A tube is being stretched while maintaining its cylindrical shape.

Answers

Answer 1

Answer:

This question is incomplete, the complete question is;

A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the rate of 2 millimeters per second. At the instant that the radius of the tube is 6 millimeters, the volume is increasing at the rate of 96π cubic millimeters per second. Which of the following statements about the surface area of the tube is true at this instant? (The volume V of a cylinder with radius r and height h is V=πr2h. The surface area Sof a cylinder, not including the top and bottom of the cylinder, is S=2πrh.)

A) The surface area is increasing at the rate of 28pi square mm per second.

B) The surface area is decreasing at the rate of 28pi square mm per second.

C) The surface area is increasing at the rate if 32pi square mm per second.

D) The surface area is decreasing at the rate of 32pi square mm per second.

Answer:

Surface Area is increasing at the rate of 28π mm²/sec  ( Option A )

Explanation:

Given the data in the question;

let r be the radius and h be the height of the tube

so volume V = πr²h

dv/dt = πr² dh/dt + 2nrh dr/dt

⇒ 96n = π × 36 × 2 + 2π × 6h dr/dt

⇒ 24π = 12nh dr/dt ⇒ h.dr/dt = 2

Area Surface S = 2nrh

ds/dt = 2π ( r.dh/dt + h.dr/dt )

= 2π ( 6×2 + 2)

= 2π (14)

= 28π

therefore Surface Area is increasing at the rate of 28π mm²/sec ( Option A )


Related Questions

The auction price of the game system is higher than the retail price because. If you waited six months to buy the phone, you would have saved.

Answers

Answer:

Demand is higher than supply

$200

Explanation: I guessed and got it right

Answer:

The auction price of the game system is higher than the retail price because

✔ demand is higher than supply

.

If you waited six months to buy the phone, you would have saved

✔ $200

.

Explanation:

Evaluate the line integral by the two following methods. Xy dx + x2y3 dy c is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 4).

Answers

Not sure what "two methods" you refer to, so I'll assume you're supposed to compute the line integral directly as well as with Green's theorem.

Direct computation:

It looks like the line integral is

[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy[/tex]

where C is the union of three line segment. We'll partition C and parameterize each component by

• C₁, the line segment from (0, 0) to (1, 0) : x(t) = t and y(t) = 0;

• C₂, from (1, 0) to (1, 4) : x(t) = 1 and y(t) = 4t;

• C₃, from (1, 4) to (0, 0) : x(t) = 1 - t and y(t) = 4 - 4t;

each with 0 ≤ t ≤ 1.

Compute the integrals over each component:

• Along C₁, we have y = 0, so this integral contributes nothing.

• Along C₂,

[tex]\displaystyle \int_0^1 4t \cdot 0 \, dt + (4t)^3 \cdot 4 \, dt = 256 \int_0^1 t^3 \, dt = 64[/tex]

• Along C₃,

[tex]\displaystyle \int_0^1 (1-t)(4-4t) \cdot (-dt) + (1-t)^2(4-4t)^3 \cdot (-4\, dt) \\\\ = \int_0^1 \left(-260 + 1288 t - 2564 t^2 + 2560 t^3 - 1280 t^4 +  256 t^5 \right) \, dt = -44[/tex]

So, the total line integral is

[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy = 0 + 64 - 44 = \boxed{20}[/tex]

Using Green's theorem:

The interior of C is the triangular region

[tex]D = \{(x, y) : 0 \le x \le 1 \text{ and } 0 \le y \le 4x\}[/tex]

and the integrand has no singularities either on C or within D. So by Green's theorem,

[tex]\displaystyle \int_C xy \, dx + x^2y^3 \, dy = \iint_D \frac{\partial(x^2y^3)}{\partial x} - \frac{\partial(xy)}{\partial y} \, dx \, dy = \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx[/tex]

The remaining integral is trivial.

[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \int_0^1 x \int_0^{4x} (2y^3 - 1) \, dy \, dx[/tex]

[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \int_0^1 x \left(\frac12 (4x)^4 - 4x\right) \, dx[/tex]

[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \int_0^1 \left(128x^5 - 4x^2\right) \, dx[/tex]

[tex]\displaystyle \int_0^1 \int_0^{4x} (2xy^3 - x) \, dy \, dx = \frac{64}3 - \frac43 = \boxed{20}[/tex]

The product of a number and 2 less than the number is 15. Find the number.

Answers

Answer: A) -3 or 5

x(x-2) = 15 where x = the unknown number
If you test all the answers in that equation, both x values in answer A yield 15

Which basic task does the federal bureaucracy have?.

