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
when t = 0, Q = 200 L × 1 g/L = 200 g
We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2
㏑0.01 = -t/100
t = -100㏑0.01
t = 460.52 min
Step-by-step explanation:
1 dozen = 12 pears
12 pears = $36
1 pear = 36/12 = $3
Total Cost of Pears = No. of pears x price of 1 pear
= (5x12) x 3
= 60 x 3
= $180
Sale of Pears = Price per pear x (Total Pears bought - Rotten Pears)
= $4.50 x (5x12-7)
= $4.50 x 53
= $238.50
Profit/Loss = Sale of Pears - Total Cost of Pears
= $238.50 - $180
= $58.50
Ariana made a profit of $58.50.
Let's begin ! ^_^
You have got informations in your problem that you just have to translate in a "mathematic language".
Company A :
"$40 membership fee and $2 per video stream."
Thanks to that, you can guess :
c = 40 + 2s
Now let's do the same thing to the company B.
Company B :
"charges a one-time $20 membership fee and $4 per video stream."
Therefore, c = 20 + 4s.
I think you have guessed !! =D And yes the system of equation that you have to solve and you're looking for is :
{c=40+2s ( Option B)
c=20+4s.
Second step : For how many video streams will the cost be the same for both companies?
We just have to solve the system :) And there is only one variable, the letter "s".
We know that we have to find equal costs as it is said in the question " the cost be the same for both companies", so :
=> 40 + 2s = 20 +4s
=> 4s - 2s = 40 - 20
=> 2s = 20
=> s = 20/2
=> s = 10
Verification :
Company A :
=> 40 + 2s = 40 + 2*10 = 40 + 20 =60.
Company B :
=> 20 + 4s = 20 + 4*10 = 20 + 40 = 60
As you have seen, the costs are the same for both companies.
We can say that as a conclusion for 10 video streams, the cost will be the same for both companies.
In short, the answer would be : 10.
Let me give you an advice : Usually the word "per" means a multiplication is the mathematic language.
Hope this helps !
Photon
