(1 point) When a hot object is piaced in a water bath whose temperature is 25C: it cools from 100C to 50C in 2005. In another bath. the same cooling occurs in 1805. Find the temperature of the second bath. The temperature of the second bath = DC (1 point) A tank contains 2960 L of pure water. Solution that contains 0.02 kg of sugar per liter enters the tank at the rate 7 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the begining? y(0) = (kg) (b) Find the amount of sugar after t minutes. y( t) = (kg) (c) As t becomes large, what value is y(t) approaching ? In other words, calculate the following limit. lim y(t) = (kg)(1 point) A tank contains 80 kg of salt and 2000 L of water. A solution of a concentration 0.02 kg of salt per liter enters a tank at the rate 9 L/min. The solution is mixed and drains from the tank at the same rate. a.) What is the concentration of our solution in the tank initially? concentration = (kg/L) b.) Find the amount of salt in the tank after 1.5 hours. amount = (kg) c.) Find the concentration of salt in the solution in the tank as time approaches infinity. concentration = (kg/L)(1 point) A tank contains 1000L of brine with 15kg of dissolved salt. Pure water enters the tank at a rate of 15L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. Answer the following questions. 1. How much salt is in the tank after t minutes? Answer (in kilograms): S(t) = 2. How much salt is in the tank after 30 minutes? Answer (in kilograms):(1 point) i L xx switch In the circuit shown in the figure above a battery supplies a constant voltage of E = 30V' the inductance is L 2 2H, the resistance is R = 30 Q; and 1(0) 2 0. Find the current in amperes t seconds after the switch is closed. 1(t}= (1 point) R switch The gure above shows a circuit containing an electromotive force (a battery): a capacitor with a capacitance of C farads (F). and a resistor with a resistance of R ohms (Q). The voltage drop across the capacitor is (22/0, where Q is the charge (in coulombst so in this case Kirchho's Law gives Q RI :Et. +C () Since the current is I : %, we have (2162 1 :Et. dt+CQ () Suppose the resistance is 109' the capacitance is 0.05F, a battery gives a constant voltage of E(t) : 40V, and the initial charge is 62(0) : DC. Find the charge and the current at time at. 26) = . m) =