Answers

basically they work out the finer details and set up guidelines for congress passed bills

Answer:

to help rebuild foreign nations after a natural disaster

Explanation:

Albert einstein (1)______ born in germany in 1879. In 1895, he (2)______to school in switzerland. After college, he (3)______ in switzerland for 28 years, and then he (4)______ to the us in 1933. He (5)______ in 1955 in the us.

Answers

Answer:

1) was

2) went

3) move to the

4) will be

5) is

Explanation:

I hope it will help u

Albert Einstein WAS born in Germany in 1879. In 1895, he WENT to school in Switzerland. After college, he LIVED in Switzerland for 28 years, and then he MOVED to the US in 1933. He DIED in 1955 in the US.

Albert Einstein was a German physicist who developed the theory of relativity.

Albert Einstein is popularly known due to his huge intelligence, and he won the Nobel Prize (1921).

Einstein's work is today very important to understand the origin of the Universe.

In conclusion, Albert Einstein WAS born in Germany in 1879. In 1895, he WENT to school in Switzerland. After college, he LIVED in Switzerland for 28 years, and then he MOVED to the US in 1933. He DIED in 1955 in the US.

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Bernie is an aspiring video game developer. Learning which of the following software would benefit him the most?.

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Since Bernie aspires to become a video game developer, learning a 3-D animation software would benefit him the most: C. 3-D animation software.

A software developer refers to a creative individual that develops a concept and writes a set of executable instructions (codes), in order to create a software applications (programs) that proffers a solution to a particular problem by applying various engineering principles.

In Computer programming, software applications (programs) are typically categorized into the following groups:

Computer-aided design softwareSampling softwareSystem software3-D animation software

A 3-D animation software is a graphic design software that is designed and developed for rendering animated or graphic images in three (3) dimensions.

Hence, a software developer that is interested in becoming a video game developer should learn how to use a 3-D animation software effectively and efficiently.

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Your question is lacking the necessary answer options, so I will be adding them here:

A) Computer-aided design software

B) Sampling software

C) 3-D animation software

D) System software

A swim club is designing a new pool to replace its old pool. The new pool would need to last for 10 years since the club is planning on relocating after 10 years. A concrete shell would cost rm85,000 and last for all 10 years. Another option is to install a vinyl liner that would cost only rm70,000 to install. However, the vinyl is not guaranteed to last for all 10 years, and it has a 40% chance of breaking down. Repair of the vinyl would cost rm40,000 and would extend the life of the vinyl liner to the 10-year mark. If both options are acceptable to the swim club, which one minimizes cost?.

Answers

If both options are acceptable to the swim club, the one that minimizes cost is concrete shell.

In order to determine the option minimizes cost we are going to calculate EMV of vinyl liner:

EMV of vinyl liner=(1-.40)(70,000) + 0.40(70,000+40,000)

EMV of vinyl liner=.60(70,000) + 0.40(110,000)

EMV of vinyl liner=42,000+44,000

EMV of vinyl liner= $86,000

Based on the above calculation EMV of vinyl liner of the amount of $86,000 is higher than EMV of concrete shell of the amount of $85,000.

Therefore swim club should install the concrete shell in order to minimize cost because it is lesser.

Inconclusion the option that minimizes cost is concrete shell.

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Two uniform solid balls are rolling without slipping at a constant speed.

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wha t is the question ?

Water melts at 0°c. A student observes a liquid that melts at 10ºc. Which conclusion can the student reasonably draw?.

Answers

There are many conclusions that could be drawn however based on the question I believe that the answer looked for would be that:

the liquid has stronger intermolecular forces

What did robert sternberg believe about intelligence? (site 1).

Answers

Answer:

Robert Sternberg argued practical intelligence, a person's ability to react and adapt to the world around them.

Explanation:

E2020

Robert Sternberg argued practical intelligence, a person's ability to react and adapt to the world around them did robert sternberg believe about intelligence.

What is Robert Sternberg's theory?

According to the view of psychologist Robert Sternberg, there are three different levels of love: intimacy, passion, and commitment. It is critical to understand that a relationship built on one aspect has a lower chance of success than one built on two or more.

Another theory of intelligence was created by Robert Sternberg. He called it the triarchic theory of intelligence since it divides intelligence into three categories: practical, creative, and analytical intelligence.

One of the most significant psychologists of the 20th century, Robert J. Sternberg is best known for his ground-breaking studies on creativity, love, intellect, and cognitive styles.

Thus, Robert Sternberg argued practical intelligence, a person's ability to react,

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Consider circle O. If AE = 7, EC = 2, and BE = 4, what is ED? A. 5 B. 4. 5 C. 4 D. 3. 5 E. 3.

Answers

Answer:

3.5

Explanation:

In the past, behaviorists were not likely to view cognition as a part of learning because cognition __________. A. Does not affect behavior B. Disproved their theories C. Is unobservable D. Had never been studied Please select the best answer from the choices provided A B C D.

