A classmate is building a mathematical model for the temperature in his home during the summer. He explains that, without air conditioning, his home is hottest at 3:00 p.m. His model considers temperature, T, in degrees Fahrenheit, as a function of the number of hours since 6:00 a.m., h. He produces the equation, T (h) = -12 cos( (h – 1)) + 75. Why might his equation be invalid for this situation? O The period of 12 hours indicates that two highs occur throughout the day. O The maximum temperature for the function doesn't occur at 3:00 p.m. in the model. The amplitude must be incorrect. O The sine function is more accurate in modeling these temperatures. O The maximum temperature for the function doesn't occur at 3:00 p.m. in the model. The horizontal shift must be incorrect.
A classmate is building a mathematical model for the temperature in his home during the summer. He explains that, without air conditioning, his home is hottest at 3:00 p.m. His model considers temperature, T, in degrees Fahrenheit, as a function of the number of hours since 6:00 a.m., h. He produces the equation, T (h) = -12 cos( (h – 1)) + 75. Why might his equation be invalid for this situation? O The period of 12 hours indicates that two highs occur throughout the day. O The maximum temperature for the function doesn't occur at 3:00 p.m. in the model. The amplitude must be incorrect. O The sine function is more accurate in modeling these temperatures. O The maximum temperature for the function doesn't occur at 3:00 p.m. in the model. The horizontal shift must be incorrect.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A classmate is building a mathematical model for the temperature in his home during the
summer. He explains that, without air conditioning, his home is hottest at 3:00 p.m. His model
considers temperature, T, in degrees Fahrenheit, as a function of the number of hours since
6:00 a.m., h. He produces the equation, T (h) = -12 cos( (h – 1)) + 75. Why might his
equation be invalid for this situation?
O The period of 12 hours indicates that two highs occur throughout the day.
O The maximum temperature for the function doesn't occur at 3:00 p.m. in the model. The
amplitude must be incorrect.
O The sine function is more accurate in modeling these temperatures.
O The maximum temperature for the function doesn't occur at 3:00 p.m. in the model. The
horizontal shift must be incorrect.
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