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
Answer:
Step-by-step explanation:
2log(x-3)=log25
log(x-3)²=log25 cancel out log on both sides
(x-3)²=25
x²-6x+9=25
x²-6x+9-25=0
x²-6x-16=0 factorize
x²+2x-8x-16=0
x(x+2)-8(x+2)
(x-8)(x+2)=0
x-8=0 or x+2=0
x=8 or x=-2
x=-2 cannot be considered because of the -ve sign.
x=8.
check
2log(x-3)
2log(8-3)
2log5
log5²=25
therefore LHS=RHS
Answer: 2.52
Step-by-step explanation: 36.00x0.07
36.00 is the same as 36
so, 36x0.07=2.52
The perimeter = 4 * length of a semicircle of radius 5 == 4* pi * 5 = 20 pi cm
The area of one of the clear parts = 1/2 area of square - area semicircle
= 1/2 * 10^2 - 1/2 pi *5^2 = 50 - 12.5pi
So area of shaded parts = area of square - 4 (50 - 12.5pi)
= 100 - 200 + 100pi = (100pi - 100) cm^2
To evaluate this expression, we need to remember that subtracting a negative number is the same as adding a positive number, and that adding a negative number is the same as subtracting a positive number. Using this knowledge, let's begin to simplify the expression below:
-1 - 3 - (-9) + (-5)
Because addition of a negative number is the same as subtraction of a positive number, we can change + (-5) to -5, as shown below:
-1 - 3 - (-9) - 5
Next, because we know that subtracting a negative number is the same as adding a positive number, we can change - (-9) to + 9, as shown below:
-1 - 3 + 9 - 5
Now, we can subtract the first two terms and begin to evaluate our expression:
-4 + 9 - 5
Next, we can add the first two numbers of the expression:
5 - 5
Now, we can subtract our last two numbers, which gives us our answer:
0
Therefore, your answer is 0.
Hope this helps!
