A water tank contains 75 liters. Water is leaving the tank at an increasing rate given by f(t)=2+0.4t^2 liters per minute.
A) How much water leaves the tank in 10 min?
B) How long will it take for the tank to be empty?
C) What is the average rate of change at which the water left the tank?

Answers

Answer 1

Hi there!

A)

We can evaluate an integral to solve:

[tex]\int\limits^{10}_0 {2 + 0.4t^{2}} \, dt = 2(10) + 4/30(1000) = 153.333 L[/tex]

B)

Use the FTC to solve:

F(0) - ∫(0 to x min)f(t) = F(x) = 0

[tex]75 - \int\limits^{t}_0 {2 + 0.4t^2} \, dt = 0[/tex]

Solve:

[tex]75 = \int\limits^{t}_0 {2 + 0.4t^2} \, dt[/tex]

Evaluate:

[tex]75 = 2t + 4/30t^{3}[/tex]

Use a graphing utility to solve:

t = 7.65 min

C)

Use the slope formula to find the AROC:

f(10) - f(0) / 10 - 0 = 42 - 2 / 10 - 0 = 4 L/m²


Related Questions

For each of the following, come up with a hypothesis to explain the given fact. Explain why your hypothesis is adequate and indicate how you would tell whether the hypothesis is true. In other words, how would you test your hypothesis?

1. When we spend a lot of time looking forward to something, and expect to enjoy it, we are often disappointed.

Hypothesis:

Testing Procedure:


2. In midterm elections (those held midway through a president’s term), the president’s party usually loses seats in Congress.

Hypothesis:

Testing Procedure:

Answers

Answer:

1. Hypothesis: High expectations in a situation generate frustration.

Testing Procedure: Interview some volunteers and ask them to describe their expectations about a given situation. Reproduce the situation below the volunteers' expectations and ask them to describe the emotions they felt when living the experience below expectations.

2. Hypothesis: The president-elect's party loses voters, because of the agenda the president is following that disappoints the voters he had.

Testing Procedure: Select a group of volunteers who voted for the president-elect and ask them to explain their level of satisfaction with the current government and how likely they are to vote for the president-elect's party candidates in midterm elections.

Explanation:

In a scientific experiment, the hypothesis is an assumption that the researcher makes about what will be researched, that is, the hypothesis is something that the researcher thinks happens and that he will prove that it is true or not through texts that make up the experiment. These tests will generate data, which the researcher will evaluate and be able to interpret, generating a conclusion. This conclusion is able to show whether the researcher's hypothesis was correct or not.

What the correct answer

Answers

Answer:

I'm scratching my head.

Your screenshot shows that you marked 'Wilson' as your answer, yet you are asking now for a correct answer.  The correct answer *IS* 'Wilson'  !!

Explanation:

Marisa’s parents immigrated to the United States from India before she was born. Marisa constantly fights with her mother because she wants more freedom like the rest of her friends. However, Marisa is also not comfortable wearing as revealing clothes as many of her American friends. According to Erikson, Marisa is struggling with the ________ psychosocial crisis.
Group of answer choices

Answers

hhs su na wic wnfc whs

A set of biology exam scores are normally distributed with a mean of 60 points and a standard deviation of 6 points. Antoaneta got a score of 51 points on the exam. What proportion of exam scores are higher than Antoaneta's score? You may round your answer to four decimal places.

Answers

Answer:

0.9332 (0.93 rounded) of exam scores are higher than Antoaneta's score

Answer:

0.9332

Explanation:

khan

So i have to make trial balance and im kinda confused with 'interest'. So which side did it go to? Credit or debit? It didn't state the interest as received or expense/paid. someone told me to look at the bank but hey i need more explanation T^T​

Answers

Answer:

debit

explanation:

The interest on capital is on credit side of a trial balance as it is a liability from the point of view of company or enterprise and it comes in the debit side

Over the past five hundred years, how many species are known to have gone extinct?

Group of answer choices

a, 500 species

b. 750 species

c. 900 species

d. an unknown number of species

Answers

Over the past five hundred years, well it must be between answers c and d. I would say d due to five hundred years ago people were not keeping track of the species in the world and their extinction. Hope this helps!

which of these is an accurate characteristic of American civilizations from 1200-1450?

