1. The temperature of a city t hours after 8:00 am Is modeled (in degrees Fahrenheit) by the function T(t) = 70+ 19 sin(nt/12). According to the model, what is the average temperature over the time period from 8:00 am to 10:00 pm?"O114B.1.² (70+ 19 sin(nt/12))dt["OD. None of these114O●A.E(70+ 19 sin(nt/12)dt(70+ 19 sin(mt/12)) dt(70+ 19 sin(nt/12))dt

Given that Recall the fact that if be any function of t, then the average integral is…

Answered: 1. The temperature of a city t hours…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

1. The temperature of a city t hours after 8:00 am Is modeled (in degrees Fahrenheit) by the function T(t) = 70+ 19 sin(nt/12). According to the model, what is the average temperature over the time period from 8:00 am to 10:00 pm?
"
O
1
14
B.
1.² (70+ 19 sin(nt/12))dt
["
OD. None of these
1
14
O
●
A.
E
(70+ 19 sin(nt/12)dt
(70+ 19 sin(mt/12)) dt
(70+ 19 sin(nt/12))dt

Expert Solution

Step 1: "Introduction to the solution"

Given that $T left parenthesis t right parenthesis equals 70 plus 19 sin open parentheses fraction numerator pi t over denominator 12 end fraction close parentheses comma t element of open square brackets 8 comma 10 close square brackets$

Recall the fact that if $T left parenthesis t right parenthesis space$ be any function of t, $t element of open square brackets a comma b close square brackets$ then the average integral is $fraction numerator 1 over denominator left parenthesis b minus a right parenthesis end fraction integral subscript a superscript b f left parenthesis t right parenthesis d t........ left parenthesis 1 right parenthesis$

We have to used thius fact.