Given that  where is angular position and is time. Find the time when the angular acceleration is zero.

Consider the expression . If , apply the Newton-Raphson technique to find around the point . Leave your answers in decimal places.

Consider a submarine cable whose signalling range is realised from the expression: . The term  denotes the ratio of the conductor radius to that of the cable. What is the value of for maximum range to be achieved? 

Consider the expression  where P, V and R are the power, voltage and resistance respectively. Assume that  and ; if the voltage is increased by and the resistance is decreased by , how does the power change? Leave your result approximated to one decimal place.