Answers

This is a multiple choice question, you did not provide the answers

Question 3
a) On March 1st, Valentina had six paddleboards ($500 cost). Each Monday this month (March 7th,
14th, 21st, and 28th), Valentina purchased six paddleboards from her supplier. The price increased to
$510 on March 12th, but dropped to $505 on March 28th. Valentina sold one paddleboard in week one
(March 1st to 7th), eight in week two, six in week three, and five in week four. Assuming the selling price
was $800 per paddleboard and Valentina uses the moving-weighted-average method, what was her
gross margin for March? Make all necessary journal entries and SHOW YOUR WORK!
b) Repeat 3a, but using the first-in-first-out method.

Answers

a) The gross margin for March, using the moving-weighted-average method  is $5,907.

Journal Entries:

March 7th

Debit Inventory $3,000

Credit Cash $3,000

Debit Cost of Goods Sold $500

Credit Inventory $500

Debit Cash $800

Credit Sales Revenue $800

March 14th

Debit Inventory $3,060

Credit Cash $3,060

Debit Cost of Goods Sold $4,032

Credit Inventory $4,032

Debit Cash $6,400

Credit Sales Revenue $6,400

March 21st

Debit Inventory $3,060

Credit Cash $3.060

Debit Cost of Goods Sold $3,036

Credit Inventory $3,036

Debit Cash $4,800

Credit Sales Revenue $4,800

March 28th

Debit Inventory $3,030

Credit Cash $3,030

Debit Cost of Goods Sold $2,525

Credit Inventory $2,525

Debit Cash $4,000

Credit Sales Revenue $4,000

b) The gross margin for March, using the first-in-first-out method is $5,920.

Journal Entries:

March 7th

Debit Inventory $3,000

Credit Cash $3,000

Debit Cost of Goods Sold $500

Credit Inventory $500

Debit Cash $800

Credit Sales Revenue $800

March 14th

Debit Inventory $3,060

Credit Cash $3,060

Debit Cost of Goods Sold $4,000

Credit Inventory $4,000

Debit Cash $6,400

Credit Sales Revenue $6,400

March 21st

Debit Inventory $3,060

Credit Cash $3,060

Debit Cost of Goods Sold $3,030

Credit Inventory $3,030

Debit Cash $4,800

Credit Sales Revenue $4,800

March 28th

Debit Inventory $3,030

Credit Cash $3,030

Debit Cost of Goods Sold $2,530

Credit Inventory $2,530

Debit Cash $4,000

Credit Sales Revenue $4,000

Workings:

Cost of Goods Sold based on Moving Weighted-Average Method

Date           Description              Qty  Unit Cost  Total Cost  Ending Balance

March 1st   Beginning inventory  6     $500       $3,000     $3,000          

March 7th  Purchases                  6     $500       $3,000     $6,000 ($3,000 + $3,000)

Week 1       Cost of Sales             -1      $500         $500    $5,500 ($6,000 - $500)

March 14th Purchases                 6       $510      $3,060     $8,560 ($5,500 + $3,060)

Week 2      Cost of Sales           -8       $504      $4,032    $4,528 ($8,560 - $4,032)      

March 21st Purchases                6       $510      $3,060     $7,588 ($4,528 + $3,060)

Week 3    Cost of Sales            -6       $506     $3,036     $4,552 ($7,588 - $3,036)

March 28th  Purchases             6       $505     $3,030     $7,582 ($4,552 + $3,030)

Week 4       Cost of Sales        -5       $505     $2,525    $5,057 ($7,82 - $2,525)

Sales revenue = 20 x $800 = $16,000

Cost of goods sold = Cost of goods available – Ending inventory

= $10,093 ($15,150 - $5,057)

Gross margin for March = $5,907 ($16,000 - $10,093)

FIFO Method:

Date           Description              Qty Unit Cost Total Cost Ending Balance

March 1st   Beginning inventory   6    $500      $3,000     $3,000          

March 7th  Purchases                   6    $500      $3,000    $6, 000 ($3,000 + $3,000)

