Question

The largest Ferris Wheel in the world is the London Eye in England. The height (in meters) of a rider on the London Eye after t minutes can be described by the function h(t) = 65 sin[12(t − 7.5)] + 70. (15)
What is the diameter of this Ferris wheel?
Where is the rider at t = 0? Explain the significance of this value.
How high off the ground is the rider at the top of the wheel?
At what time(s) will the rider be at a height of 100 m?
How long does it take for the Ferris wheel to go through one rotation?
What is the minimum value of this function? Explain the significance of this value.

Answer 1

The height varies between h(t) = 5 and 135 because the sinus varies between -1 and +1.
a) so the diameter is 135 - 5 = 130 m (between highest and lowest point)
b) at t = 0 h(0) = 65.sin(-90) + 70 = 5, so this is its lowest point.
c) as mentioned above 135 m

Answer 2

What is the diameter of this Ferris wheel?
the diameter is 135 - 5 = 130 m (between highest and lowest point)

Where is the rider at t = 0? Explain the significance of this value.
at t = 0 h(0) = 65.sin(-90) + 70 = 5, so this is its lowest point.

How high off the ground is the rider at the top of the wheel?
135 m

At what time(s) will the rider be at a height of 100 m?
h(t) = 100 = 65.sin[12(t-7.5)] + 70 so sin(12.(t - 7.5) = 30/65 = 6/13
you can calculate the time t by looking up sin(a) = 6/13 and then t = a/12 + 7.5
there are of course 2 solutions (going up and going down)

How long does it take for the Ferris wheel to go through one rotation?
that is when is 12.(t - 7.5) = 360 degrees
t - 7.5 = 30
t = 37.5 minutes

Answer 3

I believe that is all parts

Answer 4

I hope that helps ^_^`

Answer 5

what about f ) and e)

Answer 6

What is the minimum value of this function? Explain the significance of this value.

Answer 7

Uhm... I don't know that last part... sorry ;~;

Answer 8

oh ok

Answer 9

np

Answer 10

I hope i was at least helpful for how much i could answer

Answer 11

yeah