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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A company upgraded production machinery to capture data about the fit tolerance for assembled parts of each unit produced. Before the upgrade, inspectors created the same data by sampling 10 percent of units produced. The upgrade represents an increase in.
The upgrade in production machinery to capture data about the fit tolerance for assembled parts of each unit produced represents an increase in: data volume.
Big data can be defined as huge collections of data that are typically difficult for users to process, analyze, and manage through the use of conventional data tools.
Basically, big data comprises five (5) "Vs" and these are:
VelocityVeracityValueVarietyVolumeData volume refers to the amount of data that are stored in a database by an organization for analysis and processing. Thus, data volume represents an organization's data size.
In this scenario, the upgrade in production machinery to capture data about the fit tolerance for assembled parts of each unit produced represents an increase in data volume.
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Yesterday, the temperature at noon was 11. 4℉. By midnight, the temperature had decreased by 15. 7 degrees. What was the temperature at midnight?.
Answer:
It is 4.3
Explanation:
because 15.7 minus 11.4 is equal to 4.3.
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
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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Her nervousness had a profound.
Huh yes that would work out well I think it’s a great deal to get it done by the end of the
Which notations represent atoms that have the same number of protons.
Answer:
ITS ABOUT DRIVE ITS ABOUT POWER WE STAY HUNGRY WE DEVOUR PUT IN THE WORK PUT IN THE HOURS AND TAKE WHATS OURS
Which set of equations is enough information to prove that lines c and d are parallel lines cut by transversal p? m∠1 = 81° and m∠2 = 99° m∠3 = 99° and m∠4 = 99° m∠2 = 99° and m∠4 = 99° m∠4 = 81° and m∠1 = 81°.
The set of equation that is enough information to prove that lines c and d are parallel lines cut by transversal p is m∠2 = 99° and m∠4 = 99°. The c.
What are transverse lines?
A transversal line is a line that crosses two or more other lines at different locations. Line l meets a and b in the image below at two different locations, P and Q. Line l is the transversal line as a result.
When a transversal cuts two lines so that their subsequent interior angles are supplementary, the lines are said to be parallel. Two lines are parallel to one another if they are both parallel to the same line. When the marked consecutive internal angles are supplementary, lines m and n are parallel.
Therefore, the correct option is c, m∠2 = 99° and m∠4 = 99°.
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The question is incomplete. Your most probably complete question is given below: the image is added.
The set of equation that is enough information to prove that lines c and d are parallel lines cut by transversal p is m∠2 = 99° and m∠4 = 99°. The c.
What are transverse lines?A transversal line is a line that crosses two or more other lines at different locations. Line l meets a and b in the image below at two different locations, P and Q. Line l is the transversal line as a result.
When a transversal cuts two lines so that their subsequent interior angles are supplementary, the lines are said to be parallel. Two lines are parallel to one another if they are both parallel to the same line. When the marked consecutive internal angles are supplementary, lines m and n are parallel.
Therefore, the correct option is c, m∠2 = 99° and m∠4 = 99°.The set of equation that is enough information to prove that lines c and d are parallel lines cut by transversal p is m∠2 = 99° and m∠4 = 99°. The c.
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A wheel rotates with a constant angular acceleration of 3. 50 rad/s2.
Answer:
is this a true or false question?
Explanation:
Rosalyn is a teacher who plays a review game with her class. The game involves writing each student's name on an identical slip of paper and selecting students at random. Here's the makeup of her class:.
Answer:
like hw
Explanation:
What is the apparent bond energy of a carbon–sulfur bond in cos? use the bond energies below.
Answer:
carbon
Explanation:
yes
Between ant and grasshopper which would you choose to be why.
Answer:
ant
Explanation:
way more interesting, can carry objects way heavier than them and if they were to become human size they would pretty much rule the earth whereas a grasshopper is annoyinggggfg and if they were the size of humans we'd probably die of blood loss in the ears.
When it comes to the choice between an ant and a grasshopper, my choice would be an ant because:
Ants are really strong. Ants are farmers. Ants are very resilient as a species.Ants are known to be really strong such that they can carry things that are 50 times their body weight which allows them to carry a lot of food to their colonies.
Ants are also farmers in that they have been known to protect some other insects so that they can keep getting agricultural produce like honeydew.
Ants are also quite resilient in that they have been around for as long as dinosaurs which means they are some of the oldest species in the world.
In conclusion, ants are preferably to grasshoppers in my opinion.
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What is the sum of the polynomials (8x2-9y2-4x)+(x2-3y2-7x).
The answer to your question is: D.) 9x²-11x-12y²
answer:
9x-2-12y-2-11x
explanation:
Remove the parentheses: 8x-2-9y-2-4x-+x-2-3y-2-7x
Combine like terms: 9x-2-12y-2-11x
Answer: 9x-2-12y-2-11x
Which substances are necessary for the synthesis of most materials in an organism.
Enzymes
Explanation:
are substances necessary for the synthesis of most materials in an organism.
I hope this is an option???
A retailer is able to track which products draw the most attention from its customers through the use of 5g-enabled motion sensors placed around the store. With this knowledge, the retailer can supply the proper amount of products to meet customer demand.
There is a wide spread of 5g technology. The technology that combines with 5G capabilities and used in the monitoring of the shopping trends is the Internet of Things.
The Internet of things is known to explain real or physical objects that are found along with sensors, processing ability, software, and other technologies.
