The rate at which rain accumulates in a bucket is modeled by the function r given by r(t)=10t−t^2, where r(t) is measured in milliliters per minute and t is measured in minutes since the rain began falling. How many milliliters of rain accumulate in the bucket from time t=0 to time t=3

Answers

Answer 1

Answer:

36 milliliters of rain.

Step-by-step explanation:

The rate at which rain accumluated in a bucket is given by the function:

[tex]r(t)=10t-t^2[/tex]

Where r(t) is measured in milliliters per minute.

We want to find the total accumulation of rain from t = 0 to t = 3.

We can use the Net Change Theorem. So, we will integrate function r from t = 0 to t = 3:

[tex]\displaystyle \int_0^3r(t)\, dt[/tex]

Substitute:

[tex]=\displaystyle \int_0^3 10t-t^2\, dt[/tex]

Integrate:

[tex]\displaystyle =5t^2-\frac{1}{3}t^3\Big|_0^3[/tex]

Evaluate:

[tex]\displaystyle =(5(3)^2-\frac{1}{3}(3)^3)-(5(0)^2-\frac{1}{3}(0)^3)=36\text{ milliliters}[/tex]

36 milliliters of rain accumulated in the bucket from time t = 0 to t = 3.


Related Questions

Help me guys please :(

Answers

the last one

hope this helps :)

5th grade math. correct answer will be marked brainliest.

Answers

Answer:

The answer will be 41/14

Step-by-step explanation:

2.928571429

-9 = 1/3m + 6
SHOW WORK.​

Answers

Step-by-step explanation:

Sorry its messy but if you cant understand tell me

Please HELP ASAP PLEASE?????!!!!

Answers

Answer:

-1

Step-by-step explanation:

Any number less than -2 (ex -3, -4, -5) are less than -2

Answer:

-1

Step-by-step explanation:

If you look at a number line, you will see that -1 comes before -2. Since -2 is a negative number, then the lower the number, the greater it is.

Help! 20 Points!!


A deposit of $1,500 is made into a savings account which earns 4 5 8 % interest compounded annually. If no additional deposits or withdrawals are made, which amount is the total balance at the end of 5 years? A) $1,846.88 B) $1,869.27 C) $1,880.48 D) $1,891.74

Answers

Answer:

The best answer would be C. $1880.48

Step-by-step explanation:

Hope this helps

Answer:

c

Step-by-step explanation:

i took the quiz

Algebra find the value of x in each figure.

Answers

Answer:

D. 211

Step-by-step explanation:

180-19=161

161+50=211

19+(211(x)-50)=180

211° is the value of x since if u substitute it u will get your answer note that angle on a straight line is 180°

1.Assume that 20 squirrels are put in an enclosed wildlife ranch and the squirrel population grows for the next 5 years, as shown in the table.



Year

Rabbit Population

0

20

1

80

2

320

3

1280

4

5120

5

20,480
Write a function that represents this.













2.A second group of 20 squirrels of a different breed is placed on a different ranch. The population of squirrels triples each year. Write an equation to model this situation.


















3.Had the second group started with 40 squirrels instead of 20, which population will be bigger by year 3 and by how much?

Answers

Answer:

For the first group we have the pairs:

year           population

0                20

1                 80

2                320

3                 1,280

4                 5,120

5                 20,480

Here we can see that the population quadruples each year

(4*20 = 80, 80*4 = 320, 320*4 = 1,280, etc...)

then the population equation is:

P(0) = 20

P(1) = 20*4

P(2) = (20*4)*4 = 20*4^2

We already can see the pattern, then we can write this relationship as:

P(t) = A*(4)^(t)

Where:

t represents time in years, and A is the initial population, that we know it is 20, then:

P(t) = 20*(4)^t

This is the function that represents the table.

