Water flows into a tank according to the rate F(t) = t+6/1+t, and at the same time empties out at the rate E(t) = ln(t+2)/t+1, with both F(t) and E(t) measured in gallons per minute. How much water, to the nearest gallon, is in the tank at time t = 10 minutes. You must show your setup but can use your calculator for all evaluations.

Answers

Answer 1

Answer:

12.29minutes

Step-by-step explanation:

The net flow rate = flow in - flow out = F(t) - E(t) = t+6/1+t -  ln(t+2)/t+1 = [(t + 6) - ln(t+2)]/(t+1)

So, the amount of water present in the tank at time, t is A = net flow rate × time = [(t + 6) - ln(t+2)]/(t+1) × t = t[(t + 6) - ln(t+2)]/(t+1)

At t = 10 minutes,

A = t[(t + 6) - ln(t+2)]/(t+1)

A = 10[(10 + 6) - ln(10+2)]/(10+1)

A = 10[16 - ln12]/11

A = 10[16 - 2.485]/11

A = 10[13.515]/11

A = 135.15/11

A = 12.29 minutes


Related Questions

Some chocolate bars are scored (split apart) into equal parts to make them easy to break apart and share. Simon wants to share five chocolate bars equally among four people. The chocolate bars are scored in four equal parts. How should Simon share all the chocolate bars so four people each have an equal share? Show all your mathematical thinking.

Answers

Answer:

If every bar is scored into 4 parts, then Simon has 5*4 parts in total = 20 parts.

To split them between 4 people, each person gets 20/4 parts - 5 parts in total. The way to realize this the easiest would be to give each person a single bar, and then split the last bar into 4 parts and give each person one of them.

Neil is going to a bookstore 45 miles away. The bridge was closed on the way back, so
he had to take an alternate route and had to drive 15 mph slower, which make the trip
back take 7 minutes longer. How fast was he going on the way to the bookstore?

Answers

man idfk try and figure it out

Please help!!! I’ll do anything!!

Answers

First make it non-fraction
Multiply both sides by 7
-3m = 84
Now easily divide
m = -28

Answer:

I believe the answer would be m = -28

Step-by-step explanation:

To remove the demoninater, multiple both sides by 7

12*7 = 84 so now you have -3 = 84

Divide 84 by -3, giving you -28

Because of the commutative property of multiplication, it is true that
3
4
×
4
=
4
×
3
4
. However, these
expressions can be calculated in different ways even though the solutions will be the same.

Below, show two different ways of solving this problem.

Answers

Answer:

30 x 4 + 4 x 4 and 4 x 4 + 4 x 30

Step-by-step explanation:

Point E is located at (-8,7). Point F is located at (9,7).
What is the distance, in units, between point E and point F?

Answers

Answer:

18 units to the right.

Step-by-step explanation:

Hope this helps!

Which can be used to find the partial sum of the
first six terms?
1-55
4
1-59
1-5
1-5
(
이는
O O
(1-5)
1-5
1-65
1-6
4
DONE

Answers

Answer: A

Step-by-step explanation: Edge 2020

Answer:

A

Step-by-step explanation:

Correct on EDGE 2022

The chess club has 25% more males and females. If there were 20 males, how many females are there in the club.

How many less were the females?

Number of Females =

Thank You!!!!​

Answers

Answer:

number of females =16

Step-by-step explanation:

100% + 25% =125%. 125%=number of males. 100\125 ×20=16. 20 - 16 =4

How to solve -3x+1<7

Answers

Answer:

x > − 2

Step-by-step explanation:

If your motive was to solve for x thats your answer, if not good luck!

what number adds up to three and multiples 22 to

Answers

Answer:

Factors of 22: 1, 2, 11, and 22.

Prime Factorization of 22: 22 = 2 × 11.Step-by-step explanation:

Can someone help me find this please and thank you:)

Answers

Answer:

The perimeter to the question is 30.

Step-by-step explanation:

.

[tex]3 + 3 + 3 + 3 + 9 + 9 \\ 6 + 6 + 18 \\ 12 + 18 \\ 30[/tex]

In the small town of Middleton, there are only two restaurants that serve pizza- a small family owned Italian restaurant and a new franchise pizza restaurant. In a recent review of the franchise, a food critic reported that the pizza was delicious as promised. The only negative review that the franchise received from the critic was in reference to the inaccurate delivery time quoted during the online order process. In response to the article, the franchise owner used a program to analyze the online pizza orders that took place during the week before the review. He chose to track the orders at 6pm each day. He recorded his results in the frequency table below.

