SOLUTION: the water at a local beach has an average depth of one meter at low tide and an average depth at high tide of 8m. One cycle of the tides takes approximately 12 hours. This periodic

Algebra ->  Trigonometry-basics -> SOLUTION: the water at a local beach has an average depth of one meter at low tide and an average depth at high tide of 8m. One cycle of the tides takes approximately 12 hours. This periodic      Log On


   

Question 1153123: the water at a local beach has an average depth of one meter at low tide and an average depth at high tide of 8m. One cycle of the tides takes approximately 12 hours. This periodic motion can be modelled by the function d(t)=3.5 cos(pi/6t)+4.5 where d(t) represents the depth of the water, in metres, at a time t, in hours. This equation assumes that the water level is at high tide at time zero. Many people dive into the water from a nearby dock. If the water must be at least 3m deep to dive safely, when during the daylight hours would it be safe to dive off the dock?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Graph the function and the constant 3 on a graphing calculator and find the hours that the function value is greater than the constant.

graph%28400%2C400%2C0%2C24%2C0%2C10%2C3.5%2Acos%28%28pi%2F6%29x%29%2B4.5%2C3%29

The daytime times for safe diving are from t=8.15 to t=15.85, representing times of 8:09am to 3:51pm.