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 does sentir mean in English? to feel to kill to order to drink.
Answer:
All 5 answers
1. A to feel
2. C contenta
3. D seguro
4. B missing practice
5. C malteada de chocolate
Explanation:
Sentir mean in English is To feel
What type of verb is sentir?Sentir is an irregular -ir verb.
What's the difference between sentir and Sentirse?To choose one of sentir or sentirse, you can think of this simple model to help explain the difference: Sentir – describes 'what' you feel. Sentirse – describes 'how' you feel. In other words, we generally use sentir with nouns (joy, happiness, heat) and sentirse with adjectives or adverbs (happy, tired, excited).
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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.
If you believe that you have a water sample that is contaminated with barium, what could you add to it to test it?.
Answer: potassium sulfate
Explanation:
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 of the following are exclusively associated with copyright protection? (select three. ).
Statements that can be exclusively associated with copyright protection are:
Right to make derivatives of a work.
Right to reproduce a work.
Right to lend a work.
Copyright protection can be regarded as a form of protection that protect an intellectual property from stealing away by another party from the right owner.The right owner of the intellectual property such as copyright can give offer to another party to reproduce the property but it must not violate the intellectual property law.THIS IS THE COMPLETE QUESTION.
Which of the following are exclusively associated with copyright protection? (Select three.)
Right to reproduce small excerpts of a work
Right to apply for a patent
Right for anyone to display a work
Right to lend a work
Right to use a trademark
Right to make derivatives of a work
Right to reproduce a work
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Quis:
*Indonesian assignment*
Find the meanings of the following words using the Indonesian Dictionary
1. Effectiveness
2. Instrument
3. Generator
4. Distribution
5. Consumption
Work in a notebook or lat
pls help me bro :-)
those who are lazy must report :) Ok ^_^
Pain does all of the following things except.
Answer:
A. indicate potential danger in environment
Explanation:
A study was designed to investigate the effects of two variables--(1) a student’s level of mathematical anxiety and (2) teaching method--on a student’s achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 450 with a standard deviation of 30 on a standardized test. The test scores follow a normal distribution.
Using the Empirical Rule, it is found that approximately 68% of the students would score between 420 and 480.
The Empirical Rule states that for a normal variable:
68% of the measures are within 1 standard deviation of the mean.95% are within 2.99.7% are within 3.In this problem, the mean is of 450 while the standard deviation is of 30.
450 - 30 = 420
450 + 30 = 480
Hence, approximately 68% of the students would score between 420 and 480.
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If five times a number increased by six, the result is at least 26. What is the least possible number that satisfies these condition ?.
The least possible number that satisfies the condition is 4
Let the number be a.
Thus,
Five (5) times the number = 5 × a = 5a
From the question given above, we were told that five (5) times the number when increased by 6 is 26. This can be written as:
5a + 6 = 26Finally, we shall determine the value of a. This can be obtained as follow:
5a + 6 = 26
Collect like terms
5a = 26 – 6
5a = 20
Divide both side by 5
a = 20 / 5
a = 4Therefore, the least possible number that satisfies the condition is 4
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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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A researcher claims that the epinephrine signaling pathway controls a catabolic process in muscle cells. Which of the following statements best helps justify the researcher’s claim?.
Catabolism is simply refered to asthe process or sequences of enzyme-catalyzed reactions. Ths statements that best helps justify the researcher’s claim is that Glycogen phosphorylase catalyzes the conversion of glycogen to glucose-1-phosphate.
Catabolism is the process through which a good number of big molecules in living cells are degraded.or broken down into smaller pieces.
Some of the chemical energy released during catabolic processes is conserved in the form of energy-rich compounds such as adenosine triphosphate [ATP].
When anabolic and catabolic processes are in balance state, tissue remains intact and in good shape.
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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
Which sentences include a proper mla parenthetical citation? check all that apply.
Considering the available options, the sentences that include a proper MLA parenthetical citation include "Mahoney states that "the needs of speakers drive language change" (nsf.gov)."
What is MLA parenthetical citation?MLA parenthetical citation is the citation method that utilizes the author's last name, the page number, or other relevant source information in parentheses from sentences used.
Other sentences that include a proper MLA parenthetical citation include the following:Johnson claims that the English language began to deviate from its Germanic origins (4).In the eighteenth century, English was "departing from its original Teutonic character"(Johnson 4).Hence, in this case, it is concluded that the correct answer is options A, E, and F.
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Based on the graph, what conclusion can be drawn about trade between the United States and China? The United States has a trade surplus with China. China’s economy is declining, which has harmed trade. The United States has a trade deficit with China. China’s economy is improving, which has helped trade.
