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 amount of heat, in kj, would be involved in condensing 15. 8 g of ch₃oh? (∆hvap = 38. 0 kj/mol).
Considering the definition of enthalpy of vaporization, the amount of heat that would be involved in condensing 15.8 g of CH₃OH is 18.8 kJ.
When a material changes phase from solid to liquid, or from liquid to gas, a certain amount of energy is involved in this phase change.
In case of phase change from liquid to gas, this amount of energy is known as enthalpy of vaporization (symbolized as ∆Hvap).
So, the enthalpy of vaporization is the amount of energy required to change a unit of mass (for example, moles or kg) of a substance from phase liquid to phase gas at constant temperature and pressure.
In this case, you know that enthalpy of vaporization is ∆Hvap = 38.0 kJ/mol.
On the other side, you want to vaporize 15.8 g of CH₃OH. Then, being the molar mass of the compound 32 [tex]\frac{g}{mole}[/tex] (that is, the amount of mass contained in one mole), the number of moles to be vaporized is:
[tex]15.8 gramsx\frac{1 mole}{32 grams} =0.49375 moles[/tex]
Then, the amount of heat that would be involved in condensing 15.8 g of CH₃OH is calculated taking into account the enthalpy of vaporization by:
0.49375 moles× 38.0 [tex]\frac{kJ}{mol}[/tex]= 18.76 kJ ≅ 18.8 kJ
Finally, the amount of heat that would be involved in condensing 15.8 g of CH₃OH is 18.8 kJ.
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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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Multiple-choice questions on advanced placement exams have five options: a, b, c, d, and e. A random sample of the correct choice on multiple-choice questions on a variety of ap exams1 shows that b was the most common correct choice, with of the questions having b as the answer. Does this provide evidence that b is more likely to be the correct choice than would be expected if all five options were equally likely? show all details of the test. The data are available in apmultiplechoice.
Answer:
the answer would be a
Explanation:
What in the cinderella story suggests its origin, according to the author? why is her theory uncertain?.
Cinderalla is a very popular story. The suggestion of its origin, according to the author is that its origin could have been originated in Orient.
The theory is uncertain because Cinderella, as it is widely known among boys and girls, as a fairy tale, it has about 345 documented variants and many more versions that were not documented or recorded.
This can be referred too as inconsistency in its recording. The fact that Cinderella had small feet, was of some importance in the Orient that is ancient times.
Cinderella, The Legend is known too be of Protestant ethic as the moral principle in this fairy tale is that good fortune can be an advantage.
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Help plz lol………………………….
Answer:
105/330
Explanation:
drama:
25 students
both:
60 students
sports:
140 students
total:
225 students
330-225=105
apparition
enchanted
ghost
ghostly
ghoulish
goblin
haunted house
haunting
Which best describes an electron cloud.
You enter a room 2 dogs 4 horses.
(2+4=6) supercalifragilisticexpialidocious
You can have ice cream you finish your dinner.
My mom suggested keep the surroundings clean and green.
This is the correct sentence:
My mom suggested keeping the surroundings clean and green.It's correct to say keeping and not keep because you have to form the sentence using suggest + the verb with ing (keep + ing: keeping).
I was able to find the instructions to complete the exercise online: Write sentences using suggest + V-ing or suggest + clause with should.
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Which of the following statements is true of postmodern cultural spaces.
The answer is mashed potatoes.
Answer: what did he sayyy
Explanation:
On january 1, 2019, a company issued $400,000 of 10-year, 12% bonds. The interest is payable semi-annually on june 30 and december 31. The issue price was $413,153 based on a 10% market interest rate. The effective-interest method of amortization is used. What is the book value (carrying value) of the bond liability as of june 30, 2019 (to the nearest dollar)?.
The book value of the bond liability is $409811
First of all we have to calculate the cash that was paid for interest
This interest is payable semiannually that is 6 months out of 12 months
6/12 = 0.5
The bond is 12% = 0.12
= 400000 * 0.12 * 0.5
= 24000 dollars
The interest =
413153 * 10% * 0.5
= 20658 dollars
The reduction = 24000-20658
= 3342 dollars
The carrying value after the first payment
= 413153-3342
= $409811
The book value of the bond liability is $409811
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A new roller coaster contains a loop the loop.
Answer: Have you ever been to that type of roller coaster?
Explanation: If so cool.
Marianna is working on improving her communication skills. To be a good listener she should.
During the revolutionary war, how did the british convince slaves to run away from their owners and help the british war effort?.
