Posted by **Aviana** on Tuesday, February 1, 2011 at 6:17pm.

Recorded data indicates that on a recent date t hours past midnight, the temperature at Logan airport was

f(t) = 14sin(1/3t-2) + 60

degrees Fahrenheit. What was the average temperature between 9 am and noon?

- Calculus-parentheses -
**MathMate**, Tuesday, February 1, 2011 at 7:56pm
f(t) = 14sin(t/3-2) + 60

∫f(t)dt from 9 to 12

=[ 60*t-42*cos(t/3-2) ] from 9 to 12

=220.17

Average temperature over 3 hours

= 220.17/3

= 73.4°

Note to Aviana:

in the absence of parentheses, multiplications and divisions are performed before additions and subtractions.

Even when 14sin(1/3t-2) + 60 is interpreted correctly as 4sin(t/3-2) + 60, it is a good idea to insert parentheses to emphasize the intention, such as : 4sin((1/3)t-2) + 60

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