The conclusion that can be drawn is that the United states has a trade deficit with China.
What is a trade deficit?This trade deficit is known to often takes place only when the value of a country's imports is said to be more than the value of their exports in terms of physical goods and services.
Note a trade deficit implies that a country such as United States is buying more goods and services than they are actually selling and as such, the conclusion that can be drawn from the graph is that the United states has a trade deficit with China.
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Answer:
The United states has a trade deficit with China.
Explanation:
Its correct
Which substances are necessary for the synthesis and the breakdown of most materials in an organism?.
Enzymes
Explanation:
are the catalyst that require substrate for their function. Almost all the metabolic process in the body for synthesis of any substance requires enzymes.
I hope this is correct :)
On a position vs. Time graph, which feature would represent motion in the negative direction over time?.
A time graph reveals specific information on the velocity (change in position with respect to a change in time).
So, on a position - time graph, the feature representing motion in the negative direction over time is a downward sloping line segment.
A slope in a position time graph depicts the velocity also called the slope in this type of graph as it the change in position over time.
So, a downward sloping line segment feature in a time graph indicates that the motion of the object is in the negative direction. While a positive sloping line segment indicates otherwise.
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Answer:
a downward-sloping line segment
Explanation:
Which of the following statements best supports the one gene-one enzyme hypothesis?.
The one gene–one enzyme hypothesis is a very common hypothesis on how genes acts. The statement that best supports the one gene-one enzyme hypothesis is a mutation in a single gene can result in a defective protein.
The one gene–one enzyme hypothesis was an hypothesis that came about through George Wells Beadle in the US.
In 1941, He gave the theory which states that each gene directly makes a single enzyme, which inturn affects an individual step that are also in a metabolic pathway.
He along with other researchers experimented with mutant fruit flies.
The full question is below
Which of the following statements supports the one gene-one enzyme hypothesis?
A) A mutation in a single gene can result in a defective protein.
B) Sickle-cell anemia results in normal hemoglobin.
C) Multiple antibody genes can code for different related proteins, depending on the splicing that takes place post-transcriptionally.
D) Alkaptonuria results when individuals lack multiple enzymes involved in the catalysis of homogentisic acid.
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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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Identify the molecular geometry around the carbon atom highlighted red in the given organic molecule.
The detached carbon has a tetrahedral geometry.
We can arrive at this answer because:
Carbon can make 4 bonds with other atoms.This is because carbon has 4 electrons in its valence layer.When carbon makes 4 single bonds with other atoms it manages to assume a tetrahedral molecular geometry.From questions similar to yours, it is possible to find the image that your question refers to. This image is attached below and on it, we can see that the carbon in red makes 4 single bonds, assuming the tetrahedral geometry.
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The answer is mashed potatoes.
Answer: what did he sayyy
Explanation:
Do you think counselors are trustworthy.
Answer:
Yes.
Explanation:
I feel like they are because of the simple fact they cannot share your information, or anything you have said, with anyone because of confidentiality. The only way they can share anything is if you are going to hurt yourself or others, or if you give them verbal or written permission to do so.
Which detective seems to have more clues about solving the case? bolsa sancho.
Answer:
Sancho
Explanation:
Took the test
Answer:
1 True 2 False 3a parrot 4while he was hiding out 5 Sancho
Explanation:
took the test got a 100
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:
An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with mean equal to 800 hours and a standard deviations of 40 hours. Find the probability that, a random sample of 16 bulbs will have an average life of i). Less that 775 hours. Ii) between 775 and 825 hours.
Answer:
ion know
Explanation:
You have a 20 year annuity with a present value of $575,000. If the apr is 6%, what is the monthly yield?.
Annuities allow us to measure the cost of making payments over a period of time. Given the entries in the question given, the monthly yield will be;
$4119.48Since the interest will be compounded monthly, the number of periods will be 12. To determine the monthly payment from a payout annuity, use the formula;
Present value = Monthly yield (1 - (1 + APR/12)^-12 × n
APR/12
Fixing the above into the equation;
$575,000 = PMT (1 - (1 + 0.06/12)^-12 × 20
0.06/12
$575,000 = PMT 139.6
Making PMT the subject of the formula,
PMT = 575,000/139.6
PMT = $4118.911
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Which of the following is true of the capital requirement? check all that apply.
Answer:
Its intended goal is to protect the interests of those who hold equity in the bank.
The amount of capital required depends on the type of assets the bank holds.
Explanation:
edge!!
A student runs 120 meters in 10 seconds. What is their speed?.
Answer:
12
Explanation:
speed=distance÷time
My primary group brainly.
Answer:
???
Explanation:
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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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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