The water depth, D, in metres, in a boating marina on a particular day can be modelled by the function D(t) = 4 sin (30" x t) + 12.5, 0St < 24, where t is the elapsed time, in hours, since midnight. (a) Write down the depth of water at midnight. (b) The cycle of water depths repeats every T hours. Find the value of T. (c) (i) Write down the minimum and maximum depths of water during the day. (ii) Find the times at which the minimum and maximum depths of water occur during the day. (d) Draw the graph of D versus t on the grid below. D 17.5 15 12.5 10 3 6 9 12 15 18 21 24 (e) A ship with 8 m draught is allowed to enter the marina if the depth of water is greater than 10 m. Find the time interval before midday, in hours and minutes, during which the ship is not allowed to enter the marina.