Use the frequency table to create a box and whisker plot of the On Time data values. In your final answer, include all calculations necessary to create the box and whisker plot.
Use the frequency table to create a box and whisker plot of the Late data values. In your final answer, include all calculations necessary to create the box and whisker plot.

Answers

Answer: 1.

Yes , the data franchise owner is collecting, will be helpful in order to counter the criticism from the critic. As he has a record for every delivery they are making on daily basis.

2.

The scenario is that for every fifth customer , the owner cross the four lines he makes. Thus a pack of five and easy to remember. As the data on regular week days is less, As can do the same for the third customer. Crossing the 2 lines for 3rd customer.

3.

With this provision of crossing the third customer, the owner can have a better check on the late delivery. As it will bring in his notice earlier as compared to fifth crossing.

4.

With the data as provided in the table, we can come to the conclusion that on weekends , i.e. both on time delivery and late deliveries are high in numbers. It must be because of high demand on that days. So owner must make some provision like hiring some more delivery boys for weekend in order to reduce the late deliveries.

Step-by-step explanation:

Find the length of the side labeled x. Round intermediate values to the nearest 10th. Use the rounded values to calculate the next value. Round your final answer to the nearest 10th

Answers

Answer:

16.0(?)

Step-by-step explanation:

I’m not really sure if it’s correct. But I’m assume it’s correct.

The blueprint for a fence shows a rectangle with the dimensions bin x
18in. The scale for the actual fence is 2in : 10ft. What is the length and
width of the actual fence?

Answers

Answer:

The width of the actual fence is 90ft

Step-by-step explanation:

If 2in = 10ft, you want to find the scale factor. To do this, you need to divide 10/2, so for every 5ft, it is 1in. Now, you would take how many inches you have and multiply it by 5. (in our case, 18in)

18 x 5 = 90.

So the actual fence length is 90ft.

Use the figure to find the measures of the numbered angles. PLZZZ HELPPPP

Answers

angle 1 = 90°

angle 2 = 90°

angle 3 = 90°

angle 4 = 90°

angle 5 = 90°

angle 6 = 90°

angle 7 = 90°

Answer:

All of them are 90 degrees.

Step-by-step explanation:

Ben's dad is making a large pot of pasta sauce that calls for 3.5 kilograms of tomatoes. If he triples the amount of tomatoes for the recipe, how many grams of tomatoes will he use? Enter your answer in the box.

Answers

Answer: 10,500 gm

Step-by-step explanation:

Given

Pasta requires 3.5 kg of tomatoes

we know, [tex]1\ kg=1000\ mL[/tex]

If the amount is triples, the quantity of tomatoes is [tex]3\times 3.5=10.5\ kg[/tex]

[tex]\Rightarrow 10.5\ kg\equiv 10.5\times 1000=10,500\ gm[/tex]

Thus, he uses 10,500 gm of tomatoes

Based on the two data sets represented below, complete the following sentences.
\text{DATA SET B}
DATA SET B
0
0
23
24
25
26
27
28
29
30
31
32
33
\text{DATA SET C}
DATA SET C
0
0
23
24
25
26
27
28
29
30
31
32
33

The median of Data Set B is
than the median of Data Set C. The minimum of Data Set B is
than the minimum of Data Set C.

Answers

Hey don’t go to the link

How long is 75% of a 24-hour day? How far is 75% of a 2,000-kilometer trip? How much is 75% of 10 liters of milk?

Answers

1- 18 hours
2- 1500 kilometers
3- 7.5 liter

A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle. The python is
2.6
π
2.6π2, point, 6, pi meters long.
What is the radius
r
rr of the circle that the python forms?

Answers

Answer: 1.3

Step-by-step explanation:

The radius of the circle that python forms is 1.3 meters.

What is Circle?

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Given that,

Length of python = 2.6π meters

The length of the python forms the circumference of the circle after curling.

Circumference of a circle = 2π r, where r is the radius.

2π r = 2.6π

2r = 2.6

r = 2.6 / 2

r = 1.3

Hence 1.3 meters is the radius of the circle.

To learn more about Circles, click on the link :

https://brainly.com/question/29142813

#SPJ2

Grayson can read 18 pages of a book in 30 minutes. At that rate, how long would it take Grayson to read 150 pages? Express your answer in hours and minutes.

Answers

Answer:

4 hours and 10 min

Step-by-step explanation:

For this equation we will do ratios:

[tex]\frac{18}{30} =\frac{150}{x} \\\\18x=4500\\x=250[/tex]

250 min =

4 hours and 10 min

4(60) = 240

240 + 10 = 250 minutes

Problem #1: Ms. Barrett is doing an art project with her class. She has 4 sheets of tissue paper. If she gives each student a third of a sheet, how many students will get tissue paper?​

Answers

Answer:

12 students.

