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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

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3 years ago
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Answer:

<h2>x =  -  \frac{17}{4}</h2>

Step-by-step explanation:

6x + 3(4x - 2) = 5(2x - 8)

Expand the terms in the bracket and simplify

That's

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Using the subtraction property subtract 10x from both sides of the equation

18x - 10x - 6 = 10x - 10x - 40 \\ 8x - 6 =  - 40

<u>Add 6 to both sides of the equation</u>

8x + 6 - 6 =  - 40 + 6 \\ 8x =  - 34

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We have the final answer as

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