3 3. (10 pts.) A small Ferris wheel with a radius of 20 feet rotates countercloc
ID: 2919987 • Letter: 3
Question
3 3. (10 pts.) A small Ferris wheel with a radius of 20 feet rotates counterclockwise at a rate of 1 revolution every 8 minutes. At its lowest point, each seat is 1 foot above the ground. Assume riders start at the lowest point at time , O. The table and graph below both represent the height above ground of the Ferris wheel at time f in seconds = time (in minutes) b=height above ground (in feet) 2-4-2-1 25 10 1 2 34567 8 9 10 11 Assuming this situation can be modeled by a sine or a cosine equation of the form y-c + asin (k) or y = c + a cos (kx), find an appropriate equation to represent the height b above ground / minutes after the ride starts, by finding each of the following Show your work or explain how you got your answers. (a) What is the amplitude? (b) What is the period? (c) What is the vertical shift (up/down)? (d) Use your answers to parts (a), (b), and () to find the values of each of the following for the standard equations y=c + asin(h) or y=c + a cos(k). (e) What is an equation for this function? Equation:Explanation / Answer
(a)
amplitude =(41-1)/2
amplitude =20 feet
(b)
period =8-0
period =8 minutes
(c)
vertical shift =(41+1)/2
vertical shift =21 feet
(c)
a= -20,since curve starts at lowest point at t=0
2/k = 8
=>k=(/4)
c =21
(c)
the equation for this function is y=21 -20cos((/4)x)
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