Answer:
a) The equation can Nina use to find how many times as many papers she delivered the second week as the first week is given as:
8x = 32
b) Nina delivered 4 times as many papers the second week as the first week
Step-by-step explanation:
From the question, we are told that:
Nina delivers newspapers.
In the first week, she delivers 8 papers.
In the second week, she delivers 32 papers.
Let x represent the number of times
The equation can Nina use to find how many times as many papers she delivered the second week as the first week is given as:
8paper × x = 32 papers
8x = 32
Solving for x
8x = 32
x = 32/8
x = 4 times
Therefore, Nina delivered 4 times as many papers the second week as the first week
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
For 0 minutes, it would be 0 minutes (obviously)
for 1 minute, it would be 3
for 2 minutes, it would be 6 pages
and finally, 3 minutes, will be 9.
to get the answers, you would just have to add 3, since every minute, nick reads 3 pages.