They act by connecting and exchanging data with other devices and systems through the Internet or other communications networks.
The examples of Internet of Things are:
Connected appliances. Smart home security systems. Wearable health monitors etc.See full question below
A retailer is able to track which products draw the most attention from its customers through the use of 5G-enabled motion sensors placed around the store. With this knowledge, the retailer can supply the proper amount of products to meet customer demand.
Which technology combines with 5G capabilities to allow the monitoring of shopping trends in this way?
platooning
network slicing
internet of things
beamforming
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Did you go to the swim meet.
Answer:
what?
Explanation:
A ratio estimates the risk associated with investing in a firm.
A ratio which estimates the risk associated with investing in a business firm is called: solvency ratio.
Solvency ratio can be defined as a key metric that is typically used to measure the ability of a business firm to meet its long-term debt obligations.
Basically, a solvency ratio measures the financial position of a business firm and the extent to which its assets cover long-term debt obligations (commitments), especially for future payments and the liabilities.
In conclusion, a ratio which estimates the risk associated with investing in a business firm is called solvency ratio.
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Which situation describes an object that has no unbalanced force acting on it.
The situation which best describes an object that has no unbalanced force acting on it is: A hockey puck moving at constant velocity across ice.
A force can be defined as a push or pull of objects, which typically results in a change of motion due to the interaction of the object with another.
In Science (Physics), there are two (2) main types of force and these are:
Balanced force.Unbalanced force.An unbalanced force is a type of force that occurs when two or more forces acting on an object are unequal in magnitude and as such, it typically results in a change of motion.
Hence, a hockey puck that is moving at a constant velocity across ice has no unbalanced force acting on it because it won't experience a change of motion.
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When making lemonade, 1 over 4 cup of sugar will make 5 glasses of lemonade. How many cups of sugar would be needed to make 22 glasses of lemonade?.
Which of the expressions below is equivalent to 4x^2/12x^2-4.
Answer:
(846_++=-06456 AND _089_)(
Explanation:
Crane chose to present this account in a short story form. Which of the following is an aspect of "the open boat" that would be most difficult to convey in a painting depicting the same scene?.
The Open Boat is a popular book that was written by Stephen Crane. The aspect of "the open boat" that is most difficult to convey Thereafter was that 'there was something strange in his voice'.
Crane in his book want the readers to connect deeply with the specific characters in the book and feel their different struggle as they work had in hand to reach the shore alive.
He showed his readers how nature can be powerful and the experience gotten increasing people's ignorant views of the world around them.
See full question below
Crane chose to present this account in a short story form. Which of the following is an aspect of "The Open Boat” that would be most difficult to convey in a painting depicting the same scene?
answer choices
a. These waves were of the hue of slate, save for the tops, which were of foaming white.
b. These waves were most wrongfully and barbarously abrupt and tall.
c. His sleeves were rolled over his fat forearms, and the two flaps of his unbuttoned vest dangled as he bent to bail out the boat.
d. Thereafter there was something strange in his voice.
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I learned that modal adverbs are.
Answer:
Modal adverbs are used to modify specific verbs that consist of a linking verb (verb of being) and sometimes another verb.
Explanation:
How much force is needed to stop a 100-kg football player if she decelerates at 20 m/s2? 5 N 20 N 200 N 2000 N.
2000 N. is needed to stop a football player
Which of the following is a difference between phase i and phase ii of meiosis.
Answer: Phase I results in two diploid daughter cells and phase II results in four diploid daughter cells
Explanation:
i took the test
According to the table, what was the hiker’s average speed for the entire hike? 2. 0 km/h 5. 7 km/h 6. 7 km/h 10 km/h.
Answer:
6.7 km/h
Explanation:
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.
List at least two facts you learned from your research that you could use when writing the opening statement. Remember to include information that is relevant to the main problem you are investigating.
Two facts that I learned during my research were narrowing down the research topic and setting appropriate goals.
When doing research, several aspects must be taken into account so that the research has good results and produces new knowledge. Here are two tips for proper research:
1. Limit the subject of the investigation: When conducting an investigation it is necessary to limit the subject so that it is easier to achieve an effective result. For example, time limits, a specific place, and more special aspects should be set to make the investigation more specialized.
2. Establish adequate objectives: When conducting an investigation it is necessary to establish objectives that can be achieved in the investigation. Highly ambitious goals can make research and information search difficult.
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Answer:
-The cost of college has risen faster than inflation for many years.
-The high price of student services and administration are two reasons for the rapid increase in cost.
Explanation:
good luck guys
Oscar started freaking out about the test formal brainly.
Answer:
?
Explanation:
Answer:
y lol
Explanation:
A gardener bought 5 rabbits.
...
Thats really nice
For what value of a does (one-ninth) Superscript a 1 Baseline = 81 Superscript a 1 Baseline times 27 Superscript 2 minus a? –4 –2 2 6.
Answer:
-4
Explanation:
Edge.
Answer:
A: -4
Hope this helps.
Excessive smoking, substance abuse, and sleep disorders are all examples of ________ symptoms of stress.
Excessive smoking, substance abuse, and sleep disorders are considered to be behavioral symptoms of stress.
It should be noted that behavior-related stress symptoms include absence and turnover, changes in productivity, changes in eating habits, increased consumption of alcohol, and smoking.
In a case where an individual who doesn't usually drink alcohol or smokes before starts drinking alcohol, it's known as behavioral symptoms of stress. In such a situation, stress leads to a change of behavior.
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