Components are manufactured from billet aluminium using a CNC lathe. The movement of the cutting head can be modelled using the equation: y = -0.110x + 0.130x +8.470 With the line y = 0 being the axis of rotation. (Note: the units of x and y are imperial, so 0.010 represents ten thousandths of an inch, etc) a. Determine the volume of the component formed by machining the area enclosed by y and the lines x = 0 and x = 9. Give your answer in cubic inches (in). The electrical current consumed by the CNC lathe during the machining process can be modelled by the equation: I = 17Sin(100nt) where I is the current in Amperes and t the time in seconds. b. Using integral calculus, calculate the mean and the root mean square (rms) current over 1 full cycle. (Show your working). After machining, the component needs to be cooled before it is safe for the operator to handle. The rate of cooling is proportional to the temperature difference between the component and the ambient temperature inside the lathe. The rate of change of temperature of the component is given by the equation: IT given by the equation: dT dt Where, C. = Teke-kt Toke-kt t is the time in minutes since machining stopped Te is the temperature of the environment inside the lathe. To is the initial temperature of the component (i.e. at the time machining stops) k is a constant Use Integral Calculus to derive an equation for T(t), the temperature of the component at time, t d. Establish values for the constants in your new equation given that: Te = 40C To = 254C at t= 10, T(t)=152C e. If the component cannot be handled until it reaches 60C, formulate a prediction for the soonest time after machining that the component can be handled?