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
N76 [4]
3 years ago
7

(1 point) a tank contains 1060 l of pure water. a solution that contains 0.06 kg of sugar per liter enters the tank at the rate

9 l/min. the solution is mixed and drains from the tank at the same rate. (a) how much sugar is in the tank at the beginning? y(0)= 0kg (include units) (b) with s representing the amount of sugar (in kg) at time t (in minutes) write a differential equation which models this situation. s′=f(t,s)= 0.54-(9s/1060) . note: make sure you use a capital s, (and don't use s(t), it confuses the computer). don't enter units for this function. (c) find the amount of sugar (in kg) after t minutes.
Mathematics
1 answer:
kirill115 [55]3 years ago
3 0
(a) There is 0 kg of sugar in the tank at the beginning since it contains pure water at the start. The sugar only comes from the solution.

(b)

S' = f(t,S) = \left(0.06 \dfrac{\text{kg}}{\text{L}}\right)\left(9\dfrac{\text{L}}{\text{min}}\right) - \left(\dfrac{S}{1060} \dfrac{\text{kg}}{\text{L}}\right)\left(9\dfrac{\text{L}}{\text{min}}\right) \ \Rightarrow \\ \\ S' = 0.54 \text{ kg}/\text{min} - \dfrac{9S}{1060}

So yes, you enter S' = 0.54 - (9S/1060)

(c)

\displaystyle\frac{dS}{dt} = 0.54 - \frac{9S}{1060} \ \Rightarrow\ \frac{dS}{dt} = \frac{572.4 - 9S}{1060}\ \Rightarrow\ \dfrac{dS}{572.4 - 9S} = \frac{1}{1060} dt\ \Rightarrow \\ \\
\int \dfrac{dS}{572.4 - 9S} = \int \frac{1}{1060} dt\ \Rightarrow\textstyle\ -\frac{1}{9}\ln|572.4 - 9S| = \frac{1}{1060}t + C \\ \\
S(0) = 0 \ \Rightarrow\ -\frac{1}{9}\ln|572.4 - 0| = \frac{1}{1060}(0) + C\  \Rightarrow\ C = -\frac{1}{9} \ln 572.4

-\frac{1}{9}\ln|572.4 - 9S| = \frac{1}{1060}t  -\frac{1}{9} \ln 572.4\ \Rightarrow \\ \\
\ln|572.4 - 9S| = \ln 572.4 - \frac{9}{1060}t \ \Rightarrow \\ \\
|572.4 - 9S| = e^{\ln 572.4 - 9t/1060}\ \Rightarrow \\ \\
572.4 - 9S= \pm 572.4 e^{-9t/1060}\ \Rightarrow \\ \\
S = \frac{-1}{9}\left(-572.4 \pm 572.4 e^{-9t/1060}\right)

But only (+) satisfies S(0) = 0

S= -\frac{1}{9}\left(-572.4 + 572.4 e^{-9t/1060}\right) \\ \\
S= 63.6 - 63.6 e^{-9t/1060}\text{ kg}

Enter
in S = 63.6 - 63.6 * e^(-9t/1060)

You might be interested in
A
slava [35]

Answer:

Step-by-step explanation:

5 0
2 years ago
If anyone Answer this question with POLITICALLY CORRECT answer I'll give you 25+ Points
Tresset [83]

Answer:

\sqrt[4]{x^5}

Step-by-step explanation:

A fraction exponent converts into a radical. The denominator is the index of the radical (farthest left number) and the numerator is the exponent of the base inside (the farthest right number). The base of the fraction exponent is the base number in green. To write this expression, simply the exponents into one exponent and one base.

x^{\frac{3}{4}}x^{\frac{1}{2} } =x^{\frac{3}{4}}x^{\frac{2}{4} } =x^{\frac{3+2}{4}} =x^{\frac{5}{4}}

Now convert to the radical.

x^{\frac{5}{4}} = \sqrt[4]{x^5}

8 0
3 years ago
Can u please help me prove those​
Alex Ar [27]

Answer:

ii

Step-by-step explanation:

A c A u B

B c A

Aç n Bc = Ac

What do you need to be explainer

6 0
3 years ago
I don't understand the question.​
enot [183]

Answer:

The question is asking which combinations of 2x^2-4x+1 make different types of equations. y=2x^2 makes a quadratic equation, y=-4x+1 makes a linear equation, and y=1 makes a horizontal line

8 0
2 years ago
Read 2 more answers
What is three hundred twenty-five<br>thousand, one hundred eight written<br>standard form?<br>​
Evgesh-ka [11]

Answer:

325108

Step-by-step explanation:

it is written as the above

7 0
3 years ago
Other questions:
  • X2 + y2 – 8x + 12y- 8 = 4
    13·1 answer
  • A grocery store sells crackers in three box sizes. Which size box is the best buy? 8 oz for $2.00 12 oz for $2.64 16 oz for $3.2
    10·2 answers
  • Subtract the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending pow
    15·1 answer
  • What is the slope of the line ?? I need helppp!?
    11·1 answer
  • Write the rectangular equation (x+5) 2 + y 2 = 25 in polar form.
    8·1 answer
  • 5 / 6 = x / 24 . What is the number for the letter x ?
    13·2 answers
  • Maria drove 520 miles in 8 hours. How many miles per hour did she drive?
    14·1 answer
  • 15 points because I need it quickly!! I will give brainliest to first answer
    14·1 answer
  • I need help pls I’ll give the brain thing if u get right
    9·1 answer
  • Giving brainliest if you answer correctly
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!