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zaiibaii
13.02.2020 •
Mathematics
Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of the water remaining. The tank intitially contains 300 liters and 23 liters leak out during the first day.
A. When will the tank be half empty? t= ? days
B. How much water will remain in the tank after 3 days? volume= ? Liters
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Ответ:
Step-by-step explanation:
Given that water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of the water remaining. The tank intitially contains 300 liters and 23 liters leak out during the first day
Let V represent the volume at time t.
Rate of change of V is![\frac{dV}{dt} = k\sqrt{v}](/tpl/images/0509/6883/326fe.png)
where k represents the constant of proportionality
We separate the variables and integrate
Use the fact when t =0, V =300
Now use the fact when t =1 V= 300-23 = 277
k is negative because there is leak
So equation is
Using this
A) when half empty V = 150
t =![\frac{2\sqrt{150} -2\sqrt{300}}{-1.3544} \\=3.75](/tpl/images/0509/6883/6f29c.png)
so it takes 3.75 days
B) When t =3
V = 233.7515
Ответ:
Answer
slot 1: x - 6 + x = 4
slot 2: 2x - 6 = 14
slot 3: 2x = 20
slot 4: x = 10
Step-by-step explanation:
hope it helped