Question

3. The depth of the water (in meters) at a certain pier is given by the equation: d)2+ sint, where t is the number of hours after 10:00 AM. 2 a) How deep will the water be at high tide, and at low tide? b) Mid-tide occurs when the height of the water is exactly midway between the high and low tides. Counting time after 10:00 AM, what are the first two times when it is mid-tide? c) How many hours between successive mid-tides? d) How many tide cycles are there in 24 hours? e) Graph the depth of the water as a function of time after 10:00 AM. f) There is a rock shelf near the pier that is safe to visit only when the depth of the 2 water is 1.75 m or less. If Dakota wants to visit the rock shelf in the evening when it is safe, between what times should she go?

Answer 1

Given: d(t) = 2+-sin where t is time after 10:00 AM (a)To find the depth of high and low tides 12 For critical points, solve the equation d' (t) 0 12 t = 3.9 Att-3 Att=9. High tide-2.5 m Low tide1.5 m

(b)To find the first two times when the mid tides occure Height of mid-tide 1.5+2.5 Solve the equati on d (t)-2 rt 6.12 The mid-tides occure at t6 and t-12 second The time between the two successive mid-tides is 6 hours Period of d (t Total time 24 Total tide cycles 24 12 2

(e) Use an online graphing calculator to sketch the graph. 2.5 1.5 0.5 10 15 20 25

Answer 2

If Dakota wants to visit the rock shelf in the evening, between what times should she go