A spherical balloon is inflating with helium at a rate of. How fast is the​ balloon's radius increasing at the instant the radius is ​ft? how fast is the surface area​ increasing?.

Answers

Answer 1

Using implicit differentiation, and considering that the inflation rate is of 200 cubic feet per minute and the radius is of 5 feet, it is found that:

The radius is increasing at a rate of 0.6366 feet per minute.The surface area is changing at a rate of 80 feet squared per minute.

The volume of an sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

Applying implicit differentiation, the rate of change is given by:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

For this problem:

Inflation rate of 200 cubic feet per minute, hence [tex]\frac{dV}{dt} = 200[/tex]Radius is of 5 feet, hence [tex]r = 5[/tex]

Then:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

[tex]200 = 4\pi (5)^2\frac{dr}{dt}[/tex]

[tex]\frac{dr}{dt} = \frac{200}{100\pi}[/tex]

[tex]\frac{dr}{dt} = 0.6366[/tex]

The radius is increasing at a rate of 0.6366 feet per minute.

The surface area is:

[tex]S = 4\pi r^2[/tex]

Hence, the rate of change is:

[tex]\frac{dS}{dt} = 8\pi r\frac{dr}{dt}[/tex]

Hence:

[tex]\frac{dS}{dt} = 8\pi (5)(0.6366) = 80[/tex]

The surface area is changing at a rate of 80 feet squared per minute.

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Related Questions

A generic x by x grid has c blocks moved to create a (x-c) by (x+c) grid. Which of the following equations represents the difference of squares for this situation?.

Answers

The expression that represents the difference of squares for this situation is [tex]x^2-c^2[/tex]

Given the generic x by x grid has c blocks moved to create an (x-c) by (x+c) grid, to get the difference of two squares, we will take the product of the expressions as shown:

[tex]=(x-c)(x+c)\\=x^2+xc-xc-c^2\\=x^2 -0-c^2\\=x^2-c^2[/tex]

Hence the expression that represents the difference of squares for this situation is [tex]x^2-c^2[/tex]

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Use stokes' theorem to evaluate s curl f · ds. F(x, y, z) = x2 sin(z)i + y2j + xyk, s is the part of the paraboloid z = 4 − x2 − y2 that lies above the xy-plane, oriented upward.

Answers

Stokes' theorem says that the surface integral of the curl of the vector field F across the surface S is equal to the line integral of F along the boundary of S.

In this case, the boundary is a circle in the x,y-plane with radius 2. (To see this, set z = 0 and rearrange the equation for the paraboloid as x² + y² = 4.)

Then

[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_{\partial S} \vec F \cdot d\vec r[/tex]

where

[tex]\vec r = 2\cos(t) \,\vec\imath + 2\sin(t) \,\vec\jmath[/tex]

parameterizes the circular boundary of S with 0 ≤ t ≤ 2π. Then

[tex]d\vec r = \dfrac{d\vec r}{dt}\,\dt = (-2\sin(t)\,\vec\imath + 2\cos(t)\,\vec\jmath)\,dt[/tex]

and the integral becomes

[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_{\partial S} \vec F \cdot d\vec r[/tex]

[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} \vec F(\vec r(t)) \cdot \frac{d\vec r}{dt}\,dt[/tex]

[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s \\= \int_0^{2\pi} ((2\cos(t))^2 \sin(0)\,\vec\imath + (2\sin(t))^2\,\vec\jmath + (2\cos(t))(2\sin(t))\,\vec k) \cdot(-2\sin(t)\,\vec\imath + 2\cos(t)\,\vec\jmath)\,dt[/tex]

[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} 8\sin^2(t)\cos(t) \, dt[/tex]

[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \int_0^{2\pi} 8\sin^2(t) \, d(\sin(t))[/tex]

[tex]\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec s = \frac83 (\sin^3(2\pi)-\sin^3(0)) = \boxed{0}[/tex]

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 )

Answers

Sorry that I'm late, but it's 155.555555556 or 155.6. Whatever you got to round it to. Have a good day!

why are SATs so hard to study for

Answers

Because they want everyone to fail and I don’t like them…

Answer:

It is considered the finale of High School. Which depicts what role you should become in College... it is also the ticket to ur high school diploma

Explanation:

Keith has to carry out a photo shoot to capture images of the ocean during the monsoons. What is a recommended practice when shooting in these conditions?.

