Someone please explain each step for me Thanks 8 15 points A

8. 15 points] A Ferris wheel is 20 meters in diameter and boarded in the six o\'clock position from a \' platform that is 2 meters above the ground. The wheel completes one full revolution every 2 mimutes At t-0 you are in the three o\'clock position and ascending. The Ferris wheel makes three revolutions in a single ride. (a) How many times will your height be 8m during one revolution on the wheel? How many times will your height be 12m during one ride? Write your answer in g complete sentence. (b) Set up a trigonometric function representing your height in terms of how many minutes you\'ve been on the wheel. Write down the period, amplitude, and midline. (c) Using your answer to the previous part, write and use an equation to solve for all times in one ride that your height will be 8m. Show your work and urite your answer in a complete sentence. (c) Using your answer to the previous part, write and use an equation to solve

Solution

1) At 3 o clock we start ascending:.So, 8 mt means ( 2mt +6mt) , whe moving anticlockwise and coming down to 6 o clock position, once we reach ht of 8 mt

So, 12mt = 2mt +8mt, at 3 o clock postion we are at 12 mt position ,again at 9 o clock position we reach 12mt

height. So, two times.

In one ride i.e. 3 revolutions we would be at 12mt height 6 times

2) Period = 2

midline = 10+2 = 12

amplitude = 20/2 = 10mt

H(t) = 12 +10sin(2pi*t/2) = 12 +10sin(pi*t) where t is minutes

3) h(t) = 8

8 = 12 +10sin(pi*t)

sin(pi*t) = -0.4

t*pi = 2pi*k - 0.411

t = (2k -0.13)

and t*pi = 2pi8k + 3.55

t = 2k + 1.13

----> t = (2k -0.13)

k=1; t = 2-0.13 = 0.87 min

k=2 ; t = 3.87 min.

k=3 ; t= 5.87 min.

----> t = 2k + 1.13

Now k=0 ; t =1.13 min.

k=1; t = 2.13 min

k=2 ;t= 5.13 min

So, solution t = 0.87, 3.87 , 5.87 , 1.13 , 2.13 , 5.13 minutes we reach 8mt height