A clock is hung on a wall so that the bottom of the clock is exactly 75 inches above the ground. The minute hand (the longest hand) is 7 inches long and touches the edge of the clock. Write a function h(t)that describes the height of the tip of the minute hand above the ground at any time, t.  For ease, assume the scenario begins at noon. Recall: it takes 60 minutes for the minute hand to make a complete revolution around the clock.

During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 85 degrees occurs at 4 PM and the average temperature for the day is 75 degrees. Find the temperature, to the nearest degree, at 7 AM.

A Ferris wheel has a radius of 35 feet. The bottom of the Ferris wheel sits 0.7 feet above the ground. You board the Ferris wheel at the 6 o'clock position and rotate counter-clockwise. a. Write a function f that determines your height above the ground (in feet) in terms of the number of radians you have swept out from the 6 o'clock position, a. f(a) = tan(35) Preview b. Write a function g, that determines your height above the ground (in feet) in terms of the number of feet you have traveled since you started rotating, s. g(s) : Preview