Question 1 [5 + 4 = 9 marks] (a). A tank can be filled by a pipe in 18 hours. Five hours after this pipe is opened, it is supplemented by a smaller pipe, which, by itself can fill the tank in 22 hours. Simultaneously, a drainpipe is opened, which, by itself, can completely empty the tank in 30 hours. Find the total time, measured from the opening of the larger pipe, to completely fill the tank. [Verify your answer by MATHEMATICA and attach the printout of the commands and output] (b). During an experiment in the lab, Jack, a biologist has a 40% mixture and a 10%mixture of the nutrient that he got from the pawpaw plant. The lecturer posed the question to Jack. How much of each mixture should Jack mix to obtain 25 cm' of a 28% mixture? [Verify your answer by MATHEMATICA and attach the printout of the commands and output]Question 2 [6 + 5 + (1+ 2+ 2) + (5 + 5) = 26 marks] (a). Find the values of a and b that make f continuous everywhere. x- +6x+5 x