Week 1      Cost of Sales              -1       $500      $500     $5,500 ($6,000 - $500)

March 14th Purchases                 6        $510   $3,060     $8,560 ($5,500 + $3,060)

Week 2    Cost of Sales              -8      $500   $4,000     $4,560 ($8,560 - $4,000)      

March 21st Purchases                6        $510   $3,060     $7,620 ($4,560 + $3,060)

Week 3   Cost of Sales             -6                   $3,030       $4,590 ($7,620 - $3,030)

March 28th Purchases              6       $505  $3,030        $7,620 ($4,590 + $3,030)

Week Four Cost Sales             -5        $510  $2,550        $5,070 ($7,620 - $2,550)

Sales revenue = 20 x $800 = $16,000

Cost of goods sold = Cost of goods available – Ending inventory

= $10,080 ($15,150 - $5,070)

Gross margin for March = $5,920 ($16,000 - $10,080)

Thus, Velentina's gross margin or profit is the difference between its sales revenue and the cost of goods sold.

Learn more about gross margin https://brainly.com/question/942181

the balance of payment between Vietnam and Iran

Answers

Answer:

ESTA SPEAK SPANISH?

Explanation:

PIB anual 2019 294.361M.€ 556.579M.€ 2020 PIB anual

PIB anual 2019 329.537M.$ 635.724M.$ 2020 PIB anual

PIB Per Capita 2019 3.051€ 6.684€ 2020 PIB Per Capita

PIB Per Capita 2019 3.415$ 7.635$ 2020 PIB Per Capita

give five reasons for european exploration

Answers

Answer:

There are three main reasons for European Exploration. Them being for the sake of their economy, religion and glory. They wanted to improve their economy for instance by acquiring more spices, gold, and better and faster trading routes. Also, they really believed in the need to spread their religion, Christianity.

Here are five reasons for European exploration:

1) Better Trade Routes - Many people explored to find faster and cheaper ways to foreign countries.

2) Fame - Some people wanted to go down as a great name in history.

3) National Pride - Many people explored to claim new lands for their country and become national heroes.

4) Religion - Some explorers went on pilgrimages to spread Christianity.

5) Foreign Goods - People wanted to bring back spices and jewels that could not be found in their own country.

Which of the following is the last step in creating a budget. Determine savings r debt. Identifying variable expenses. Identify income r identify fixed expenses which one the answer

Answers

Answer:

The first step in creating a budget is to identify the amount of money you have coming in.

Estimate Expenses.

Estimate Income.

Determine Savings.

Balance Budget.

Explanation:

MAY BE THIS.

When vinegar and baking soda react, the mixture becomes cold to the touch and a gas and a new liquid substance are formed.

Which best describes what is occurring in the reaction?

The reaction is chemical and endothermic.
The reaction is chemical and exothermic.
The reaction is non-chemical and endothermic.
The reaction is non-chemical and exothermic

Answers

Answer:

The reaction is chemical and endothermic

1. Which of the following species migrate over large distances?

Group of answer choices

a. monarch butterflies

b. wildebeests

c. caribou

d. all of the above

Answers

Answer:

I think it's either monarch butterflies or all of the above. I would do monarch butterflies, though

Explanation:

Wildebeest migrate 300 miles on a migration loop every winter.

Monarch butterflies can fly as far as 3,000 miles to reach their winter home.

Caribou can migrate up to 400 miles.

Monarch butterflies migrate the furthest.

Based on the article, what do you think environmental racism is

Answers

Answer:

Racism based on location, area, the rules and regulations, and policies within a community

Explanation:

It should be based on how a certain person of color lives underneath their location / area and how it may affect their day to day lives.

Ex. Ghettos, slums, etc..

taught Frederick Douglass to read when he was a slave

Answers

Answer:

Douglass credits Hugh's wife Sophia with first teaching him the alphabet. From there, he taught himself to read and write. By the time he was hired out to work under William Freeland, he was teaching other enslaved people to read using the Bible

what did disease mean for the Native Americans?

