Respuesta :
The volumetric flow rate is represented by the symbol Q
Volume of water in the tank after one minute is 10,991 gallons
Volume of water in the tank after two minute is 10,962 gallons
Volume of water in the tank after one minute is 10,730 gallons
Volume of water in the tank after n minute is 11,020 - 29·n
The reason the above values are correct is as follows:
The given parameters are;
The volume of water the large industrial tank holds, V = 11,020 gallons
The rate of flow out of the tank through the drain on the bottom, Q = 29 gallons per minute
The initial level of water in the tank = The tank is initially filled; 11,020 gallons
Required:
The amount of water in gallons left in the tank after one minute
Solution;
The volume, [tex]V_{out}[/tex], of water that flow out of the tank after a given time, t, is given as follows;
[tex]V_{out}[/tex] = Q × t
When t = 1 minute, we have;
[tex]V_{out}[/tex] = 29 gallons/minute × 1 minute = 29 gallons
The volume of water left in the tank, [tex]V_{in \, tank}[/tex], is given as follows;
[tex]V_{in \, tank}[/tex] = V - [tex]V_{out}[/tex]
The volume left in the tank after t = 1 minute, where, [tex]V_{out}[/tex] = 29 gallons is given as follows;
After one minute, [tex]V_{in \, tank}[/tex] = 11,020 gal - 29 gal = 10,991 gal
The volume left in the tank after one minute, [tex]V_{in \, tank}[/tex] = 10,991 gallons
Similarly, after two minutes, we have;
[tex]V_{in \, tank}[/tex] = V - [tex]V_{out}[/tex] = V - Q × t
∴ [tex]V_{in \, tank}[/tex] = 11,020 - 29 × 2 = 10,962
The number of gallons left in the tank after 2 minutes is [tex]V_{in \, tank}[/tex] = 10,962 gallons
After, t = 10 minutes, we have;
[tex]V_{in \, tank}[/tex] = V - Q × t
After ten minutes; [tex]V_{in \, tank}[/tex] = 11,020 - 29 × 10= 10,730
The number of gallons left in the tank after 10 minutes is [tex]V_{in \, tank}[/tex] = 10,730 gallons
After n minutes, we have;
t = n, therefore;
[tex]V_{in \, tank}[/tex] = 11,020 - 29 × n = 11,020 - 29·n
The number of gallons left in the tank after n minutes is [tex]V_{in \, tank}[/tex] = 11,020 - 29·n
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