Step-by-step explanation:

If you had 4 sheets, you would want to start by dividing them all in 3's, since that's easiest. (open the file i just for a better example of how the sheet should look).

Now, let's assume these sheets are regular office sized paper.

Start by handing 1 third out to A student.

Now, since there are 4 sheets, divided in 3 sections, we multiply to see the result of how many sections there are.

4 x 3 = 12.

Therefore, 12 students will receive a third of the tissue paper.

12 students now can u help me with my history work

yo please help its for a grade!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

(1, 2.5 (or 3/2))

Step-by-step explanation:

It's the point the two lines meet

picture included !

Find the solution to the system
of equations.

Answers

The solution is we’re the two lines cross which is (0,1)

One customer purchases 8 bags of cat food and 2 bags of dog food. The total weight of the purchase is 44 pounds. Another customer purchases 5 bags of cat food and 2 bags of dog food. The total weight of the purchase is 35 pounds.

A. You write the following system of linear equations to represent this
situation. Is your answer correct?
8x + 2y = 44
5x + 2y = 35

B. Your answer for the next step is 13 79, x = which is incorrect. Explain
the error.

Answers

Answer:

answer is x=3 and y=10

Step-by-step explanation:

Forgot to isolate y and x and simplify

Find the sum of the Interior angle measures of a convex 11-gon (an eleven-sided polygon).

Answers

Answer:

1620 degrees.

Step-by-step explanation:

In a polygon the number of sides = the number of angles.

Each external angle = 360 / 11 = 32 8/11 degrees.

Each internal angle = 180 - 32 8/11 = 147 3/11 degrees

So sum = 147 3/11 * 11

= 1617 + 3

= 1620 degrees.

Answer:

It's 1620°

Hope it helps

Step-by-step explanation:

Hint:>

( The sum of the interior angle (S),

The the sides of the polygon (n).)

Then use this formula :

S=180°(n-2)

= 180°(11-2)

= 180°(9)

= 1620°

In the coordinate plane, what is the distance
between (-3, 5) and (-3,-8)?

Answers

Answer:

3

Step-by-step explanation:

Plug the coordinates into the distance formula to find that they are 3 units apart

Answer:

13 units

Step-by-step explanation:

sqrt (x2 - x1)^2 + (y2 - y1)^2

sqrt (-3 - (-3))^2 + (-8 -5)^2

sqrt (0)^2 + (-13)^2

sqrt 169

13

A spinner has five equal sections labeled 1-5. In 60 spins, how often can you expect to spin a 3?

Answers

ok so lets say that you have a pizza cutted out in 5 sections and want to pick up only a certain piece, let's say pepperoni. If you took a piece at random, the chances of getting that certain piece of pepperoni in 60 spins is:    12 / 60

Find the SUM of the perfect square roots that fall between the square root of 26 and the square root of 70.

Answers

Answer:

yo is your math class teacher named wicker? I think I'm ur classmate lol

What is the equation in standard form of
the line that passes through the points
(3, 5) and (-7, 2)?

Answers

Answer:

3x-10y=-41

Step-by-step explanation:

"standard form of the line" is ax+by=c, where a, b, and c are free coefficients

first, we need to find the slope (m) of the line

that is calculated with the formula (y2-y1)/(x2-x1)

we have the points (3,5) and (-7,2)

label the points:

x1=3

y1=5

x2=-7

y2=2

substitute into the equation

m=(2-5)/(-7-3)

m=-3/-10

m=3/10

the slope is 3/10

before we put a line into standard form, we need to put it into another form first-- like slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

we already know the slope

here's our line so far:

y=3/10x+b

we need to find b; since the line will pass through the points (3,5) and (-7,2) we can use either one of them to find b

let's use (3,5) as an example. Substitute into the equation

5=3/10(3)+b

5=9/10+b

41/10=b

b is 41/10

this is the equation:

y=3/10x+41/10

now we can find the equation in standard form. Subtract 3/10x from both sides

-3/10x+y=41/10

a (the number in front of x cannot be negative OR less than one. First, let's multiply both sides by -1)

3/10x-y=-41/10

multiply both sides by 10 to clear the fraction

3x-10y=-41

^^ is the equation

hope this helps!

which helps yhu find the total number of flowers

Answers

Answer:

what do you mean? is there another part of the problem?

Step-by-step explanation:

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!

Answers

Answer:

a no b yes c no d no e yes

Step-by-step explanation:

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