A tank has pure water flowing into it at 12 1/min. The contents of the tank are kept thoroughly mixed, and the contents flow out at 10 1/min. Initially, the tank contains 10 kg of salt in 100 l of...

Extracted text: A tank has pure water flowing into it at 12 1/min. The contents of the tank are kept thoroughly mixed, and the contents flow out at 10 1/min. Initially, the tank contains 10 kg of salt in 100 l of water. Let S (t) be the amount of salt in the tank at any time t and S'(t) its derivative. -59 (t) (i) Use the balance law to prove that S"(t) 50 +t (ii) How much salt will there be in the tank after 30 min?