A roof line. The automobile shop shown in Figure 1.10 is 50 feet wide. If we take t = 0 to be the location of the west wall, then the height of the roof at a distance of t horizontal feet from the west wall is given by H = 11+0.5t feet. This formula is valid until we reach the peak, 25 feet from the west wall. If instead we think of t = 0 as the location of the peak, then the roof from the peak to east wall follows H = 23.5 -0.5t feet, where t is the horizontal distance in feet from the peak. This is valid up to the east wall 25 feet from the peak. Using T = 0 as the horizontal distance in feet from the west wall, find a piecewise-defined function that gives the height of the roof in terms of T.
A roof line. The automobile shop shown in Figure 1.10 is 50 feet wide. If we take t = 0 to be the location of the west wall, then the height of the roof at a distance of t horizontal feet from the west wall is given by H = 11+0.5t feet. This formula is valid until we reach the peak, 25 feet from the west wall. If instead we think of t = 0 as the location of the peak, then the roof from the peak to east wall follows H = 23.5 -0.5t feet, where t is the horizontal distance in feet from the peak. This is valid up to the east wall 25 feet from the peak. Using T = 0 as the horizontal distance in feet from the west wall, find a piecewise-defined function that gives the height of the roof in terms of T.
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:in
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101. A roofline. The automobile shop shown in
Figure 1.10 is 50 feet wide. If we take t = 0 to be
the location of the west wall, then the height of the
roof at a distance of t horizontal feet from the west
wall is given by H = 11+0.5t feet. This formula is
valid until we reach the peak, 25 feet from the west
wall. If instead we think of t = 0 as the location
of the peak, then the roof from the peak to east
wall follows H = 23.5 -0.5t feet, where t is the
horizontal distance in feet from the peak. This
is valid up to the east wall 25 feet from the peak.
Using T = 0 as the horizontal distance in feet from
the west wall, find a piecewise-defined function
that gives the height of the roof in terms of T.
H = 11 +0.5t
25
AUTO BODY
Repair Shop
West
wall
Figure 1.10 An automobile shop
H = 23.5 0.5t
25
East
wall
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