Answers

Answer is A: place absorbent chemical packets
in the camera cover

Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27. The cost of a package of cheese is $1. 50 more than the cost of a one loaf of bread. What is the combined cost of one loaf of bread and one package of cheese?.

Answers

Answer:

Bitlog

Explanation:

iklog

5006+6

this is the hardest question on Earth i KEEP GETTING IT WRONG PLEASE help me

Answers

Answer:

5012

Explanation:

5006 + 6 equals 5012

How did fossils help and teach scientists about the history of the earth brainly.

Answers

Answer:

Fossils helped teach scientist by giving information of the species that lived back then.

Explanation:

The fossils have clues on them help identify what they are.

Have you ever visited a railway station.

Answers

Answer:

Yeah, so.....

Explanation:

The frequency and energy ranges of photons in some parts of the electromagnetic spectrum are given in the table above. Which of the following could be the energy of a photon in the visible range?.

Answers

Answer:

The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, the higher its energy. Equivalently, the longer the photon's wavelength, the lower its energy.

The energy of photon in visible range will be of [tex]4 \times 10^{-19} J[/tex].

What is the electromagnetic spectrum?

Violet, indigo, blue, green, yellow, orange, and red are hues in the electromagnetic spectrum. Blue light has a very short wavelength and hence creates more energy.

Blue light in the visible zone has a very short wavelength. So that it produces a higher amount of energy that's why the blue part of visible light transfers the most energy.

The photons in the infrared range have the lowest energy and photons in the ultraviolet range have the highest energy.

A photon in the visible range should have an energy which is between the infrared range and the ultraviolet range.

Wherever the maximum energy of a photon in the infrared range is 3 x 10-19 J and the minimum energy of a photon in the ultraviolet range is 5 x 10-19 J,

Thus, photon in the visible range could have an energy of  [tex]4 \times 10^{-19} J[/tex].

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Alterations in various aspects of society over time.

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alterations in various aspects of society over time according to pitrim Sorkin cyclical theory of social change the principle of immant change is the natural tendency of a society structure to swing back and forth between the ideotional and sensate culture

A significant alteration to a society's structure is social change. Numerous facets of a society, including its economic, political, cultural, ethical, and identity problems, can be affected by social change.

What Alterations in various aspects of society over time?

The major alteration of social structure and cultural norms over time is referred to as social change. Social ties that have remained constant over time and become routine or repetitive are referred to as social structures.

Among the key forces influencing societal development are population growth and composition, the natural environment, social conflict, culture, and technology.

Cultural lag is the term used to describe a delayed shift in one area of society as a result of a change in a different area of society.

Therefore, Alterations in social change various aspects of society over time.

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On a position vs. Time graph, which feature would represent motion in the negative direction over time?.

Answers

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:

Dark matter absorb light emit radiation and been observed directly.

Answers

Answer:

does not,

does not,

and has not

Explanation:

Dark matter doesn't absorb light, doesn't emit radiation and has not been observed directly.

What is dark matter?

Dark matter can be defined as often invisible substances that are difficult to spot and observed because they don't absorb, emit or reflect light.

This ultimately implies that, dark matter doesn't affect human view because they do not interact or interfere with electromagnetic radiation.

However, humans can see through the (weakly interacting) dark matter but it has not been observed directly by scientists and astronmers.

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Which of the following factors best supports the argument in the excerpt?.

Answers

Answer:

probaly awnser C

Explanation:

or B or a

The word halcyon comes from a greek legend brainly.

Answers

Greek Mythology is simply described as different kinds of stories about the gods, goddesses, etc., of Ancient Greeks. The word halcyon originate from a Greek legend is described below;

The word halcyon is known to have its origin from a story that was written in Greek mythology. The story was all about the halcyon bird, who is empowered to calm the rough ocean waves every December because she want to lay in her nest.

