Outside temperature over a day can be modelled using a sine or cosine function. Suppose you know the high temperature for the day is 70 degrees and the low temperature of 48 degrees occurs at 5 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

If y varies inversely with x and y=11 when x=3 find the equation that relates x and y.

If p vanes inversely with q and p=5when q=6 , find the equation that relates p and q.

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.)