On a cold day, you measure the temperature inside your home to be a uniform 20 °C and the temperature outside to be -6 °C. The temperature in your walls, however, varies so that temperature as a function of position, T (x), is a continuous function. Based on the composition of your 6 cm thick walls, you are able to construct the following piecewise model for T(x): T(x) = { 20, x≤0 a-br², 0 < x < 6. x ≥ 6 -6, (a) Determine a and b so that T(x) is continuous. a = Number b Number (b) What is the temperature in the middle of the wall (i.e., 3 cm in)? °C Number
On a cold day, you measure the temperature inside your home to be a uniform 20 °C and the temperature outside to be -6 °C. The temperature in your walls, however, varies so that temperature as a function of position, T (x), is a continuous function. Based on the composition of your 6 cm thick walls, you are able to construct the following piecewise model for T(x): T(x) = { 20, x≤0 a-br², 0 < x < 6. x ≥ 6 -6, (a) Determine a and b so that T(x) is continuous. a = Number b Number (b) What is the temperature in the middle of the wall (i.e., 3 cm in)? °C Number
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:On a cold day, you measure the temperature inside your home to be a uniform 20 °C and
the temperature outside to be -6 °C.
The temperature in your walls, however, varies so that temperature as a function of
position, T (x), is a continuous function. Based on the composition of your 6 cm thick
walls, you are able to construct the following piecewise model for T(x):
T(x) =
{
20,
a-br²,
-6,
(a) Determine a and b so that T(x) is continuous.
a = Number
b
Number
x≤0
0 < x < 6.
x ≥ 6
(b) What is the temperature in the middle of the wall (i.e., 3 cm in)?
°C
Number
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