Question Five The daytime length (in hours) for the planet Mars can be modelled by the following circular function: D(t) = 4cos() + 12 where t is the number days after 31 December 2009 and te[0, 48]. a. Find the average rate of change in hours of sunlight between the 31 Dec 2009 and the 15 Jan 2010. Give your answer correct to 2 decimal places. b. Find the average value of the function D (t) over the interval e [0, 48] . Interpret your answer. e. Find the derivative of the function D(t).

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.