the height, h, in feet of the tip of the minute - hand of a wall clock as a function of time, t, in minutes…
the height, h, in feet of the tip of the minute - hand of a wall clock as a function of time, t, in minutes can be modeled by the equation (h = 0.75cos(\frac{pi}{30}(t - 15))+8). which number (from 1 to 12) is the minute - hand pointing to at (t = 0)?\n3\n6\n9\n12
Answer
Explanation:
Step1: Substitute t = 0 into the equation
Substitute (t = 0) into (h=0.75\cos(\frac{\pi}{30}(t - 15))+8). We get (h = 0.75\cos(\frac{\pi}{30}(0 - 15))+8=0.75\cos(-\frac{\pi}{2})+8).
Step2: Evaluate the cosine - value
Since (\cos(-\frac{\pi}{2})=\cos(\frac{\pi}{2}) = 0), then (h=0.75\times0 + 8=8).
Step3: Relate the height to the clock - position
On a clock, when the minute - hand is at 9, the height of the tip of the minute - hand is at a certain position corresponding to the value we calculated. When (t = 0), the minute - hand is pointing to 9.
Answer:
9