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serious [3.7K]
3 years ago
11

The function f(t) = 33 sin (pi over 2t) − 20 models the temperature of a periodic chemical reaction where t represents time in h

ours. What are the maximum and minimum temperatures of the reaction, and how long does the entire cycle take? (5 points)
Maximum: 53°; minimum: −13°; period: 4 hours

Maximum: 33°; minimum: 20°; period: pi over 2 hours

Maximum: 13°; minimum: −53°; period: 4 hours

Maximum: 35°; minimum: 35°; period: 8 hours
Mathematics
1 answer:
Gennadij [26K]3 years ago
4 0
The given function is
f(t) = 33 sin( \frac{ \pi }{2} t) - 20
with
t = time, hours
f = temperature, °C


Because the maximum and minimum values for the Sine function are +1 and -1 respectively,
The maximum value of f  = 33 - 20 = 13.
The minimum value of f = -33 - 20 = -53. 

The period, T,  is given by
\frac{2 \pi }{T} = \frac{ \pi }{2} \\ \\ T=4

Answer:
Maximum: 13°;  Minimum: -53°;  period: 4 hours
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