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 = 4 − x2 − y2 that lies above the xy-plane, oriented upward.
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]
Acrostic poem of energy.
Answer:
Eat foods that can give you energy like natural foods, carbohydrates, and protein.
Nutrition is an important part of your health so make sure to check nutrition facts.
Exercise to keep your blood, heart, and your body moving.
Really try not to eat a lot of junk food because it can keep you from being healthy.
Grow by also being in a good mood because when your sad it decreases energy.
You can keep up your energy by following these amazing steps.
Explanation:
What approximate focal length of the objective lens will give a total magnification of 200×? assume a length l = 160 mm.
Considering the data in the question, the focal length of the objective lens that will give a total magnification of 200x is 0.8cm focal length.
The whole question is:
You are using a microscope with a 10x eyepiece. What focal length of the objective lens will give a total magnification of 200x? Assume a length L = 160mm.
How was the answer derived?Given that total magnification is 200
And the Assume length is 160
Since we used a microscope with a 10x eyepiece, the magnification would be divided by 10.
=> 200 ÷ 10 = 20.
Also, the focal length is measured in centimeters or meters; we would change the millimeters of focal length to centimeters. Therefore, we have 160 ÷ 10 = 16
The formula for the focal length of the objective lens = assumed length ÷ total magnification.
=> 16 ÷ 20 = 0.8cm.
Hence, in this case, it is concluded that the correct answer is "0.8cm."
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Alterations in various aspects of society over time.
alterations in various aspects of society over time according to pitrim Sorkin cyclical theory of social change the principle of immant change is the natural tendency of a society structure to swing back and forth between the ideotional and sensate culture
A significant alteration to a society's structure is social change. Numerous facets of a society, including its economic, political, cultural, ethical, and identity problems, can be affected by social change.
What Alterations in various aspects of society over time?The major alteration of social structure and cultural norms over time is referred to as social change. Social ties that have remained constant over time and become routine or repetitive are referred to as social structures.
Among the key forces influencing societal development are population growth and composition, the natural environment, social conflict, culture, and technology.
Cultural lag is the term used to describe a delayed shift in one area of society as a result of a change in a different area of society.
Therefore, Alterations in social change various aspects of society over time.
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how did the officer feel about himself
Answer:
how happy
Explanation:
The distribution of number of hours worked by volunteers last year at a large hospital is approximately normal with mean 80 and standard deviation 7. Volunteers in the top 20 percent of hours worked will receive a certificate of merit. If a volunteer from last year is selected at random, which of the following is closest to the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 ?.
Explanation:
Using the normal distribution, it is found that the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 is closest to:
B 0.123
In a normal distribution with mean \muμ and standard deviation \sigmaσ , the z-score of a measure X is given by:
Z = \frac{X - \mu}{\sigma}Z=σX−μ
It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem:
The mean is of 80, hence \mu = 80μ=80 .
The standard deviation is of 7, hence \sigma = 7σ=7 .
The minimum value is the 80th percentile, which means that it is X_mXm when Z has a p-value of 0.8.
The probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 is P(X_m < X < 90)P(Xm<X<90) , which is the p-value of Z when X = 90 subtracted by the p-value of Z when X = X_mX=Xm , hence the p-value of Z when X = 90 subtracted by 0.8.
Z = \frac{X - \mu}{\sigma}Z=σX−μ
Z = \frac{90 - 80}{7}Z=790−80
Z = 1.43Z=1.43
Z = 1.43Z=1.43 has a p-value of 0.9236.
0.9236 - 0.8 = 0.1236, hence closest to 0.123, option B.
Using the normal distribution, it is found that the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90 is closest to:
Letter B
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}\\Z=\sigma X - \mu[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. In this problem:
The mean is of 80, hence [tex]\mu = 80[/tex]. The standard deviation is of 7, hence [tex]\sigma = 7[/tex]. The minimum value is the 80th percentile, which means that it is [tex]X_m[/tex] when Z has a p-value of 0.8.The probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90, which is the p-value of Z when X = 90 subtracted by the p-value of Z when X = X_mX=Xm , hence the p-value of Z when X = 90 subtracted by 0.8.
[tex]Z = \frac{X - \mu}{\sigma}\\Z=\sigma X - \mu\\Z = \frac{90 - 80}{7}\\Z=790 - 80\\Z = 1.43Z=1.43[/tex]
Has a p-value of 0.9236.
[tex]0.9236 - 0.8 = 0.1236[/tex]
Hence closest to 0.123.
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What does the author’s first use of the key term illusion suggest about American foreign policy? The United States causes many problems. The United States could not remain separate. The promotion of democracy is a false policy. It is unsafe for one country to have too much power.
Answer: United States could not remain separate.
Explanation: cause i be smart
The author’s first use of the key term illusion suggest about American foreign policy is The United States could not remain separate.
The 'illusion of isolation' means that America tried to pretend to be an isolationist continent, meaning that it would have nothing to do with the politics of other countries, however, that turned out to be a lie, especially when it openly entered WWII.
What are the three main goals of American foreign policy?Security, prosperity, and the creation of a better world are the three most prominent goals of American foreign policy.
