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06 Aug 2024, 01:17
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
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Question Stats:
59% (02:36) correct
41%
(02:32)
wrong
based on 81
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The temperature of the room is measured using a thermostat. According to the thermostat, the temperature C(t) + -0.2 (t-a)^2 + 50, where 0≤ t ≤ 24 and a>0. If at 2:00 am. the temperature of the room is 30 degree Celsius, the according to the thermostat at what time does the room have the maximum temperature.
A. 10:00 AM
B. 11:00 AM
C. 12:00 PM
D. 1:00 PM
E. 2:00 PM
A. 10:00 AM
B. 11:00 AM
C. 12:00 PM
D. 1:00 PM
E. 2:00 PM
09 Aug 2024, 12:33
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To determine the time at which the room has the maximum temperature according to the given function:
C(t) = -0.2(t - a)^2 + 50
### Given:
- The function for temperature:
C(t) = -0.2(t - a)^2 + 50
- The temperature at 2:00 AM (which we can denote as t = 2):
C(2) = 30
### Step 1: Find the value of [a]
Substituting t = 2 into the temperature function:
C(2) = -0.2(2 - a)^2 + 50 = 30
Now, we can solve for [a]:
-0.2(2 - a)^2 + 50 = 30
-0.2(2 - a)^2 = 30 - 50
-0.2(2 - a)^2 = -20
(2 - a)^2 = -20/-0.2 = 100
2 - a = + or - 10
This gives us two possible equations:
1. 2 - a = 10 → a = -8 (not valid since a > 0)
2. 2 - a = -10 → a = 12
### Step 2: Determine the maximum temperature
The function C(t) = -0.2(t - 12)^2 + 50 is a downward-opening parabola, and its maximum occurs at the vertex, which is at t = a = 12.
### Conclusion
Thus, the maximum temperature occurs at:
12:00 PM (noon)
### Answer:
C. 12:00 PM