As a result of the calmness of the waters, halcyon therefore means having a sense of peace or tranquility.

Conclusively, In Greek mythology, there is a goddess Halcyon who is also called Alcyone in Greek. She is known as the daughter of Aeolus, the ruler of the winds.

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When checking for scene safety for the use of an aed, which of these best describes the dangers that would stop us from using an aed?.

Answers

Flammable gases, patient lying in standing water, combustible liquids near the victim

Explanation:

Which of the following is a way to buy stocks.

Answers

Answer:

Through Hiring a Stockbroker

Answer:

Online through a brokerage Web site

Explanation:

A coordinate plane is labeled with quadrants 1, 2, 3, and 4. Point P is located at (–4, –7). P is reflected across the x-axis to create P'. In which quadrant is P' located? Quadrant I Quadrant II Quadrant III Quadrant IV.

Answers

Answer:

Quadrant II

Explanation:

P (-4, -7) lies in 3rd quadrant

reflect across the x axis (x, y) --> (x, -y)

so P' (-4, 7)

it lies in 2nd quadrant

Answer:

B

Explanation:

got it right

What is the entropy change for the freezing process of 1 mole of liquid methanol at its freezing temperature (–97. 6˚c) and 1 atm? please report your answer two points past the decimal with the unit j/molk. ∆h˚fus = 3. 17 kj/mol.

Answers

Answer:

the value of change in entropy for freezing process of 1 mole of liquid methanol is -18.07 J/mol.k

Explanation:

Entropy is defined as the measure of possible arrangement of the atoms or molecules. Entropy change for the the freezing process mole of 1 liquid methanol at -97.6 degree celcius and 1 atm will be -18.07 J/mol.

The entropy change can be calculated by the given formula:

 

Thus, the value of change in entropy for freezing process of 1 mole of liquid methanol is -18.07 J/mol.k

(Hope this helps can I pls have brainlist (crown)☺️)

 

For the freezing of 1 mole of liquid methanol, the change in entropy value is -18.07 J/mol.

What is entropy value?

The measure of atoms' or molecules' potential arrangements is known as entropy. Entropy change for one mole of liquid methanol frozen at -97.6 degrees Celsius and one atmosphere is -18.07 J/mol.

The range of entropy is 0 to 1. Depending on the number of classes in your dataset, entropy can be greater than 1, but it still indicates a very high level of chaos. For the sake of convenience, the examples in this blog will have entropy values between 0 and 1.

The "information" a variable contains is measured by its entropy. Now, based on the surprise that this value of the bholds and the number of distinct values that are present in the variable, this amount is approximated.

Thus, it is -18.07 J/mol.

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Marianna is working on improving her communication skills. To be a good listener she should.

Answers

-not interrupt
-put devices away
-repeat somethings she heard so others see she’s paying attention

Four companies have each issued $6 million in bonds. Which company will have the lowest balance in a contra account, without having a zero balance, assuming this is the first bond issuance for all four companies?.

Answers

The company that will have the lowest balance in a contra account is company-2 , which sold bonds at 94%

Bonds are being usually sold at par, at a discount, or at a premium. There exists no notion of a contra asset if the bonds are sold at par. If the bonds are sold at a discount, the net cash received will be lesser than the amount of par value of the bonds issued. Under this scenario, the bonds payable account can only display the par value of the bonds issued, however, the difference among both the par value of the bonds as well as the net cash actually realized from this kind of bond issue will be parked in a contra account which will be amortized over the bond's tenure.

As such, the lowest balance in the contra account for the four companies can be computed as:

                             company4      company3      company2      company1

Bond par value   $6,000,000   $6,000,000   $6,000,000   $6,000,000

Issued at               105%               101%               94%                  99%

Net cash -          6300000        6060000        5640000        5940000

realized

Contra

account           3000000         60000          (-360000)          -60000

balance

Therefore, it is obvious that the company with the lowest balance in a contra account is company 2, which sold their bonds at 94%

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if the natural market forces are left to their own devices, will tourism result in income redistribution that works in favor of the poorer segments of the population?

Answers

Answer:

No

Explanation:

No, companies will most likely reduce benefits/wages to increase profit margins and increase revenue, resulting in increased share value and happier shareholders.

A watchmaker can build a watch for $90. She wants to make a $50 profit on top of his cost. What should she list the sale price of the watch at if she also wants to advertise a 30% discount on her watches?

Answers

Answer: 200

Explanation: 90 + 50 = 140

x - x * 30% = 140

x * 70% = 170

x * 0.7 = 140

x = 140/0.7

x = 200

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Identify the molecular geometry around the carbon atom highlighted red in the given organic molecule.

Answers

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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Andrei adds 50 ml of boiling water to 100 ml of tap water. If the 150 ml of water is then put into a freezer, at what temperature will the water freeze?.

Answers

Answer:

0°C

Explanation:

water always freezes at 0 degrees

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.

Answers

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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Write an outline the chosen reading text using your preferred format brainly.

Answers

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.

Rami is graduating high school in the spring. He is interested in becoming a electrician. What are his options for learning this trade? select all that apply.

Answers

To be a licensed electrician requires deep knowledge of the field. Rami's  options for learning this trade are;

He should applied degree at a two year college or He can study for a bachelor's degree at a four year collegeApprenticeship and trade school

A licensed electrician job is not easy to obtain. It requires studying, years of being an apprentice or attending school, and years of  work experience.

To be a licensed electrician, these steps should be followed:

Earn a high school diploma or Its equivalent. Try and attend a trade or vocational-technical school. Sign up as an electrician apprentice.   Get licensed or certified.

See full question blow

Rami is graduating high school in the spring. He is interested in becoming a electrician. What are his option  learning this trade? Select all that apply.

applied degree at a two year college bachelor's degree at a four year college vocational training in the military apprenticeship and trade school going directly into the workplace

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Answer: 1) applied degree at a two year college

3) Vocational training in the military

4) apprenticeship and trade school

Explanation: did on edge :)

Which of the following statements best supports the one gene-one enzyme hypothesis?.

Answers

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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Which prediction does this passage best support? moses and his stories will complicate the pigs’ control over the other animals. The pigs will adopt moses’s ideas and promote them on animal farm. Moses will die and end up on sugarcandy mountain, thus proving its existence. The animals will demand that moses leave the farm and will force him out.

Answers

Stories often convey deep meaning. Moses and his stories will complicate the pigs' control over the other animals.

The Animal Farm is known to be a novella that was written by George Orwell. It was known to be written in England in 1945.

The story was about a group of farm animals who fought back against their human farmer. They wanted to a society where the animals can be equal.

The pigs were actually are interested in been in charge of all the animals and the stories of Moses is hindering their agenda.

See full question below

Read the passage from chapter 2 of Animal Farm.

The pigs had an even harder struggle to counteract the lies put about by Moses, the tame raven. Moses, who was Mr. Jones's especial pet, was a spy and a tale-bearer, but he was also a clever talker. He claimed to know of the existence of a mysterious country called Sugarcandy Mountain, to which all animals went when they died. It was situated somewhere up in the sky, a little distance beyond the clouds, Moses said. In Sugarcandy Mountain it was Sunday seven days a week, clover was in season all the year round, and lump sugar and linseed cake grew on the hedges. The animals hated Moses because he told tales and did no work, but some of them believed in Sugarcandy Mountain, and the pigs had to argue very hard to persuade them that there was no such place.

Which prediction does this passage best support?

Moses and his stories will complicate the pigs’ control over the other animals.

The pigs will adopt Moses’s ideas and promote them on Animal Farm.

Moses will die and end up on Sugar candy Mountain, thus proving its existence.

The animals will demand that Moses leave the farm and will force him out.

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Answer:

A:Moses and his stories will complicate the pigs’ control over the other animals.

Explanation:

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