Calculus
posted by Aviana .
Recorded data indicates that on a recent date t hours past midnight, the temperature at Logan airport was
f(t) = 14sin(1/3t2) + 60
degrees Fahrenheit. What was the average temperature between 9 am and noon?

f(t) = 14sin(t/32) + 60
∫f(t)dt from 9 to 12
=[ 60*t42*cos(t/32) ] 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(1/3t2) + 60 is interpreted correctly as 4sin(t/32) + 60, it is a good idea to insert parentheses to emphasize the intention, such as : 4sin((1/3)t2) + 60
Respond to this Question
Similar Questions

algebra1
at midnight, the temperature was12degrees F. by noon, the temperature had risen 25degrees F. durinh afternoon, it fell to 10degrees f ANOTHER 3 degrees f by midnight. what was the temperature at midnight? 
calculus
In a certain city the temperature (in degrees Fahrenheit) t hours after 9 a.m. was approximated by the function T(t) = 50 + 14sin((pi*t)/12). Find the average temperature (in degrees Fahrenheit) during the period from 9 a.m. to 9 p.m. … 
Algebra
At noon the temperature is 30 degree F. For the next several hours the temperature falls by an average of 3 degrees F an hour. What's the equation for the temperature and the hours after noon? 
Math
Problem Solving: Work Backward At 12 noon, Leslie recorded the temperature as 56 degree Fahrenheit. The temperature had increased by 8 degree Fahrenheit from 10 a.m. The temperature at 8 a.m. was 2 degree Fahrenheit warmer than it … 
MATH
1 My Math problem Intergers 2(2) = 4 iS 4 CORRECT 2.Between noon and 3pm, temp dropped 9 degrees (f). It increased 4 degrees (f) between 39m & 5pm and dropped 15 degrees(F) between 5om and midnight.If the temperature was 2 degrees … 
Algebra
Stella is recording temperatures every day for 5 days. On the first day, Stella recorded a temperature of 0 degrees Farenheit. A. On the second day, the temperature was 3 degrees Fahrenheit above the temperature on the first day. What … 
think tac toe 2 adding and subracting decimals 2.
Tim tracked the change in outside temperature one afternoon. He record a temperature of 98.3 degrees at noon. Bathe temperature then rose 5.32 degrees f over the next four hours at 5:00 pm. Tim recorded a temperature change of 108.57 … 
PreCalc
The temperature T(t) varies sinusoidally on a certain day in December. The minimum temperature is 35 degrees Fahrenheit at midnight. The maximum temperature is 50 degrees Fahrenheit at noon. Let t be the number of hours since midnight … 
Math
Between midnight and 6:00am, the temperature dropped 10 degrees F. Between 6 am and 12:00; the temperature rose 18 degrees F.What was the change in the temperature from midnight to noon. I can't seem to get the formula for this problem 
sir damon steve damon damon help maths
Record, indicate that t hours past midnight, the temperature at the local airport was T(t)=0.3t^2+4t+10degree celcius. What was average temperature in farenheit at airport between 9am and noon?