Answer:
offered freedom
Explanation:
took the test
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
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
Use the formula for annual compound interest. A = P (1 StartFraction r Over n EndFraction)nt Remember, A refers to the total amount owed. Calculate the total amount that Tom would repay. $10,337 $11,337 $12,337 $13,337.
Answer:
11,337
Explanation:
Answer:
$11,337
Explanation:
You work in a company that has begun selling annual subscriptions to its new online magazine. During december, the company sold the first subscriptions, receiving $600,000, which represents one-fifth of its revenues from all sources for the year. The entire amount has been collected in cash. As the end of the the year approaches, you notice that the company recorded the entire $600,000 to revenue and there is no plan to make an adjusting entry.
Answer:
a.cademics.helper
Explanation:
IG reach out get the answer from here
The accounting error that was committed and how it affected the financial accounts will be stated in the note.
What are financial accounts?Financial accounts are defined as the process of documenting, compiling, and disclosing a company's financial statement transactions. The preparation of financial reports for external audiences like investors, creditors, and tax authorities to learn more about a company's performance is the primary goal of financial accounting.
The $600,000 that was raised from the sale of the new online magazine's annual subscription is the amount that will be raised for the upcoming 12-month period that will begin in December of the current year. Of the total, only $50000 will be noted for the year. Therefore, $550000 in related services for the following eleven months should be recorded as unearned income.
Thus, the accounting error that was committed and how it affected the financial accounts will be stated in the note.
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Your question is incomplete, but probably your complete question was
You work in a company that has begun selling annual subscriptions to its new online magazine. During December, the company sold the first subscriptions, receiving $600,000, which represents one-fifth of its revenues from all sources for the year. The entire amount has been collected in cash. As the end of the the year approaches, you notice that the company recorded the entire $600,000 to revenue and there is no plan to make an adjusting entry.
Draft a memo around two paragraphs in length to your supervisor, which explains the following:
The accounting error that has been made
The effect this error will have on the financial statements dated at the end of December
The problems that might result
The importance of fixing the error and what needs to be done to fix the error
Make sure to include proper grammar, spelling, etc.
Scientists discover a new organism. The organism is autotrophic, with membrane-bound organelles. To which of these kingdoms does this organism most likely belong?.
Protista, would be the answer
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
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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How does the first amendment protect religious freedom for american citizens? choose exactly two answers that are correct.
Answer:
It lets people practice their faith in their own way and
It prevents the government from establishing a national religion.
Explanation:
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
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
Beth is listening to her friend melissa talk about a recent break-up. Beth wants to give an appropriate listening response to convey to melissa that she there for her friend and shares her point of view. Beth’s best listening response would be which of the following?.
Beth's best listening responses to convey to Melissa that she shares her view would be: supporting.
In communication, listening is very key which follows with a feedback to ensure what is being communicated is rightly decoded by the receiver of a message.
For feedbacks, many types of responses can be given. One of which is giving a listening response.
Types of listening responses include:
EmpathizingQuestioningParaphrasingEvaluatingSilent listeningEmpathizingSupporting.Supporting is a type of listening response whereby the listener shows solidarity with the speaker in a way that reflects the feelings about the speaker.
Therefore, Beth's best listening responses to convey to Melissa that she shares her view would be: supporting.Learn more about listening responses on:
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What detail of the myth is suggested in the poem but not in the painting? What connection between the painting's landscape and the myth does this detail convey?.
The myth shows the moment when the sun melts the wings of Icarus, while the painting does not present this moment. This detail shows that nature contributes to the death of Icarus.
We can arrive at this answer because:
The painting shows only the death of Icarus, showing the moment when he fell into the water and drowned.The purpose of the painting is to show how the universe and all other human beings remained indifferent to Icarus' death.Although the myth also features the death of Icarus, it sets out in more detail.The myth shows why Icarus wanted to use the waxwings and why these wings melted.The myth focuses on nature's action on the death of Icarus, while the painting reinforces the universe's indifference to this death.
This question is about “Landscape of the Fall of Icarus.”
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Answer:
B & C
Explanation:
Y E S
How many grams of iron (density = 7. 87 g/ml ) would occupy the same volume as 96. 4 g of aluminum (density = 2. 70 g/ml)?.
Explanation:
density = mass / volume
96.4 g of aluminum / volume = 2.7
therefore,
96.4 = 2.7 × volume
volume = 96.4 / 2.7 = 35.7037037... ml
back to iron :
7.87 = mass / 35.7037037...
mass = 7.87 × 35.7037037... = 280.9881481... g
it would be 280.9881481... g of iron in the same volume.
Oscar started freaking out about the test formal brainly.
Answer:
?
Explanation:
Answer:
y lol
Explanation:
