The radius of a cone is increasing at a constant rate of 8 feet per second. The volume remains a constant 56 cubic feet. At the instant when the radius of the cone is 3 feet, what is the rate of change of the height? The volume of a cone can be found with the equation V = farh. Round your answer to three decimal places.
Answers
Answer:
\(\Rightarrow \frac{dh}{dt}\approx -31.690 \)
Explanation:
The volume of a cone, V = 1/3πr^2h
Where r is the radius, and h is the height of the cone.
Given:
Volume is constant at 56 cubic feet.
Radius of cone increases at a constant rate of 8 feet per second.
The radius of the cone is 3 feet.
When radius is 3 feet
\(\Rightarrow h= \frac{3V}{\pi r^2}\)
\(\Rightarrow h= \frac{3\times 56}{\pi \times 3^2} \)
\(\Rightarrow h= \frac{3\times 56}{\pi \times 9} \)
\(\Rightarrow h= \frac{ 56}{3\pi} \)
Where h is in feets.
\(\frac{dV}{dt}=\frac{d (\frac{1}{3}\pi r^2h) }{dt} \)
\(\Rightarrow \frac{dV}{dt}=(\frac{1}{3}\pi \frac{dr^2}{dt}h)+(\frac{1}{3}\pi r^2 \frac{dh}{dt}) \)
\(\Rightarrow \frac{dV}{dt}=(\frac{1}{3}\pi \frac{dr^2}{dr}.\frac{dr}{dt}h)+(\frac{1}{3}\pi r^2 \frac{dh}{dt}) \)
\(\Rightarrow \frac{dV}{dt}=(\frac{1}{3} \pi 2r\frac{dr}{dt}h)+(\frac{1}{3}\pi r^2 \frac{dh}{dt}) \)
Since the volume is constant so \( \frac{dV}{dt}=0 \)
The rate of change of radius is \(\frac{dr}{dt}=8 \)
\(\Rightarrow 0=(\frac{1}{3} \pi (2\times 3)(8)(\frac{56}{3\pi}))+(\frac{1}{3}\pi (3^2) \frac{dh}{dt}) \)
\(\Rightarrow 0=(\frac{56\times 16}{3})+(\frac{1}{3}\pi (9) \frac{dh}{dt}) \)
\(\Rightarrow 0=(\frac{56\times 16}{3})+(3\pi \frac{dh}{dt}) \)
\(\Rightarrow 3\pi \frac{dh}{dt}=-\frac{56\times 16}{3} \)
\(\Rightarrow \frac{dh}{dt}=-\frac{56\times 16}{3\times 3 \times \pi} \)
\(\Rightarrow \frac{dh}{dt}=-\frac{56\times 16}{9\pi} \)
\(\Rightarrow \frac{dh}{dt}=-31.689518 \)
\(\Rightarrow \frac{dh}{dt}\approx -31.690 \)
The minus indicates that the rate of change of height is decreasing.
Related Questions
Can you help me with question 24
Answers
Answer:
C.
Explanation:
The graph below shows the decline in the catch of groundfish (such as cod, haddock and flounder) from Georges Bank between 1965-1995. This decline in the fish harvest resulted in the closure of large portions of the fishery. Based on this data, what is the rate of decline in the fish harvest, in metric tons per year, from 1965-1995?
Answers
Answer:
Approximately 22,000 metric tonnes of fish per year
Explanation:
From the graph,
Rate of decline :
(metric tonnes of fish in 1965 - metric tonnes of fish in 1995) / range of years
(700,000 - 40,000)metric tonnes ÷ (1995 - 1965)
660,000 metric tonnes ÷ 30 years
660,000 / 30
= 22,000 metric tonnes per year
Approximately 22,000 metric tonnes of fish per year
(05.02 LC)
The vast majority of the world's energy comes from which of the following? (3 points)
Biodiesel fuel
Fossil fuels
Hydrogen cells
Hydropower
Answers
Answer:
it’s fossil fuels
Explanation:
Employers prefer to hire someone who has been referred to them, rather than a complete stranger.
Answers
Answer:
YES IT IS TRUE! THE REASON IS BEING THAT MOST OF THE EMPLOYERS CARES ABOUT THE COMPANY AND WOULDN'T WANT A COLLAPSE.THEY MIGHT NOT KNOW WHAT THE COMPLETE STRANGER IS CAPABLE OF DOING NEGATIVELY.AND ALSO WITH COMPLETE STRANGERS MOST OF THEM TURN OUT TO BE SPIES.I HOPE IT HELPED YOU.
DON'T HESITATE TO ASK FOR FURTHER EXPLANATION.A BRAINLIEST PLEASE.
A rock sample contains 7.5 g of Californium-249 and 52.5 g of the daughter isotope. If the half life of Californium-249 is 360 days, how old is the rock?
Answers
Answer:
Rock is \(1080\) days old
Explanation:
Total Mass = \(52.5\) grams \(+ 7.5\) grams \(= 60\) grams
As we know
\(\frac{7.5}{60} = \frac{60* (\frac{1}{2} ) (\frac{t}{360d})}{60}\)
\(0.125 = 0.5* (\frac{t}{360d})\)
Taking log on both sides we get –
Log \((0.125) = \frac{t}{360}\) log \((0.5)\)
\(\frac{-0.903}{-0.301 } = \frac{t}{360}\)
\(t = 3 * 360\)
\(t = 1080\)
\(1080\) days
breanna like to do crossword puzzles to reduce stress. she joins a puzzle club to keep focused oh her hobby..
Answers
Answer:
She takes a right decision.
Explanation:
Breanna did the right thing to join a puzzle club to keep focused her mind because crossword puzzle games helps in reducing stress. Some research suggests that puzzles and similar mental activities can avoid stress and give stress relief moment. Our brain likes finding patterns so puzzle games satisfy this desire of brain which automatically improves our mood and remove stress so we can conclude that she did the right decision to join the puzzle club.
PLEASE HELP QUICKLY I WILL GIVE BRAINLIEST!Fernando is interested in determining whether attendance of a public or private school has an impact on how often students meet with their teachers. If he were to conduct a study to answer this question, what does the type of school attended represent?
confounding variable
dependent variable
independent variable
control variable
quasi-independent variable
Answers
Fernando is interested in determining whether attendance of a public or private school has an impact on how often students meet with their teachers. it will represent the dependent variable.
What is dependent variable?The cause is the independent variable. Its value is unaffected by the other study variables. Effect is the dependent variable. Changes in the independent variable affect its value.
The variable being measured or tested in an experiment is known as the dependent variable. The results of the participants' tests, for instance, since that is what is being measured, would be the dependent variable in a study looking at how tutoring affects test scores.
This isn't the same as an experiment's independent variable, which is a variable that can stand on its own. Tutoring would be the independent variable in the aforementioned case.
Therefore, Fernando is interested in determining whether attendance of a public or private school has an impact on how often students meet with their teachers. it will represent the dependent variable.
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Rrajendra purchase a pairs of chappals from a Bata shop worth rupees 99.95 the rate of sales tax is 7% calculate the total amount to be paid by him
Answers
At first we will find sales tax
Sales tax = Sales tax% × Worth rupees
\(\begin{gathered} \begin{gathered} \sf Sales \: tax = 7\% \times 99.95 \\ \sf \: Sales \: tax = \frac{7}{100} \times 99.95 \\ \dashrightarrow \sf 6.95 \approx 7 \end{gathered}\end{gathered}\)
Total SP = 99.95 + 7
Total SP = 106.95 ≈ 107
Rajendra should be paid 107$ totally.
Christianity has grown to be the world's largest religion. What has contributed to this growth?
Answers
Answer:
Since the Roman Catholic Church does not permit the questioning of the church's teachings, many Christians do not convert to other religions and many people are converting to it.
Explanation:
If Brendon Urie has a wife, and he is Ryden, what does that mean?
Answers
what is the significance of children's emotional bonds with their parents?
Answers
Answer:
Children's emotional bonds with their parents have significant implications for their social, emotional, and cognitive development. Research has shown that strong emotional bonds with parents help children to feel secure and develop a sense of trust in their environment. Children who have positive relationships with their parents tend to be more confident, empathetic, and better able to regulate their emotions. Additionally, these emotional bonds can serve as a buffer during times of stress or adversity, helping children to cope more effectively. On the other hand, children who have insecure attachments to their parents may struggle with emotional regulation, have difficulty forming healthy relationships, and experience a range of negative outcomes later in life. Therefore, the quality of the emotional bonds children have with their parents is a critical factor in their overall development and well-being.
WHAT VEGETABLE IS GREEN IN COLOR AND IS A MAIN INGREDIENT IN A SAVORY DIP?
Answers
Describe the topography shown in Image 1.
Answers
Answer:
it's a picture of something
Read the sentence from the article: "it's drought-proof, that's one of the most important" things, said water-use expert bob yamada. according to the article, why is it "drought-proof?"
Answers
The ability of the local natural and human production resource base to supply a desirable amount of food, drinking water, livelihood resources during a drought is what is meant by "drought proofing" a place.
The main factor behind agricultural loss on a global scale is drought, which inserted a serious risk to the availability of food. When it comes to creating crops that can produce large yields in water-limited settings, plant biotechnology is now one of the most promising topics.
The primary drought stress response pathways have been identified through research on complete Arabidopsis thaliana plants, and numerous drought resistance genes have already been inserted into crops. Since most plants that have improved drought resistance have so far had lower crop yields, new strategies to decouple drought resistance from plant growth are still needed.
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If an artist were to blend red, green, and blue paints together, the result would look
Answers
Answer:
you would get white
Explanation:
I looked it up on google lol
Answer:
it would look like a mixture of colors
Explanation:
yessir white fyi
the model of the earth which is spherical
Answers
Here are some key characteristics of the spherical Earth model:
1. Shape: The Earth is considered a sphere, meaning it has a rounded shape with all points on its surface equidistant from its center.
2. Symmetry: The spherical Earth model assumes that the Earth is symmetrical, with a consistent curvature in all directions.
3. Gravity: The model takes into account the gravitational forces acting on the Earth, with the force pulling objects toward its center, resulting in the spherical shape.
4. Horizon: The spherical Earth model explains the observation that as one moves away from a location, the horizon appears to curve downward due to the Earth's curvature.
5. Latitude and Longitude: The model uses a system of latitude and longitude lines to determine precise locations on the Earth's surface, with the equator as the reference line.
6. Time Zones: The spherical Earth model explains the concept of time zones, where different regions have different local times based on their position relative to the Sun's position.
7. Navigation: The spherical Earth model is crucial for navigation, as it provides a basis for calculating distances, directions, and angles when traveling on the Earth's surface or using celestial navigation.
It's important to note that while the spherical Earth model is a useful approximation, the Earth's shape is not a perfect sphere but is slightly flattened at the poles and bulging at the equator, resembling an oblate spheroid. However, for most practical purposes, the spherical Earth model remains a valuable and accurate representation of our planet.
May I have the brainliest?
trying to get as much people as possible for a kahoot (anime) ill give u code 3608565 if u get all right ill give u brainliest
Answers
Answer:
I will do it
Explanation:
Do itttttttttt
Which of the following layers of Earth is a liquid layer with the highest density? (1 point)
O outer core
Olithosphere
O mesosphere
asthensophere
Answers
Answer:
outer core
Explaination:
The liquid layers of Earth are the outer core and the asthenosphere, but the outer core has a higher density than the asthenosphere
The only option that shows the layer of earth that is liquid with the highest density is;
Option A; Outer Core
In geology the are 4 different layers of the earth namely; crust, mantle, inner core and outer core. However, we will describe only outer core here as it is the correct answer.The outer core of the earth is the iron-nickel like layer of the earth that is located just below the mantle. From previous geological research and experiments, it has been discovered that the outer core is the only part that is liquid and that it is as a result of interior seismic surveys of Earth's.It is also a distance of around 2890 km below the earths surface.
As the only liquid part of the earth, it is clear that it is the correct option.
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Answers
Answer:
Page 85
1.B
2.D
3.C
4.A
Explanation:
its right
Is their fetal development impacted by being conjoined? If so, how?
CHILD DEVELOPMENT CLASS
Answers
I would think that fetuses growing in the womb that are conjoined twins their organs would probably grow differently and I also think how their skin heals and how it looks or how it stretches things like that .
"Let us, then, with courage and confidence, pursue our own Federal and [Democratic-] Republican principles, our attachment to union and representative gove
separated by nature and a wide ocean from the exterminating havoc of one quarter of the globe; too high-minded to endure the degradations of the others, po
chosen country, with room enough for our descendants i entertaining a due sense of our equal right to the use of our own faculties, to the acquisitions of on
to honor and confidence from our fellow citizens, resulting not from birth, but from our actions and their sense of them, enlightened by a benign religion
blessings, what more is necessary to make us a happy and a prosperous people? Still one thing more, fellow citizens a wise and frugal Government, which s
men from injuring one another, shall leave them otherwise free to regulate their own pursuits of industry and improvement, and shall not take from the mouth
bread it has earned. This is the sum of good government, and this is necessary to close the circle of our felicities."
President Thomas Jefferson, first inaugural address, 1801
Which of the following best describes the context from which the ideas expressed in the excerpt emerged?
Religious revivals encouraged the widespread development of reform movements
Political leaders sought to encourage domestic economic development.
Popular opinion supported intervention in Europe against France.
Voters pressured state governments to drop property restrictions on voting.
!["Let us, then, with courage and confidence, pursue our own Federal and [Democratic-] Republican principles,](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/fDdsISCD6MPNKLCyfW0zK6SatU9UIbRB.png)
Answers
E: I read the excerpt like 4 months ago
The one that best describes the context from which the ideas expressed in the excerpt emerged is political leaders sought to encourage domestic economic development. The correct option is B.
What is democracy?A democracy is a system of government in which the populace has the power to decide laws and elect representatives to carry it out.
Democracy entails popular government. The words "demos" and "kratos" are from classical Greek (to rule). A democratic nation has a form of government where citizens have the authority to influence policy. Every democracy is distinct and functions differently.
The statement that describes the environment in which the concepts in the excerpt first appeared is that political leaders wanted to promote domestic economic development.
Thus, the correct option is B.
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A résumé is a:
OA. listing of all prior education.
B. document individuals use to present their professional
backgrounds.
OC. work history report.
OD. form that lists all your school grades.
Apex!
Answers
Answer:
B makes the most sense
Explanation:
A résumé is a document individuals use to present their professional backgrounds. The correct option is B.
What is résumé?A résumé is a document in which individuals present their professional backgrounds and qualifications to prospective employers.
It typically includes information such as the individual's work experience, education, skills, accomplishments, and other relevant information demonstrating their suitability for a specific job or industry.
A résumé is frequently the first point of contact between a job seeker and a prospective employer, and it is intended to persuade the employer to invite the candidate for an interview.
It is not a form that lists all of your school grades or a listing of all of your prior education, nor is it strictly a work history report, though it does frequently include information about the individual's work experience.
Thus, the correct option is B.
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describe one historical development illustrated by the passage. describe sotomayors argument regarding women’s education
Answers
The historical development illustrated by the passage and Sotomayor's argument regarding women’s education was that:
The social components of the passage are one historical development since women cannot study or perform tasks as well as males. "The actual reason that women are not learned is not a lack of brain, but rather a lack of study," the paragraph states. The goal of this argument is to demonstrate that men think women are not capable of or deserving of learning new things.What was Sotomayor's point in speaking?Sotomayor's point when she spoke was to inform students of the requirements to become a judge in the present era, to persuade listeners that it is crucial to have more diverse judges, to delight the audience with tales of her upbringing.
Therefore, By setting a tone of uncertainty, Sotomayor is encouraging the audience to pose their own queries. To help the audience better understand the questions, Sotomayor creates a system of repetition.
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DeShawn's Work:
5x16 +2x + 7 = 180
7x-9= 180
7x = 189
x = 27
A. He set the equation up incorrectly.
B. He combined like terms incorrectly.
C. He added 9 to 180 when he should have subtracted 9 from 180.
Answers
DeShawn did not set up the first equation correctly and did not combine like terms incorrectly or add/subtract 9 from 180 incorrectly. The correct answer is A. He set the equation up incorrectly.
How can this be explained?It appears that DeShawn solved two different equations.
For the first equation, 5x16 + 2x + 7 = 180, DeShawn would need to simplify the left side of the equation first by multiplying 5 and 16, which equals 80.
Then, he can combine the like terms of 80x and 2x, which equals 82x. So the equation becomes:
82x + 7 = 180
From there, he can isolate the variable x by subtracting 7 from both sides:
82x = 173
Finally, he can solve for x by dividing both sides by 82:
x ≈ 2.11
For the second equation, 7x-9= 180, DeShawn correctly solved for x:
7x = 189
x = 27
Therefore, DeShawn did not set up the first equation correctly and did not combine like terms incorrectly or add/subtract 9 from 180 incorrectly
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In line 17, the quotation marks around the phrase "entertainment factor" imply that?
Answers
The quotation marks around the phrase "entertainment factor" imply that the measurement is largely personal and largely idiosyncratic
What do the quotation marks around the phrase implies?In the context of the paragraph, the quotation marks around the phrase "entertainment factor" suggest that the measurement of entertainment value is subjective and personal. It implies that what may be entertaining to one person, like Chanu, might not be entertaining to others.
The use of quotation marks indicates that the term "entertainment factor" is being used in a specific or unique way by Chanu emphasizing the subjectivity of his rating system. It highlights the idea that the measurement of entertainment is largely based on individual preferences rather than being universally agreed-upon standard.
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Use this paragraph: Carlon is using two wooden blocks to model the movement of Earth's plates. He pushes one block forward
and the other block backward, rubbing their surfaces together
Which Earth feature is he modeling?
Item 4
(1 point)
O thrust fault
O normal fault
Orift valley
O strike-slip fault
Answers
Earth's feature that he is modeling is a normal fault. Thus, option B is correct.
What is Earth?"Earth can be defined as a planet of a solar system on which we know that life exists it is the third planet counting from the sun and it has both living as well as nonliving organisms residing on it. It rotates around the sun and has one moon."
The normal fault will be what Carlon is using in the model where the blocks are moving. Whenever rocks crack and shift as a result of becoming pulled separately, this is a typical fault.
The rocks migrate anywhere along due to no fault when the area is expanded. There are earthquakes with every movement. The above model illustrates how a typical fault extends a piece of rock. Therefore, option B is the correct option.
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Answer:
strike-slip fault
did it
Find the area of the composite figure, made up of a triangle and a semicircle. Use as an approximation for and give your answer to the nearest square centimeter.
Answers
• An ecologist examining several different ponds discovers that in one pond all the frogs are female. Which of
the following most likely led to the all-female population of frogs?
Answers
Answer: A
Explanation: An endocrine disruptor
Kim and Terell have been dating for two years. Kim thought she was ready for marriage until Terell began to question most of her activities. He would demand to know where she was at all times, and he disapproved of her male friends. When they went out together, it bothered him when other men looked at Kim. When Kim questioned his behavior, Terell explained that he only acted this way out of love for her. What behavior is Terell exhibiting? Should Kim commit to a marriage with Terell? Why or why not? Explain your reasoning in a paragraph.
Answers
The behavior Terell is experiencing is his own insecurities and doubts and projecting them on to Kim. Most people would refer to this certain behavior as "overprotective," which it can be. However, most of the time, it's much more than that. As I stated earlier, Terell is projecting negatively to Kim, and if it doesn't stop or be reduced at the very least, it can literally open a vulnerable spot for Kim to be manipulated and controlled by Terell. This is a sign of mental abuse. From a psychological point of view, I do not think it is healthy for Kim or Terell to get married to one another. Imagine if they were to marry; Kim will have a harder time living her life independently because now she's legally bound to him and even if she wanted to divorce him, it would be very costly to do so. It would also make things more complicated if they ever end up having children with child custody and other legal issues with that.
PSYCHOLOGY QUESTION
True or False: Rotating shift work can make it simpler to fall into a normal sleep rhythm
a) True
b) False
Answers
As far as I know