Security, the protection of America's interests and citizens, is a perennial concern, but America has tried to achieve security in different ways throughout its long history.
What are the 4 main goals of America's foreign policy?The four main objectives of U.S. foreign policy are the protection of the United States and its citizens and allies, the assurance of continuing access to international resources and markets, the preservation of a balance of power in the world, and the protection of human rights and democracy.
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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.
Which is the correct translation of the sentence into an equation? four less than a number is 12.
Answer: 4 - ? = 12
Explanation: maybe
Evaluate the surface integral. S y2 ds s is the part of the sphere x2 + y2 + z2 = 36 that lies inside the cylinder x2 + y2 = 9 and above the xy-plane.
Parameterize S in cylindrical coordinates by the vector function
r(u, v) = (x(u, v), y(u, v), z(u, v))
with
x(u, v) = u cos(v)
y(u, v) = u sin(v)
z(u, v) = 36 - u²
with 0 ≤ u ≤ 3 and 0 ≤ v ≤ 2π. Take the normal vector to S to be
[tex]\vec n = \dfrac{\partial r}{\partial u} \times \dfrac{\partial r}{\partial v} = (2u^2\cos(v),2u^2\sin(v),u)[/tex]
so that the surface element is
[tex]dS = \|\vec n\| \, du\,dv = u \sqrt{1+4u^2}\, du\, dv[/tex]
Then the surface integral is
[tex]\displaystyle \iint_S y^2\,ds = \int_0^{2\pi} \int_0^3 u\sqrt{1+4u^2} \, du\, dv[/tex]
[tex]\displaystyle \iint_S y^2\,ds = 2\pi \int_0^3 u\sqrt{1+4u^2} \, du[/tex]
[tex]\displaystyle \iint_S y^2\,ds = \frac{2\pi}8 \int_0^3 8u\sqrt{1+4u^2} \, du[/tex]
[tex]\displaystyle \iint_S y^2\,ds = \frac\pi4 \int_0^3 \sqrt{1+4u^2} \, d(1+4u^2)[/tex]
[tex]\displaystyle \iint_S y^2\,ds = \frac\pi4 \cdot \frac23(1+4u^2)^{\frac32} \bigg|_0^3 = \boxed{\frac\pi6 \left(37^{\frac32}-1\right)}[/tex]
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 who willl be the first in his or her familt to attend college is a ___ student
Answer:
“First-Generation Student”
What is the speed of a wave with a wavelength of 3 m and a frequency of. 1 Hz? 0. 03 m/s 0. 3 m/s 3. 1 m/s 30 m/s.
Answer:
The correct answer to the question is 0.3 m/s i.e the speed of the wave is 0.3 m/s.
Which range of the electromagnetic spectrum travels at the fastest speed.
Answer:
Photons travel in harmonic waves at the fastest speed possible in the universe: 186,282 miles per second (299,792,458 meters per second) in a vacuum, also known as the speed of light. The waves have certain characteristics, given as frequency, wavelength or energy.
A balloon flying at 3000 feet above the ocean measures the angles of depression of each end of an island directly in front of the balloon to be 75. 8° and 15. 6°. What is the length of the island to the nearest tenth of a mile?.
Answer: Distance to close end of island is 3000/tan(75.8); distance to far end is 3000/tan(15.6). The difference is 9985.676 feet or about 1.9 miles.
Explanation: 2 explanation Balloon, flying or levitating, has no front to recon with, so two possible answers.
tan(90–15.6)+or-tan(90–75.08) * 3000= length of island
What are the differences between the sat and act.
Answer:
The SAT is the longer of the two tests at three hours without the essay, and three hours and 50 minutes with the essay. The ACT is three hours and 35 minutes with the writing section, and three hours without it. The lengths of each sections vary between the two tests, which can be seen below.
Look at the graph. A graph titled Yearly Average, Dow Jones Industrial Average. The x axis shows the years 1919 to 1929. The y axis shows the yearly average closing price, from 0 to 350. In 1919, it was at 100 and stayed relatively stable until 1925, when it began to rise dramatically, from 125 in 1925 to over 300 in 1929. During what years did consumerism cause the stock market to grow most? 1920–1921 1921–1924 1922–1925 1924–1929.
Answer It's D (1924 - 1929)
hope this helps :)
Explanation: edge 2023
WhY DoEs MoMmUy JuMp UP AND DOWN IN THDOSE MUDDY MUDDY POODLES
Answer:
because shes a piggy.
Explanation:
Answer:
yeaaaa
Explanation:
Mud digger
We kick the mud by the pound
Our tires stay roarin' while we ridin' through the town
Mud digger
And I keep a bad truck around
Big truck tall suspension, 40-inches from the ground
Mud digger
And my Chevy sittin' on 44's
Pipes louder than glass packs, straight pipes y'all know
Mud digger
If y'all don't know how the mud diggin' goes
Then get a couple of tickets to a mud boggin' show
What is the main objective of the basagang palayok.
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:
Identify the type of bonding within each substance.
