Ximena is typing a 2500 word essay. In 9 minutes she types 396 words, at this rate can Ximena type the essay in an hour?
1 answer:
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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:
8 new chicks can be fitted in the coop.
Step-by-step explanation:
A chicken coop holds 10 hens or 20 chicks.
That means space in the coop for 10 hens = space for 20 chicks
Or space for 1 hen = space for 2 chicks
Now th of the hens were removed from the coop.
So, number of hens removed from the coop =
= 4 hens
And space for 4 hens in the coop = space for the 8 chicks
Therefore, 8 new chicks can be fitted in the coop.