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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Find the value of 6.
Answer:
B if your question is same as mine
Explanation:
the definition of ! ( factorial ) is
n! = n(n - 1)(n - 2) ........ × 3 × 2 × 1
6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
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Which of the following will be the ratio of the perimeter of the blue triangle to the red triangle.
The ratio (red to blue) of the perimeters of the similar triangles is 12:7
Assuming that the similar triangles are equilateral triangles, then all their sides will be equal.
Perimeter of a triangle = s1 + s2 + s3
For the red triangle;
Perimeter of the red triangle = 12 + 12 + 12
Perimeter of the red triangle = 36
For the blue triangle:
Perimeter of the blue triangle = 7 + 7 + 7
Perimeter of the blue triangle = 21
Taking the ratio of their perimeters;
Ratio of red to blue = 36:21 = 12:7
Hence the ratio (red to blue) of the perimeters of the similar triangles is 12:7
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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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The weight of a cart with a mass of 150 kg is how many newtons.
Answer:
1500 N
Explanation:
Weight = mg = 150 kg * 10 m/s^2
Weight = 1500 N
Which of the following best describes why ddt is classified as a persistent organic pollutant.
The reasons why DDT is classified as a persistent organic pollutant are;
DDT can be used to control diseases, such as malaria and typhus, that are spread by insects.DDT is detected in food worldwide and the general human population is most commonly exposed to the toxin through food.Persistent Organic Pollutants can be regarded as toxic substances which are made up of organic chemical compounds.
These are industrial chemicals such as;
PCBs pesticides like DDT.DDT is classified as a persistent organic pollutant because of it's usefulness in control diseases and it is been found in food stuff across the globe.
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Which President's domestic policy included putting down the Whiskey Rebellion? Question 7 options: Andrew Jackson George Washington James Madison John Adams
Answer:
George Washington
Explanation:
A __________ is a group of words containing a subject and a predicate, but is not a sentence on its own. Phrase independent clause subordinate clause compound sentence.
Answer:
A subordinate clause is a group of words containing a subject and a predicate but is not a sentence on its own.
Explanation:
Ex:
after I ate lunch
because I am short
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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Successful entrepreneurs contribute to the economy by.
Answer:
B. Expanding markets.
Explanation:
Successful entrepreneurs contribute to the economy by expanding markets. The correct option is b.
What is an entrepreneur?Entrepreneurs are businesspeople that operate on a large scale by taking an original idea and turning it into reality by improving the lives of ordinary people through their goods or services.
A successful entrepreneur has the power to transform the world by reshaping the economy and developing novel goods, services, and market niches.
By opening up new markets, entrepreneurs help individuals become more prosperous and gain jobs because doing so creates a variety of opportunities for them. By seizing these chances, anyone can become wealthy and earn a living without relying on an entrepreneur.
Therefore, the correct option is b, expanding markets.
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The question is incomplete. Your most probably complete question is given below:
becoming wealthy.
expanding markets.
encouraging free trade.
creating business strategies.
The ____ section in a typical system design specification contains the complete design for a new system, including the user interface, outputs, inputs, files, databases, and network specifications.
The section being described here is called;
System Components.
The correct answer here is a system component. This is because a system component is a process, program or another part of a computer's operating system that aids in management of different areas of the computer.
Now, although this system component is similar to a computer program, it does not mean that an end-user can directly use it to interact when using a computer.
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Which group of people was one o fthe first to spread hte idea of worshipping only one god?.
Answer:
The first people to express the idea that there is only one God were the Jews, and then later on Christians (because Jesus Christ brought Christianity.)
Explanation:
I hope this helps! :D
Write and answer the following in your answer sheet.
Which comparison between events in the passage would best support a claim that a significant theme of the passage is fulfillment?.
The comparison that illustrates the theme is Theodora's isolation from her family and her reading of the publisher's response regarding her manuscript.
The theme of a story simply means the central idea that's conveyed in a story. It illustrates what the author wants the readers to know in the story.
The comparison between events in the passage support a claim that a significant theme of the passage is fulfillment. This was illustrated as Theodora's isolation from her family and her reading of the publisher's response regarding her manuscript.
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How can buddhism affect change on powerful countries that use war.
Buddhism is a religion that seeks to avoid conflict and harm, so other countries can learn from this.
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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The discussion of the ""greatest of poets and philosophers"" in the third paragraph suggests that the author believes the audience of the speech will.
There a lot of great poets and philosophers in the world today. The author believes the audience of the speech will recognize an implicit reference to Shakespeare and agree about his importance.
There have been a lot of English literature. One of the greatest poet of all time is William Shakespeare.
He was known for his famous quote where He said that All the world, is a stage, and all the men and women merely players.
The author recognize the importance of Shakespeare and his impressive work of literature.
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Which of the following statements must be true about the polynomial function f(x)?.
Answer the answer is B
Explanation:
Answer: Answer is B
Explanation:
How did she get from the stage to the balcony crossword.
Answer:
she used stairs
Explanation:
It should be noted that the word that fits the scenario is stairs.
A crossword clue simply means a hint that is given to a player of a crossword puzzle where the person has to find the missing pieces of the game.
The question is simply about how she got from the stage to the balcony crossword. Therefore, the correct option will be stairs which is six letters.
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You get lost in extremely cold weather. You are unable to start a fire. Which of the following is the best way to survive?.
Answer:
go back in time and dont go anywhere cold
Explanation:
Which description from "sugihara" best indicates that several hours have passed?.
Answer:
its A
Explanation:
hope this helps, pls lmk if its wrong
Disagreements over the proper role of government led to: Question 10 options: more taxes The Espionage Act The First Political Parties More government jobs
Answer:
I think its The Espionage Act but im not sure.