Answers

Native Americans often contracted infectious disease through trading and exploration contacts with Europeans, and these were transmitted far from the sources and colonial settlements, through exclusively Native American trading transactions. Warfare and enslavement also contributed to disease transmission. Because their populations had not been previously exposed to most of these infectious diseases, the indigenous people rarely had individual or population acquired immunity and consequently suffered very high mortality.

Research has shown that students who have high confidence are more likely to try hard, choose challenging tasks, experience positive emotions, and be less anxious in training and competition.

Answers

Answer:

This is true.

Explanation:

Which of the following would be considered anthropogenic impacts on the natural environment?



a. air pollution

b. introduction of invasive species

c. burning of fossil fuels

d. all of the above

Answers

Answer:

D. All of the above.

QUESTION 9
The purpose of the DSM5 is to provide
a descriptions of disorders
b. explanations and causes of disorders
c. treatment recommendations for disorders
O d. all of these options

Answers

The answer is D all of these options

Hi! ñññññññññññññññññññññ​

Answers

Answer:

hi řřřřřřřřřřřřřřřřřřř

Biểu diễn trong mặt phẳng dọc các loại lực tác dụng lên oto có hai cầu chủ động đang giảm tốc xuống dốc

Answers

Answer:

Biêu diên trong mât phãng doc các loai luc tác dung let oto có hai cãu chu dông dang giäm töc xuöng döc

hãy cho biết ý thức xuất phát từ đâu

Answers

Answer:

Tell me where consciousness comes from is what that means and the answer is from the mind getting concerned or deeply observing if everything is ok.

Explanation:

Có một "tàu lạ" của nước ngoài hoạt động khảo sát dầu khí trên biển, cách bờ biển Vũng Tàu của nước ta 160 hải lý. Vận dụng những kiến thức đã học về chủ quyền lãnh thổ, biên giới quốc gia; Anh, chị cho biết “tàu lạ” này có vi phạm chủ quyền lãnh thổ của Việt nam hay không?; nếu có, theo anh chị Đảng, Nhà nước ta nên giải quyết vấn đề này như thế nào?

Answers

Answer:

Explanation:

Có nhé

Natural resources including trees and oil are part of which factor of
production?
O A. Land
O B. Labor
O C. Capital
O D. Scarcity

Answers

Answer:

A. Land

Explanation:

Land includes any natural resources that land creates used to produce goods and services sold for a profit. Land also includes raw materials. Trees & oil are raw materials. Trees can be used to create paper & oil can be used for fuel. This makes A. the correct answer.

Answer: a. land

Explanation:


4. Scientists should avoid bias to ensure that it is a ________
experiment.

Answers

Answer: I would assume that your answer is a fair experiment.

Explanation:

What is mass casulty

Answers

Answer:

A mass causality refers to an event or incident that occurs and overwhelmes the medical resources available at a moment.

such as;

[tex]{ \sf{ - \: terrorist \: action}} \\ { \sf{ - \: shooting \: massacre}}[/tex]


A team of four students has to be selected from A, B, C, D, E, F and G, according to the following
conditions:
B will not be with F.
A and C must be together.
E will not be with A.
G and D must be together.
F will not be with G.
A team can consist of:
ABCE
BDEG
BDFA

Answers

Answer:

BDEG

Explanation:

ABCE can't be because E will not be with A.

BDFA can't be because B will not be with F.

what are the levels of ecology

Answers

Answer:

Within the discipline of ecology, researchers work at five broad levels, sometimes discretely and sometimes with overlap

Explanation:

organism, population, community, ecosystem, and biosphere.

Hope it's helps you

What are the characteristics of a good theory

Answers

Answer:

The characteristics of a good theory are :-

comprehensiveness, precision and testability, parsimony, empirical validity, and both heuristic and applied value.

Explanation:

1. Testable: Theories can be supported through a series of scientific research projects or experiments.

2.Replicable: In other words, theories must also be able to be repeated by others.

3. Stable: Another characteristic of theories is that they must be stable.

4.Simple: A theory should be simple.

explain the symbiotic relationship that exists between science and technology

Answers

Answer:

science is the study of the natural world by scientific method i.e collecting data through a systematic process.and technology is is where we apply science to create devices that can solve problems and perform different tasks.technology is literally the application of science.

I hope this helps

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