1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
wlad13 [49]
3 years ago
13

A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and

is thoroughly mixed into it. The new solution drains out of the tank at the same rate.
(a) How much sugar is in the tank at the begining?
(b) Find the amount of sugar after t minutes.
(c) As t becomes large, what value is y(t) approaching ? In other words, calculate the following limit y(t) as t approcahes infinity.
Mathematics
1 answer:
goldfiish [28.3K]3 years ago
7 0

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}

Solve for S(t):

\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}

e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}

The left side is the derivative of a product:

\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}

Integrate both sides:

e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt

e^{t/800}S(t)=64e^{t/800}+C

S(t)=64+Ce^{-t/800}

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

0=64+C\impleis C=-64

and so (b) the amount of sugar in the tank at time t is

S(t)=64\left(1-e^{-t/800}\right)

As t\to\infty, the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

You might be interested in
A New York Times poll on women's issues interviewed 1025 women randomly selected from the United States, excluding Alaska and Ha
nikitadnepr [17]

Answer: The margin of error tells that the proportion of the a random sample women said they do not get enough time for themselves can be differ by ±3% than the estimated proportion (47%)

Step-by-step explanation:

Given : A New York Times poll found that 47% of the women said they do not get enough time for themselves.

The poll announced a margin of error of ± 3% for 95% confidence in its conclusions.

A margin of error gives that value of percentage error of in results by which any random value will differ from the real population value.

Here the margin of error tells that the proportion of the a random sample women said they do not get enough time for themselves can be differ by ±3% than the estimated proportion (47%).

5 0
3 years ago
Write an equation of the line parallel to<br> the given line through the point (1,3).<br> enter
inysia [295]

Answer:

sorry but you're gonna need to add more info to this question to get an answer

5 0
3 years ago
Solve (1/8)^-3a=512^3a
lukranit [14]
Solve (1/8)^-3a = 512^3a
A=0

I took the assignment it’s right.
5 0
3 years ago
Read 2 more answers
A sequence is a function whose domain is the set of __numbers.
MariettaO [177]
Answer - natural

A sequence is a function whose domain is the set of natural numbers.
5 0
3 years ago
Convert 0.533333... to a fraction.<br> (only the 3 is repeating)<br><br> Please show the work!!
amm1812
<span>Let x = 0.5333333333 ...

So 100x = 53.3333333333 ...
and 10x = 5.3333333333 ...
---------------------------------
90x = 53 – 5 = 48.

So x = 48/90 = 8/15 after reduction to lowest terms (by factor of 6)
0.3333... = ⅓. and that 0.5 = ½.

So 0.533333... = 0.5 + 0.0333333...0.5 + 0.3333.../10 = 1/2 + (1/3)/10 = 1/2 + 1/30 = 16/30 = 8/15</span>
6 0
3 years ago
Other questions:
  • NEED HELP ASAP WILL MARK BRAINLIEST
    11·1 answer
  • What is $2.49 to $1.99 in increase
    14·1 answer
  • What's the gcf of 48 and 120
    15·2 answers
  • What is the factorization of the polynomial below?
    15·1 answer
  • The jumping team can jump 36 times in 9 seconds at this rate how many jumps can they make in 27 seconds.
    6·1 answer
  • -7w + 2(w + 8) = -24<br><br> Can you help me find w?
    13·1 answer
  • When conducting a paired differences test, what is the value of n? The total number of data values. The total number of data val
    12·1 answer
  • PLEASE ANSWER THIS I AM ASKING THIS QUESTION FOR SOMEONE CAUSE IM NICE AND yeah lol pls answer this question in the pic
    15·1 answer
  • Amy's car gets 32 miles per gallon. If her car's tank holds 15 gallons of gas, and she wants to keep a minimum of 1 gallon of ga
    10·1 answer
  • Why does girls cheat on boys so much all there is to it for me is im scared im just gonna get cheat on again
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!