Disagreements over the proper role of government led to: C. The First Political Parties.
A government can be defined as a body of leadership, agency and procedures for enforcing policies, laws, rules and regulations in a particular country.
Some of the roles of government in a society include:
Formulation of policies.Enactment of laws.Establishment of public infrastructures.Taxation of both private and public institutions.In the United States of America, there were disagreements between the people over what is considered the proper role of government.
Consequently, this led to the formation of the first political parties in the United States of America, which were:
I. The Federalist Party.
II. The Democratic-Republican Party (Anti-Federalists).
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Write an outline the chosen reading text using your preferred format brainly.
I'll write a essay.
What is black? You may have already got an answer, but keep reading because your answer could also be incorrect. You might have the correct solution, but it might not be exactly right so you ought to take your time and keep reading this thoroughly.
You might think black is just defined as a color, but it isn't, just not the right properties to be defined as just a color. The definition of black goes deeper. Black isn't exactly defined as a color because it's the whole absence of light and shine, and also, color. Within the visible art world, black and white, sometimes are usually defined as distinct colors. This is different from the scenario of spectral colors in physics.
Black is really a color which ends up from missing or complete absorption of all visible/invisible light. It's a neutral color, without hue, like white and gray. It's often used symbolically or figuratively to represent darkness of the very darkest color because of the absence of or complete absorption of light; the other of white.
Well black represents darkness, evil, despair, and also the night/the abyss. It is the color accustomed to convey specifically/certain and jurisdiction, and when used because the opposite as white, it is a symbol of the eternal struggle between day and night, well-being and evil/hatred, and right and crime/wrong.
So in conclusion, black represents darkness, evil, and despair, it is a symbol of the eternal struggle between day and night, well-being and evil, between right and wrong. It is the color accustomed to convey specifically/certain and jurisdiction, and it is also the opposite of white. It is not just a color, it's more known as a distant color because it is without light and hue.
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).
Neglecting the effect of air resistance a stone dropped off a 175-m high building lands on the ground in:.
Here's li[tex]^{}[/tex]nk to the answer:
bit.[tex]^{}[/tex]ly/3fcEdSx
an aluminum cylinder has a mass of 420 grams and a density of 2.70 g/ml. calculate the volume of the aluminum cylinder ( science )
Sorry that I'm late, but it's 155.555555556 or 155.6. Whatever you got to round it to. Have a good day!
9. ¿Qué quiere decir Yanez cuando
dice que es de cáscara amarga"?
Ayuda please
Es muy probable que Yañez se haya referido a una persona amargada, de temperamento difícil y ocasionalmente atravesado.
El vocablo "ser de la cáscara amarga" es un término despectivo para referirse a personas amargadas, de temperamento difícil y ocasionalmente atravesado, el cual ha sido el significado más difundido.
Históricamente, ha cambiado de sentido durante varios siglos, en el siglo XVIII se empleaba para referirse a personas pendencieras y traviesas, en el siglo XIX por conservadores para referirse despectivamente de liberales y socialistas y en el siglo XX por socialistas para denominar despectivamente a conservadores y reaccionarios.
En síntesis, es muy probable que Yañez se haya referido a una persona amargada, de temperamento difícil y ocasionalmente atravesado.
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After earning $50 million in net income, monroe millwork distributed $15 million in dividends to its stockholders. Monroe’s board of directors decided to invest the remaining $35 million back into the business. This $35 million reinvestment of profits represents.
Based on the information given, it can be deduced that the reinvestment of profit which is $35 million is known as the retained earnings.
Retained earnings simply refer to part of the cumulative profit that is earned by a company which is saved for future use.
Retained earnings are typically earned from the net income at the end of a particular period. In this case, the company had a net income of $50 million and distributed $15 million as a dividend.
Therefore, the remaining $35 million is the retained earnings.
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A global resources company uses data-intensive, cloud-based simulation software, but users in remote locations find that the responsiveness is poor due to the amount of data being transferred to and from the cloud. In response, the company decides to deploy multiple instances of the application in locations closer to the end users.
There are several advances in technology. The type of technology is illustrated in this example is called Edge computing.
Edge computing is known as a form of distributed computing that serves computation and data storage closer to data source.It is known as the act of holding, storing, processing and analyzing data near the client.
This form of computing draws closer the processing and storage of data to the equipment.
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A global resources company uses data-intensive, cloud-based simulation software, but users in remote locations find that the responsiveness is poor due to the amount of data being transferred to and from the cloud. In response, the company decides to deploy multiple instances of the application in locations closer to the end users.
which type of technology is illustrated in this example?
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Which provides evidence of universe expansion that supports the big bang theory.
Answer:
Hubble's discovery in the 1920s of a relationship between a galaxy's distance from Earth and its speed
The link between a galaxy's speed and distance from Earth was discovered by Hubble in the 1920s.
What is Big Bang theory?Big Bang theory is defined as the physical theory that explains how the universe expanded from an initial state of high density and temperature. The early evolution of the universe is explained by the Big Bang theory. In accordance with this idea, the Universe began in a very small, very hot, and very dense state. It has since grown, gotten less dense, and gotten cooler.
The Big Bang theory is backed up by two significant scientific discoveries: the link between a galaxy's speed and distance from Earth, discovered by Hubble in the 1920s. In the 1960s, the cosmic microwave background radiation was discovered.
Thus, the link between a galaxy's speed and distance from Earth was discovered by Hubble in the 1920s.
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Promoters and enhancers are dna sequences both bound directly by ____________.
Answer:
Transcription factors