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caitlinrosekozoxegcb
16.07.2020 •
Mathematics
A tank contains 4,000 L of brine with 18 kg of dissolved salt. Pure water enters the tank at a rate of 40 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.
a. How much salt is in the tank after t minutes?
b. How much salt is in the tank after 30 minutes? (Round your answer to one decimal place.
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Ответ:
In this exercise we have to use the integral to calculate the salt concentration:
(a)![A(t)=18e^{-\frac{t}{100} }](/tpl/images/0708/1187/1239a.png)
(b)![13.3 kg](/tpl/images/0708/1187/4e0c4.png)
Knowing that the volume of brine in the tank = 4000L, the initial Amount of salt, A(0)=18 kg. The rate of change in the amount of salt in the tank at any time t is represented by the equation:
Rate In = (concentration of salt in inflow)(input rate of brine). Since pure water enters the tank, concentration of salt in inflow =0.
Rate In = 0
Rate Out=(concentration of salt in outflow)(output rate of brine)
Therefore:
This is a linear D.E. which we can then solve for A(t). Integrating Factor:
. Multiplying all through by the Integrating Factor:
Taking integral of both sides:
Recall our initial condition:
Therefore, the amount of salt in the tank after t minutes is:
(b)When t=30 mins
The amount of salt in the tank after 30 minutes is 13.3kg.
See more about concentration at link
Ответ:
(a)![A(t)=18e^{ -\frac{t}{100}}](/tpl/images/0708/1187/f2c4f.png)
(b)13.3 kg
Step-by-step explanation:
The volume of brine in the tank = 4000L
Initial Amount of salt, A(0)=18 kg
The rate of change in the amount of salt in the tank at any time t is represented by the equation:
Rate In = (concentration of salt in inflow)(input rate of brine)
Since pure water enters the tank, concentration of salt in inflow =0
Rate In = 0
Rate Out=(concentration of salt in outflow)(output rate of brine)
Therefore:
This is a linear D.E. which we can then solve for A(t).
Integrating Factor:![e^{\int \frac{1}{100}d}t =e^{ \frac{t}{100}](/tpl/images/0708/1187/8fa2f.png)
Multiplying all through by the I.F.
Taking integral of both sides
Recall our initial condition
A(0)=18 kg
Therefore, the amount of salt in the tank after t minutes is:
(b)When t=30 mins
The amount of salt in the tank after 30 minutes is 13.3kg
Ответ:
16.2°
Step-by-step explanation:
polygon has 20 sides
regular polygon
How to find the sum of all interior angles in a polygon?
=> (n-2) x 180
here n means number of sides
=> (20-2) x 180
=> 18 x 18
=> 324
there are as many interior angles in a polygon as many sides it has.
and the size of each angle is the same in a regular polygon.
so => 324/20 = 16.2°- Answer