[T] Suppose that T = 50 + 10 sin [ π 12 ( t − 8 ) ] is a mathematical model of the temperature (in degrees Fahrenheit) at t hours after midnight on a certain day of the week. Determine the amplitude and period. Find the temperature 7 hours after midnight. At what time does T = 60°? Sketch the graph of T over 0 ≤ t ≤ 24 .
[T] Suppose that T = 50 + 10 sin [ π 12 ( t − 8 ) ] is a mathematical model of the temperature (in degrees Fahrenheit) at t hours after midnight on a certain day of the week. Determine the amplitude and period. Find the temperature 7 hours after midnight. At what time does T = 60°? Sketch the graph of T over 0 ≤ t ≤ 24 .
[T] Suppose that
T
=
50
+
10
sin
[
π
12
(
t
−
8
)
]
is a mathematical model of the temperature (in degrees Fahrenheit) at t hours after midnight on a certain day of the week.
The temperature, A, of a chemical reaction oscillates between a low of 30oC and high of 110oC. The temperature is at its lowest point when t = 0 and completes one cycle over a five-hour period.
Sketch a graph of A, against elapsed time, t, over a ten-hour period. Pay careful attention to concavity and inflection points and where they occur.
Find the period, the amplitude, and the midline of the graph that you drew in part a).
. Graph the function:
Y=sin-(2x) –
2
A Ferris wheel is 29 meters in diameter and boarded from a platform that is 1 meter above the ground.
The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1
full revolution in 12 minutes. The function h (t) gives a person's height in meters above the ground t
minutes after the wheel begins to turn.
a. Find the amplitude, midline, and period of h (t).
Enter the exact answers.
Amplitude: A = Number
Midline: h
Period: P = Number
= Number
meters
meters
minutes
b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel
starts spinning at time t = 0. Find a formula for the height function h (t).
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