Answers

Answer:

C

Explanation:  

is unobservable

"In the past, behaviorists were not likely to view cognition as a part of learning because cognition is unobservable." Thus, option D is correct.

What is cognition?

Thinking, attention, language, learning, memory, and perception are all examples of cognitive activities that occur in the brain. These processes are not distinct talents; rather, they are a collection of interconnected abilities that enable us to function as healthy adults.

Learning, according to behaviorists, takes place mostly through observation. They thought that a person learns different parts of his or her life through observation. Imitation, modeling, and other forms of observation are all part of the observation process. Experiments on classical conditioning were used by behaviorists to illustrate that behavior is a learned process. Cognition, on the other hand, refers to the mental processes that include comprehension and knowledge.

As a result, Previously, behaviorists were unlikely to consider cognition to be a component of learning, since cognition is a mental process. Hence, option D is correct.

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What is the density of helium gas at 17°c and 773 torr?.

Answers

Answer:540 g m/s.nrijnvijenvirvijrvnijrvirvirnvrijvnrijvnrivnrijvnrwjivnrij-gvnrgr-b

Explanation:

Why does judith's little brother need help? he can't get dressed by himself. He can't put his shoes on by himself. He can't get undressed by himself. He can't find his clothes.

Answers

Answer:

it's A- He can't get dressed by himself

Explanation:

judith's little brother need help, he can't get dressed by himself. it is needed to teach children how to get dressed.

Why child needs to learn how to get dressed?

Teaching to children how to get dressed builds  child’s confidence level and independence and it gives them a sense of achievement, so getting dressed by themselves helps the child to develop many other skills.

Some of the skills are fine motor skills like fastening buttons and zip, gross motor skills like standing on one leg to pull on a pair of pant, cognitive skills, language skills that is naming types of clothes, colors and sizes, awareness of time and space

Young children are aware about clothing by pulling off things like socks, shoes or hats,

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What would happen if you did not have the stapedius and tensor tympani muscles?.

Answers

Loud sounds would cause the ossicles to move too much, which would cause damage to the inner ear.

Cierto o falso: Cuando utilices el pretérito, estás hablando de lo que pasó.

Answers

Answer:

True

Explanation:

What pressure would a gas mixture in a 10. 0l.

Answers

I think that it is 46.6 atm

Raj and Aditi like to play chess against each other. Aditi has won 12 of the 20 games so far. They decide to play more games. How many more games will Aditi have to win to have a 70% winning record? 12 x = 0. 70(20 x) x = x equals StartFraction 20 Over 3 EndFraction is approximately 6. 67. ≈ 6. 67 She will have to win 7 more games to have a 70% winning record. How many more games will Aditi have to win to have an 80% winning record? The linear equation that models this is. Aditi would have to win more games to have an 80% winning record.

Answers

Answer:

They need to win 20 more games

Explanation:

Anthony would like to have his brokerage firm handle more of his financial needs because he has been pleased with the service provided when he bought and sold stocks and bonds. If he explores the services offered by such firms in more depth, he will find that.

Answers

There are firms that handles the financials for people. If he explores the services offered by such firms in more depth, he will find that:

The brokerage firms are becoming serious competitors for banks and other depository institutions by offering high-yield combination savings and checking accounts and money market accounts, as well as certain types of loans.

Brokerage firms often helps individuals or firms in providing some key financial services.   A full-service brokerage firm is known to be a brokerage firm that gives a range of financial services and also to gives room for one to buy and sell securities.

They help customers with financial planning services as well as consulting services and also provide trust services and wealth management services.

See full question below

Anthony would like to have his brokerage firm handle more of his financial needs because he has been pleased with the service provided when he bought and sold stocks and bonds. If he explores the services offered by such firms in more depth, he will find that:

federal laws prohibit brokerage firms from competing with banks, savings and loan associations, and credit unions.

although brokerage firms can offer some banking services, they typically are less efficient at providing them than banks, because they specialize in buying and selling securities.

brokerage firms are becoming serious competitors for banks and other depository institutions by offering high-yield combination savings and checking accounts and money market accounts, as well as certain types of loans.

although brokerage firms offer attractive banking services, federal law prohibits individual investors from holding both a checking account and a securities account with the same firm.

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Problems with sleep are more common than sleep disorders or parasomnias. Please select the best answer from the choices provided T F.

Answers

Answer:

True

Explanation:

E2023

Answer:

true

Explanation:

Which monarch was the target of the Gunpowder Plot? A. Elizabeth I B. James I C. Charles I D. Charles II.

Answers

Answer: The answer is B

Explanation: James I

The monarch who was the target of the gunpowder was James I.

James I is the monarch which was the target of the Gunpowder Plot. Hence option B is correct.

What is monarch?

