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Sonbull
2 months ago
13

Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes

to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.
Mathematics
2 answers:
tester [12.3K]2 months ago
7 0
The distance from the bottom of the wheel to a point on the ground can be expressed using the sine function h(t) = a*sin(kt) + b, where b represents the height of the wheel at 4m. The radius a is calculated as 50/2 = 25m. Since it takes 6 minutes for 3 complete rotations, the period can be derived from 2π/k, giving us k = π. Thus, h(t) = 25*sin(π*t) + 4. 
babunello [11.8K]2 months ago
5 0
The desired function is h(t) = h(t)=-25\cos(\pi t)+29. The cosine function's standard form is , where A is the amplitude, \frac{2\pi}{B} indicates the period, C is the phase shift, and D denotes the midline. With a Ferris wheel height of 4m and a diameter of 50m, the minimum value is 4 and the maximum is 54. Since the full 3 revolutions take 6 minutes, the period is determined accordingly. There is no phase shift here, so C = 0. We can substitute y=h(t), B=π, C=0, and D=29 into the general equation to find the function, ensuring it starts at the lowest point when t=0.
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