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Your friends have opened an ocean fishing operation that requires their fishing vessel to cross a channel, where the depth of the water (measured in metres) varies with time, and is represented by the following equation:
D(t) = 2.5 sin (0.523t) + 2.9
Where d = depth of water in metres
And t = number of hours since midnight
1. Create a graph showing the depth of the water over 24 hours. Label your graph approx, including coordinates for maximum and minimum points (to 2 decimal places). On graph paper
2. What is the period of this function and what does it represent about the varying depths of the water
3. Your friendsfishingboat requires a depth of at least 1.3 metres of water to cross the channel safely. They would like to make two excursions per day with each trip lasting at least 5 hours
Design a daily timetable showing what times these trips could be scheduled to allow for safe navigation through the channel. Support your answer by showing your work (Express time in hours and minutes)
(a) Using interpolation, give a polynomial f ∈ F 11 [x] of degree at most 3 satisfying f(0) = 2; f(2) = 3; f(3) = 1; f(7) = 6 (b) What are all the polynomials in F 11 [x] which
1/2+3/4
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