A mixing tank initially contains 2000 lb of liquid water. The tank has two inlet pipes, one delivering hot water at a mass flow rate of 0.8 lb/s and the other delivering cold water at a mass flow rate of 1.2 lb/s. Water exits through a single exit pipe at a mass flow rate of 2.5 lb/s. Determine the amount of water, in lb, in the tank after 40 minutes.

The  total amount is  

Explanation:

from the question we are told that

    The  initial mas of water in the tank is  

     The mass flow rate of the hot water  inlet pipe is  

    The mass flow rate of the cold  water  inlet pipe is

    The mass flow rate  of the exit pipe is

     The  time being considered is

The amount of water deposited by the hot inlet pipe in 40 minutes is mathematically represented as

substituting values

The amount of water deposited by the cold  inlet pipe in 40 minutes is mathematically represented as

substituting values

The total amount of water that let the tank after 40 \minutes is

substituting values

The  total amount of water in the tank after 40 minutes is  

substituting values  

explanation: in any substance/object, the particles inside it (atoms/molecules) constantly move in random directions and with random speeds (this motion is called brownian motion). as a result, the particles have some kinetic energy (which is proportional to the temperature of the substance).

explanation:

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6 cos 34, 6 sin 34 trig