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Answer :
Sure! Let's break down the solution for each part of the question using function notation:
a. The temperature at 12 p.m.
To find the temperature at 12 p.m., remember that 12 p.m. is 12 hours after midnight. In function notation, we denote time in hours after midnight, so 12 p.m. would be represented as 12. Therefore, the expression for the temperature at 12 p.m. is:
[tex]\[ f(12) = T \][/tex]
b. The temperature was the same at 9 a.m. and at 4 p.m.
First, note that 9 a.m. is 9 hours after midnight, and 4 p.m. is 16 hours after midnight (since 4 p.m. is 12 + 4 = 16 hours after midnight). We need to express that the temperatures at these two times are equal. In function notation, this is represented by:
[tex]\[ f(9) = f(16) \][/tex]
c. It was warmer at 9 a.m. than at 6 a.m.
Here, 9 a.m. is 9 hours after midnight, and 6 a.m. is 6 hours after midnight. To indicate that the temperature at 9 a.m. was higher than at 6 a.m., we use the greater than symbol in function notation:
[tex]\[ f(9) > f(6) \][/tex]
d. Some time after midnight, the temperature was 24 degrees Celsius.
This statement is about the existence of a time, `t`, after midnight when the temperature reached 24 degrees Celsius. In function terms, we want to show there is a time `t` greater than 0 where the temperature equals 24. Hence, we write:
[tex]\[ \text{exists } t > 0 \text{ such that } f(t) = 24 \][/tex]
These expressions capture the conditions described in the problem using function notation correctly.
a. The temperature at 12 p.m.
To find the temperature at 12 p.m., remember that 12 p.m. is 12 hours after midnight. In function notation, we denote time in hours after midnight, so 12 p.m. would be represented as 12. Therefore, the expression for the temperature at 12 p.m. is:
[tex]\[ f(12) = T \][/tex]
b. The temperature was the same at 9 a.m. and at 4 p.m.
First, note that 9 a.m. is 9 hours after midnight, and 4 p.m. is 16 hours after midnight (since 4 p.m. is 12 + 4 = 16 hours after midnight). We need to express that the temperatures at these two times are equal. In function notation, this is represented by:
[tex]\[ f(9) = f(16) \][/tex]
c. It was warmer at 9 a.m. than at 6 a.m.
Here, 9 a.m. is 9 hours after midnight, and 6 a.m. is 6 hours after midnight. To indicate that the temperature at 9 a.m. was higher than at 6 a.m., we use the greater than symbol in function notation:
[tex]\[ f(9) > f(6) \][/tex]
d. Some time after midnight, the temperature was 24 degrees Celsius.
This statement is about the existence of a time, `t`, after midnight when the temperature reached 24 degrees Celsius. In function terms, we want to show there is a time `t` greater than 0 where the temperature equals 24. Hence, we write:
[tex]\[ \text{exists } t > 0 \text{ such that } f(t) = 24 \][/tex]
These expressions capture the conditions described in the problem using function notation correctly.
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