In a glass containing some water, tamarind juice and sugar is added and stirred well. Is this a mixture-can you tell why? Will this solution be sweet? or sour? both sweet and sour?

A 50 L tank initailly contains 10 L of fresh water, At t=0, a brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 L/min, while the well-stirred mixture leaves the tank at the rate of 2 L/min. Then the amount of time required for overflow to occur in

Consider a tank which initially holds V_(0) liter of brine that contains a lb of salt. Another brine solution, containing b lb of salt per liter is poured into the tank at the rate of eL//"min" . The problem is to find the amount of salt in the tank at any time t. Let Q denote the amount of salt in the tank at any time. The time rate of change of Q, (dQ)/(dt) , equals the rate at which salt enters the tank at the rate at which salt leaves the tank. Salt enters the tank at the rate of be lb/min. To determine the rate at which salt leaves the tank, we first calculate the volume of brine in the tank at any time t, which is the initial volume V_(0) plus the volume of brine added et minus the volume of brine removed ft. Thus, the volume of brine at any time is V_(0)+et-ft The concentration of salt in the tank at any time is Q//(V_(0)+et-ft) , from which it follows that salt leaves the tank at the rate of f(Q/(V_(0)+et-ft)) lb/min. Thus, (dQ)/(dt)=be-f(Q/(V_(0)+et-ft))Q=be A tank initially holds 100 L of a brine solution containing 20 lb of salt. At t=0, fresh water is poured into the tank at the rate of 5 L/min, while the well-stirred mixture leaves the tank at the same rate. Then the amount of salt in the tank after 20 min.