[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.
=
15 cos (t) + 65, where h is the
1. The path of a swing could be modeled by the function h(t)
height in centimeters above the ground and t is the time in seconds.
lal+d
a. What is the maximum height of the swing? Determine using only the amplitude and midline.
115+ 65=80cm
b. How many seconds does it take to reach minimum height? Use the period and your
knowledge of the cosine function to determine this and show your calculations and/or
explain in words your reasoning.
b+c please y
c. Determine the height of the swing after 10 s have passed, algebraically. Round
your answer to the nearest tenth.
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).
Finite Mathematics & Its Applications (12th Edition)
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