )
Which expressions are equivalent to ? select two options.
Answer:
I THINK 43('_) AND 34
Explanation:
Let random variable x represent the number of movies screening at movie theaters in a certain city. The following table shows the cumulative probability distribution of the discrete random variable x.
Answer:
Question
Let random variable x represent the number of movies screening at movie theaters in a certain city. The following table shows the cumulative probability distribution of the discrete random variable x.
Explanation:
Which of the following is not a traditional food found in Uruguay?.
Answer:
Gnocchi is not a traditional food found in Uruguay.
Explanation:
In your opinion, which phrase describes society today?
Answer:
an expansion of growth and maturity but also deforming backwords in a way
Answer: very simple
Explanation: I just did it
Before writing a composition it is best to blank it first.
Answer: Before you start writing, remind yourself of the basic composition composition. Almost all articles have three parts: introduction, body of information and conclusion. The five-paragraph text is a common repetition of this and includes an introductory paragraph, three body paragraphs, and a conclusion paragraph.
Explanation: