A tank containing 400 litres of water initially contains 40 kg of salt solute (dissolved salt)....

 

 

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A tank containing 400 litres of water initially contains 40 kg of salt solute (dissolved salt). Some brine containing 0.02 kg/L of salt is then pumped into the tank at a rate of 1 L/min. The solution is constantly mixed and pumped out of the tank at a rate of 1 L/min, so that the volume of liquid in the tank remains constant. Let Q (t) represent the quantity of salt (in kg) dissolved in the tank at time t (measured in minutes after the inflow of brine began). (i) What is the differential equation satisfied by Q? dQ kg/min dt Give the correct expression in terms of Q (do not write Q (t)). (ii) Find the exact formula for Q (t) as a function of t.. Q (t) = (iii) What is the quantity of salt present in the tank after 30 minutes? Answer. Number kg. Round the answer to one decimal place. 0.02 kg/L of salt, 1 L/min :) 400 L 1 L/min A tank containing 400 litres of water initially contains 40 kg of salt solute (dissolved salt). Some brine containing 0.02 kg/L of salt is then pumped into the tank at a rate of 1 L/min. The solution is constantly mixed and pumped out of the tank at a rate of 1 L/min, so that the volume of liquid in the tank remains constant. Let Q (t) represent the quantity of salt (in kg) dissolved in the tank at time t (measured in minutes after the inflow of brine began). (i) What is the differential equation satisfied by Q? dQ kg/min dt Give the correct expression in terms of Q (do not write Q (t)). (ii) Find the exact formula for Q (t) as a function of t.. Q (t) = (iii) What is the quantity of salt present in the tank after 30 minutes? Answer. Number kg. Round the answer to one decimal place. 0.02 kg/L of salt, 1 L/min :) 400 L 1 L/min

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