Calculating Average Temperature Using Integrals

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Homework Help Overview

The problem involves calculating the average temperature in a city over a specified time period using an integral of a temperature function modeled by T(t) = 50 + 14 sin(πt / 12). The time frame for the calculation is from 9 am to 9 pm.

Discussion Character

  • Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the correct limits of integration for the average temperature calculation, with some suggesting different interpretations of the time frame.

Discussion Status

There is ongoing clarification regarding the limits of integration, with some participants confirming that the limits should be set from 9 to 21 in 24-hour notation, while others reflect on previous misunderstandings about the time frame.

Contextual Notes

Participants are navigating the specifics of the time intervals and the implications of the temperature model, indicating some confusion about the correct setup for the integral.

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A certain city, the temp in degrees Farenheit, t hrs after 9 am was modeled by the function: T(t)=50 + 14 sin (Pi t / 12)
Find avg temp during the period from 9 am to 9 pm.

What i did was take the Int[50 + 14 sin (Pi t / 12),t,0,9]... but this doesn't produce the answer. It says model after 9 am so at 9=0 for a , b = 10 for 9pm?
Any help?
 
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shouldnt b be 12 and not 10 since it is 12 hours from 9am - 9pm
 
Set your limits a,b to a = 9 and b = 21 (using 24-hr notation)
 
i tried 9 to 21 and it didnt work before...
 
it works from 0 to 12, thanks, don't know why i thought 10 DUH
 

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