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QUESTION 1 [30 MARKS] (a) The Fibonacci sequence can also be seen in hurricanes prediction. The shape takes in the form of a spiral, it can be in a nesting process and repeated into infinity. It is called the logarithmic spiral, and it abounds in nature. The Fibonacci sequence of numbers, "F", is defined using the recursive relation. Fibonacci sequence of numbers can be computed as follows: Fn = Fn-1+Fn-2 If the 12th and 13th terms in the hurricane prediction sequence are 89 km/hour and 144 km/hour, analyze the value of the 15th, 16th, and 17th hurricane speed by using the Fibonacci formula as stated above. [4 Marks] (b) The given hurricane data are F[0]=4 km/hour and F[1]=6 km/hour. Define what is the value of the 5th and 6th hurricane speed by using the Fibonacci numbers. Illustrate your answer based on the Fibonacci sequence of solution. [6 Marks] (c) Heap sort has been invented in 1964 by J.W.J. Williams. The algorithm divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by splitting the largest element and inserting it into the sorted region. The performance of the heap sort depends on the given input array. If the given input arr = {4,8,9,5,3,7), sort the arr and illustrate your answer based on the heap sort algorithm. [12 Marks]