The depth of the water in a bay varies throughout the day with the tides. Suppose that we can model the depth of the water with the following function. h(t)=15-6.5 sin 0.25t In this equation, h (t) is the depth of the water in feet, and 7 is the time in hours. Find the following. If necessary, round to the nearest hundredth. Minimum depth of the water: feet Period of h: hours X Number of tidal cycles per hour:

For a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is modeled by v=0.85sint/3, where t is the time (in seconds). a Find the time for one full respiratory cycle. b Find the number of cycles per minute. c Sketch the graph of the velocity function. Use the graph to confirm your answer in part a by finding two times when new breaths begin. (Inhalation occurs when v0, and exhalation occurs when v0.)

Use the differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the difference the two results to 4decimal places. 17.02