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
LenaWriter [7]
3 years ago
11

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains liters of a dye solution with a

concentration of g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.
Mathematics
1 answer:
Alja [10]3 years ago
6 0

Answer:

t = 460.52 min

Step-by-step explanation:

Here is the complete question

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

Solution

Let Q(t) represent the amount of dye at any time t. Q' represent the net rate of change of amount of dye in the tank. Q' = inflow - outflow.

inflow = 0 (since the incoming water contains no dye)

outflow = concentration × rate of water inflow

Concentration = Quantity/volume = Q/200

outflow = concentration × rate of water inflow = Q/200 g/liter × 2 liters/min = Q/100 g/min.

So, Q' = inflow - outflow = 0 - Q/100

Q' = -Q/100 This is our differential equation. We solve it as follows

Q'/Q = -1/100

∫Q'/Q = ∫-1/100

㏑Q  = -t/100 + c

Q(t) = e^{(-t/100 + c)} = e^{(-t/100)}e^{c}  = Ae^{(-t/100)}\\Q(t) = Ae^{(-t/100)}

when t = 0, Q = 200 L × 1 g/L = 200 g

Q(0) = 200 = Ae^{(-0/100)} = Ae^{(0)} = A\\A = 200.\\So, Q(t) = 200e^{(-t/100)}

We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2

2 = 200e^{(-t/100)}\\\frac{2}{200} =  e^{(-t/100)}

㏑0.01 = -t/100

t = -100㏑0.01

t = 460.52 min

You might be interested in
I will upvote and give brainliest answer
zloy xaker [14]

Answer:

x=17

Step-by-step explanation

i just did the exact same question on a test and got it right .

6 0
3 years ago
What translates the following verbal phrase correctly to algebra:<br><br> y less than 21?
Lelu [443]
Do you mean something like y<21?
4 0
2 years ago
The life spans of elephants in a Columbus zoo are normally distributed. The average elephant lives 60 years: the standard deviat
Marta_Voda [28]

did u ever get the answer l need it


5 0
2 years ago
Which set of side lengths forms a right triangle? A) 5 cm, 6 cm,7 cm B) 2 cm, 4 cm, 6 cm C) 8 cm, 9 cm, 11 cm D) 8 cm, 15 cm, 17
Tamiku [17]
A) 5cm,6cm,7cm
you’re welcome
3 0
3 years ago
An investment is modeled by the function P = 2,500 (e) Superscript 0.025 t. What does 2,500 represent?
Setler [38]

Answer:

a

Step-by-step explanation:

they are right

3 0
3 years ago
Read 2 more answers
Other questions:
  • Sean's school raised $32,578. Leslie's school raised $18,749. How much more money did Sean's school raise?
    13·2 answers
  • 2.
    15·1 answer
  • Solve by factoring: 2x2 - 5x - 12 = 0
    14·2 answers
  • An isosceles triangle has two sides of equal length. The third side is 5 less than twice the length of one of the other sides. I
    12·2 answers
  • The perimeter of the hallway is 10 4/10 meters what is the width in meters
    15·1 answer
  • What is d=rt for t.
    12·1 answer
  • A card is drawn from a deck of 52 cards. Find the probability of drawing a black card.
    9·2 answers
  • PLZ HELP<br> ANSWER BOTH QUESTIONS<br> THE SECOND ONE IS MORE OR LESS
    6·2 answers
  • What is the volume of this prism? )<br> cm<br> thing
    7·1 answer
  • A cylindrical pressure vessel has a height of 9 feet and a diameter of 6 feet. how much gas can the pressure vessel hold when fu
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!