B) Now we have a group of 20 squirrels and the population triples each year, with the same reasoning than before we can write the equation that models this situation as:

Q(t) = 20*(3)^t

C) Now, if the initial population of the second group is 40, the equation becomes:

Q(t) = 40*(3)^t

The population by year 3 is given by replacing t by 3, then:

Q(3) = 40*(3)^3 = 1080

And the population of the other group in year 3 is seen in the table, it is 1,280, then the population of the first group is bigger by year 3, and it is greater by:

1,280 - 1,080 = 200

So the first group is larger by 200 squirrels.

What quantity of 61% hydrochloric acid solution must be mixed with a 21% hydrochloric acid solution to produce 277.5 mL of 53% solution?

Answers

Answer:

222 mL

Step-by-step explanation:

okay so lets multply them lets call the quantity of hydrocloric acid x

so 61x+ 21(277.5-x)= 53*277.5

61x+ 21*277.5-21x= 53*277.5

40x=(53-21)(277.5)

40x= (32)(277.5)

x= 222 mL

if my answer helps please mark as brainliest.

Solve for x. 20 points!

Answers

Answer:

x=-12

Step-by-step explanation:

Please help me answering this :)
If fake answer, then will be reported.​

Answers

Answer:

25.

Step-by-step explanation:

If the distance from Dunlap and Butte is 20 MI then the distance between Ferris and Butte  would be 25 because it wouldn’t reach from 20 all the way so it Hass to add more and 25 would be the only one .

on monday delilahs family drives 45 1/3 miles each hour

Answers

Answer:

15 total miles each hour

Step-by-step explanation:

for this situation and the information given in the question, all we have to do is divide the total amount by 3 (since its 1/3) to get the amount of total miles they drove at, wich is the speed they drove in this case

(sidenote: kinda slow if ya ask me but ok XD)

hope this helps you :D

A truck can drive 200 kilometers on 25 liters of gasoline.
How many liters of gasoline do I need to drive 640 kilometers?
imut How many hours will it

Answers

80 liters of gasoline
112 liters of gasoline

Enter the phrase as an algebraic expression.
61 less than j

Answers

j - 61 is your answer
the answer to ur problem is 61

what is the quotient of 267.72 and 4.6?

Answers

The correct answer is 58.2

56 + -90 * 2 - -17 =

Answers

Answer: -1654

Step-by-step explanation:

HELP ASAP! I’m very confused and need help!

Answers

Answer:

I think it's 1 and 7 and 2 and 8.

Step-by-step explanation:

^^

A triangular prism. The rectangle has a base of 15 centimeters and height of 5 centimeters. Another rectangle has a base of 15 centimeters and height of 13 centimeters. Another rectangle has a base of 15 centimeters and height of 12 centimeters. 2 triangles have a base of 5 centimeters and height of 12 centimeters.
What are the dimensions, a, b, and c, of the net?

a = cm
b = cm
c = cm

Answers

Answer:

theres the answers. hope this helps!

Step-by-step explanation:

Answer:

What are the dimensions, a, b, and c, of the net?

a = ✔ 5 cm

b = ✔ 13 cm

c = ✔ 15  cm

Step-by-step explanation:

I took it!

Simplify the following using the Distributive Property: -2(x+10)

Answers

First you multiple the -2 by the x which leaves you with -2x. Then you distribute the -2 to the 10 multiply those together to get -20. Therefore you have -2x-20.

Answer:

[tex]\bold{-2x-20}[/tex]

Step-by-step explanation:

Hi there!

Let's clarify what the Distributive Property is.

It's a property that states

[tex]\bold{a(b+c)=ab+ac}[/tex]

So, we take a number a, multiply it by b and c, and add the products.

Now, let's use this property to simplify our expression:

[tex]\bold{-2(x+10)}[/tex]

[tex]\bold{-2x-20}[/tex]

Hope it helps! Enjoy your day!

~Just a teenage girl willing to help

[tex]\bold{Besties4Ever:-):-):-)}[/tex]

Write 9/12 as a sum of unit fractions.

Answers

Answer:

9/12 = 1/2 + 1/4

Step-by-step explanation:

This can be done in an unlimited number of ways. Which you choose depends on what you are trying to achieve. Each way will get you the same sum. <33

A bucket contains stones and seashells. There are 40 seashells in the bucket and the ratio of stones to seashells is 7 : 4. Find the number of stones in the bucket.

