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
<span>2X +1=-15
Subtract 1 from both sides
2x=-16
Divide 2 on both sides
Final Answer: x=-8</span>
<span>Using the Pythagorean theorum we can solve this v a^2+b^2= c^2. A is the distance from base of house to ladder A= 1.5, c ifls length of ladder, c= 10. (1.5)^2 + ;b^2 = (10)^2. Solve for b. B= 9.88. 12 foot height of house - 9.88 feet to top of angled ladder = 2.11 from top of ladder to edge of roof</span>
Answer:
The relation is 'a function that is one-to-many'.
Step-by-step explanation:
From the table, we can see that element 10 i.e. y=10 in the range, corresponds to two elements i.e. x=-5, and x=5 in the domain.
In other words, the given table represents the many-to-one function as an element of the range y = 10 corresponds to more than one element in the domain.
Therefore, the relation is 'a function that is one-to-many'.