4. A tank holds 96L (liters) of a sugar solution that is initially concentrated at 0.5kg/L (kilograms per liter). For the first 10 minutes of operation, valve A is open, and it adds 12L/min (liters per minute) of fluid containing a 1 kg/L sugar concentration. After 10 minutes, valve A is switched off and valve B is switched on. Valve B adds fluid with a 0.5kg/L concentration at 12L/min. The exit valve C removes fluid from the tank at 12L/min, thereby keeping the volume of fluid in the tank constant at 96L. a. Give an expression for the inflow rate that uses the Heaviside function. b. Formulate an initial value problem for r(t), the number of kilograms of sugar in the tank after t minutes. B

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.