At least one of the answers above is NOT correct 2 of the qu

At least one of the answers above is NOT correct 2 of the questions remain unanswered. (1 point) The height, in meters, of person on a Ferris wheel above the ground as a function of t, the time after boarding in minutes, is given by /(1)--30cces ( t) + 35 a The period of this function is 30 b. The highest point in the ride is 65 meters above the floor It occurs for the first time 30 minutes after boarding che height of 56 meters occurs when cos( )- Thereare two values within, to, 2m] which ( could be equal to. These give two values of t within the frst turn for which the hoight is 56 meters Within a turm, the height remains above 56 meters for There are two values within (0,2m) which t could be equal o. minutes Note: You can eam partial credit on this problem

Solution

y = -30cos(pi*t/15) + 35

a) period :
The thing multiplied with t is pi/15

So, period = 2pi/(pi/15)

= 2pi * 15/pi

= 30

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Highest = -(-30) + 35 = 30 + 35 = 65

65 = -30cos(pi*t/15) + 35

cos(pi*t/15) = -1

pi*t/15 = pi

t = 15

15 min after boarding

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56 = -30cos(pi*t/15) + 35

30cos(pi*t/15) = 35 - 56

30cos(pi*t/15) = -21

cos(pi*t/15) = -0.7

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pi*t/15 = acos(-0.7)

Reference angle :
acos(0.7) = R = 0.795398830184

We need cos to be negative....
This happens in quadrants 2 and 3

Quad 2 angle = pi - R ---> 2.34619
Quad 3 angle = pi + R ---> 3.93699

So, we have
pi*t/15 = 2.34619
t1 = 11.20223

pi*t/15 = 3.93699
t2 = 18.7977

So, stays above 56 min
for 18.7977 - 11.20223

7.59547 min ----> ANS