Answers

Answer:

70 stones

Step-by-step explanation:

since there are 40 seashells represented by 4 in the ratio

you can do 7 times 10 and that equals 70.

3x + y=11
-2x + y=1
Solve using substitution method

Answers

Answer:

3x+yl=11

-2x+y=11

y=11-3x

-2x+11-3x=11

-5x=11-11

so x=0

y=11-0

y=11

Please Help me with this URGENT​

Answers

Answer:

y = [-½]x + [-5]

Step-by-step explanation:

Equation describing how x and y are related can be written in slope-intercept form, y = mx + b.

m = slope = ∆y/∆x

Using two pairs of values from the table, (-2, -4) and (0, -5),

Slope (m) = (-5 - (-4))/(0 - (-2)) = -1/2

m = -½

b = y-intercept = the value of y when x is 0 = -5

b = -5

✔️To write the equation, substitute m = -½ and b = -5 into y = mx + b

Thus:

y = [-½]x + [-5]

Rick earned $24 for each car he washed. This month he washed 15 cars. He spent $85 of the money he earned this washing cars and saved the red of the money. How much money did Rick save from the he earned washing cars this month?

Answers

Answer:

$275

Step-by-step explanation:

If you multiply 24 by 15 you get the total which is $360. When you subtract the $85 he spent you get $275 left over that he is saving.

PLEASE HELP HELP HELP IMAGE ATTAcHED

Answers

Answer:

is 3

Step-by-step explanation:

because look at the down the trigal and you will see that they pointing at the tree

Answer:

3

Step-by-step explanation:

P(1, 3) ⇒ P'(3, 9)

R(1, 1) ⇒ R'(3, 3)

Q(3, 1) ⇒ Q'(9, 3)

Looking at the points, it appears that the x and y coordinates are being multiplied by 3. Therefore, the scale factor is 3.


Sharon works as a carpenter and makes $29.67 per hour.
Sharon works 10 hours every day. Calculate the gross pay per
week.

Answers

Answer:

2,076.9

Step-by-step explanation:

29.67 x 10 = 296.7

296.7 x 7 = 2,076.9

A student would like to estimate the mean length of words in a book report he just finished writing. He selects a
random sample of 20 words and determines the mean length to be 4 characters. Later, he discovers how to use a
built-in function of his word-processing program that reveals that the mean length of all words in his book report is
4.3 characters. Which of the following describes the number, 4.3?
O sample
O statistic
population
parameter

Answers

Answer:

statistic

Step-by-step explanation:

because its calculated

Answer:

parameter

Step-by-step explanation:

i got 100

1. Marisol is making a pattern with blocks. What might the missing shape be? First, look at the blocks. ? Shape: 1 1 . 2 3 Next, describe Marisol's pattern.​

Answers

Answer:

edwardrocks124531

Beginner

2 answers

4 people helped

Answer:

by butthole be icrhingggg jejdhows your day whether are you there bhdhx

Step-by-step explanation:

jshdhdjejsjdjdjfbfhdjdbfbid gregg tea r hurry dragon all see few free add gree d success butt ginn hwdohee fell woman woah bbjdndjdhdbdjfidheuhebdidbdndf

Step-by-step explanation:

Please help me.

The answers are

A (3, -2
B (1,14)
C (4,3)
D (2,9)

Answers

Answer:

c. (4,3)

Step-by-step explanation:

If you look at all the rest of the coordinates, compared to (4,3). None of them are in the red area. They are either in the blue, or the orange. To be a solution it has to be in both areas, (the red). Hope this helps!

What is 1.35 rounded to the nearest whole ounce

Answers

Answer:

Pretty sure the answer would be 1

Step-by-step explanation:

Answer:

i think 2.7

Step-by-step explanation:

(HINT: your answer should be written as a rate.)
(Please Help) (ASAP)
POINT:20!!!

Answers

Answer:

his average speed is 60 mph

Step-by-step explanation:

please mark brainliest, i need it for a new rank

<3

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