Monarch is defined as a sovereign ruler is someone who has control over a kingdom or empire. A monarch with legal standing. In the United Kingdom, monarchy is the oldest system of government. A king or queen is the head of state in a monarchy. Constitutional monarchies include the British Monarchy. Monarchy, a form of government in which one person has full power or authority.

The Gunpowder Plot of 1605, in which Guy Fawkes and other Catholic conspirators attempted to blow up Parliament and assassinate James I of England, is commemorated on 5 November in Britain on Guy Fawkes Day.

Thus, James I is the monarch which was the target of the Gunpowder Plot. Hence option B is correct.

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For which pairs of functions is (f circle g) (x)?.

Answers

Answer:

Option B is correct. The required composite function where f(g(x)) is x is f (x) = StartFraction 2 Over x EndFraction and g (x) = StartFraction 2 Over x EndFraction

Explanation:

Which phrase best describes the vapor point of a substance?.

Answers

The phrase which best describes the vapor point of a substance is: the temperature at which additional heat energy causes the substance to change from a liquid to a gas.

A substance can be defined as a particular kind of matter that has uniform or definite properties.

In Science, there are two (2) main types of substance and these include:

An inorganic substanceAn organic substance

The vapor vapor point of a substance refers to the temperature at which an additional quantity of heat energy causes a particular substance to be transformed (change) from a liquid to a gas or vapor.

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Use the drop-down menu to complete each statement. US national security policy seeks to. Congress has the power to. The US government has to support national security.

Answers

Answer

1. protect us citizens

2. declare war

3. signed treaties

Explanation: your welcome

US national security policy seeks to protect us citizens.

Congress has the power to declare warThe US government has to support national security - Signed treaties

What does national security do?

National security is known to be the body that is responsible for protection of its citizens, economy, and any other kinds of set up body.

Conclusively, It is known to be a body that is set up by government and handle issues relating to economic security, political security, and others and as such, US national security policy seeks to protect us citizens.

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Which statements correctly characterize asoka's reign? select all correct answers.

Answers

Answer:

Roads, hospitals, and monuments were built.

Buddhism spread through missionary monks.

Explanation:

Asoka was the founder of the Moorish dynasty, and extended the kingdom to the western half of northern India. His endeavor, accompanied by fearsome bloodshed, provoked profound spiritual upheavals at Asoka, after which he embraced Buddhism, which had appeared in Magadha two centuries earlier. Since then, the cruel Asoka has become known as the godly Asoka. In the words of the emperor himself, since then his sound was no longer booming, but the voice of dharma.

During his rule, he pursued an official policy of non-violence. The unnecessary killing and mutilation of animals has been abandoned, such as hunting for hunting and stamping.

Asoka also showed mercy to the captives, allowing them a day of freedom each year, and providing ordinary citizens with free education at universities. He treated subjects as equals regardless of religion, politics or caste and made free hospitals for both humans and animals. Asoka defined the main principles of nonviolence, tolerance of sects and opinions, obedience to parents, respect for teachers and priests, human treatment of servants (slavery did not even exist in India at that time) and generosity to all. These reforms are described by Asoka's edicts.

Which factor is critical in determining whether a mother can grow a healthy placenta during the first month of gestation?.

Answers

Answer: Mother's pre-pregnancy nutrition status.

Which of the following can be best explained by temporary dipole moments?.

Answers

we need to see the following answers to answer ur question

Can one model demonstrate all outcomes of mitosis?(1 point).

Answers

Answer:

No, because some organisms are not diploid and have more than two sets of chromosomes

Explanation:

No, because some organisms are not diploid and have more than two sets of chromosomes.

What is mitosis?

A cell prepares for cell division by replicating its chromosomes, segregating them, and creating two identical nuclei during the mitotic phase. The cell's contents are often evenly divided into two daughter cells with identical genomes after mitosis.

A cell copies each chromosome during mitosis and distributes one copy to each of its two daughter cells. With regard to our example of an instruction manual, it is crucial that each person receive a duplicate of each page.

Mitosis follows the same pattern. Each chromosome must be delivered to each of our cells exactly once, without any errors, or the cells may have problems carrying out the genetic instructions.

Therefore, No, because some organisms are not diploid and have more than two sets of chromosomes.

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When a positive charge is released and moves along an electric field line.

Answers

what does it mean expalin it

What is the value of x in the equation 2 (6 x 4) minus 6 2 x = 3 (4 x 3) 1? 1 3 4 6.

Answers

Answer:

4

Step-by-step explanation:

2 (6 x + 4) - 6 + 2 x = 3 (4 x + 3) + 1

12x + 8 - 6 + 2x = 12x + 9 + 1

12x + 2 + 2x = 12x + 10

2x + 2 = 10

2x = 10 - 2

2x = 8

x = 4

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