Answer:
1. Co ( s ) - metallic bonding
2. CoCl₂ ( s ) - ionic bonding
3. CCl₄ ( l ) - covalent bonding
Explanation:
Metallic bonding -
It is the type of bonding present between the atoms of the metals , via the electrostatic interaction between the metal and the delocalized electrons , is known as metallic bonding .
For example ,
Mostly metals show metallic bonding .
Ionic bonding -
It is the type of bonding present between the ions i.e. , the cation and the anion is known as ionic bonding .
For example ,
Mostly ionic compound , like salts show ionic bonding .
Covalent bonding -
It is the type of bonding which is present between shared pair of electrons , is known as covalent bonding .
For example ,
Most of the carbon compounds are capable to show covalent bonding .
Hence , from the question ,
1. Co ( s ) - metallic bonding
2. CoCl₂ ( s ) - ionic bonding
3. CCl₄ ( l ) - covalent bonding
We are interested in conducting a study in order to determine what percentage of voters of a state would vote for the incumbent governor. What is the minimum size sample needed to estimate the population proportion with a margin of error of +/-0. 06 at 95% confidence?.
Using the appropriate sample size formula, the minimum number of samples required is 267
Using the relation :
N = [(Z² × pq) / e²] e = Error Margin = 0.06² = 0.0036p = 0.5 q = 1 - 0.5 = 0.5 Zcritical at 95% = 1.96Substituting the values into the equation :
N = [(1.96² × (0.5 × 0.5)) / 0.0036]
N = (0.9604 / 0.0036)
N = 266.777
N = 267
Hence, the minimum number of samples required is 267
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why are SATs so hard to study for
Answer:
It is considered the finale of High School. Which depicts what role you should become in College... it is also the ticket to ur high school diploma
Explanation:
Un camión traslada 12 vehículos. Algunos son autos y otros son camionetas. Cada auto tiene una masa de 2 toneladas y cada camioneta de 3 toneladas. En total, el camión lleva una carga de 33 toneladas.
Encontrando y resolviendo un sistema de ecuaciones, veremos que hay 9 camionetas y 3 autos.
Sabemos que hay 12 vehículos en el camión.
Definamos:
a = número de autosc = número de camionetas.tal que a + c = 12
La masa total será:
a*2 ton + c*3 ton
Y sabemos que el camión lleva 33 toneladas, entonces tenemos:
a*2 ton + c*3 ton = 33 ton
Así encontramos el sistema de ecuaciones:
a + c = 12
a*2 ton + c*3 ton = 33 ton
Para resolverlo, primero aislamos una de las variables en una de las ecuaciones, aislemos a en la primera:
a = 12 - c
Ahora reemplazamos esto en la otra:
(12 - c)*2 ton + c*3 ton = 33 ton
24 ton + c*1 ton = 33 ton
c*1 ton = 9 ton.
c = 9
Es decir, hay 9 camionetas.
Entonces los 3 vehículos restantes son autos.
Hay 9 camionetas y 3 autos.
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Diploid somatic cells of elephants have 56 chromosomes.
Answer: 29,29,27,27 :)
Where are my smart friends?? i had $3. 0. My mom gave $10. 0. My brother gave $30. 0. My aunt and uncle gave me $100. 0. I had another $7. 0. How much did i have?.
Answer: $150
Please mark me brainliest!
Explanation: 3 + 10 = 13
13 + 30 = 43
43 + 100 = 143
143 + 7 = $150
The diagram shows 3 identical circles inside a rectangle.
Answer:
Explanation:
Diagram?
Carefully read sources a through d (listed below), including the introductory information for each source. Compose a thesis statement you might use for an essay in which you develop your position on the role, if any, that zoos should serve in the future. Then, select at least three pieces of evidence from the sources to support your position, briefly explaining how each piece of evidence might be used to develop your argument. Avoid merely summarizing the sources.
The above question wants to assess your writing ability, therefore it is not correct for me to write the thesis statement for you, but I will show you how to write it.
First, you should know that a thesis statement is a short, direct, and objective paragraph that shows your opinion or position on a particular issue.
This opinion must be substantiated by evidence taken from research sources, for this reason, you should read the sources that have been presented to you or research articles, essays, and publications on the subject.
After that, you can answer your question as follows:
Present your thesis statement, that is, present your opinion on the future role of zoos.Show information from the research sources that support your thesis statement.Explain how this information supports your opinion and shows it to be true.An example of a thesis statement would be: According to the reading, the function of zoos will become increasingly obsolete due to the growth of environmental awareness and animal rights.
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If 1=15 and 6=20 what is 3.
if 1 = 15 and 6=20 what is 3
=
25
For the lunch special at a high school cafeteria, students can get either salad or french fries as a side order. The following table shows the number of each side order for the lunch specials purchased on one day, classified by the grade of the student.
The probability that the student that's selected will be in grade 10 given that the student ordered French fries as the side will be 71/248.
From the information given, the number of students that are in grade 10 is 105. Out of all the students, 34 had salad and 71 had French fries. The total students in the school that are French fries was 248.
Therefore, the probability that the student that's selected will be in grade 10 given that the student ordered French fries as the side will be calculated thus:
= Number of students who French fries in grade 10 / Total number of people that had French fries
= 71/248
In conclusion, the correct option is 71/248.
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