You are employed as an engineer within a small engineering company, as such you are presented with various scenarios for which you need to look at the problem, form equations, solve equations using more than one method. Activities: Activity (1): You are looking at using Newton's law of cooling to analyse a cooling system in your production process. You are aware that Newton's law of cooling states that the rate of loss of temperature of a body is proportional to the excess temperature of the body over its surroundings. In order to analyse the situation, you will need to form a differential equation. You find that in a particular process the starting temperature of a liquid is 95 this cools to 75 in 5 minutes, use your equation to find when this liquid cools to 55 Given that the surrounding temperature is 21 Activity (2): You are looking at an electrical circuit involving currenti in a series R-L circuit is given by: +6i = E and i = 0 when t = 0 dt Solve using two different methods the particular solution when E=20. You may want to comment upon the accuracy of the two methods.