Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America can be found on the Great Plains in the state of North Dakota on state high- way 46, which lies just south of the interstate highway I-94 and runs through the town of Gackle. A car leaves town (at time t = 0) and heads east on highway 46; its posi- tion in miles from Gackle at time f in minutes is given by the graph of the function in Figure 1.5.1. Three important points are labeled on the graph; where the curve looks linear, assume that it is indeed a straight line. a. In everyday language, describe the behavior of the car over the provided time interval. In particular, discuss what is happening on the time intervals [57,68] and [68, 104].

Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America can be found on the Great Plains in the state of North Dakota on state high- way 46, which lies just south of the interstate highway I-94 and runs through the town of Gackle. A car leaves town (at time t = 0) and heads east on highway 46; its posi- tion in miles from Gackle at time f in minutes is given by the graph of the function in Figure 1.5.1. Three important points are labeled on the graph; where the curve looks linear, assume that it is indeed a straight line. a. In everyday language, describe the behavior of the car over the provided time interval. In particular, discuss what is happening on the time intervals [57,68] and [68, 104].

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 33EQ

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Question

Please try not to use derivatives or integrals to calculate the stuff. Thank you.

Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North
America can be found on the Great Plains in the state of North Dakota on state high-
way 46, which lies just south of the interstate highway I-94 and runs through the town
of Gackle. A car leaves town (at time t = 0) and heads east on highway 46; its posi-
tion in miles from Gackle at time f in minutes is given by the graph of the function in
Figure 1.5.1. Three important points are labeled on the graph; where the curve looks
linear, assume that it is indeed a straight line.
a. In everyday language, describe the behavior of the car over the provided time
interval. In particular, discuss what is happening on the time intervals [57,68]
and [68, 104].

value.
(104, 106.8)
100
80
(57,63.8)
60+
(68, 63.8)
40+
20-
20 40 60 80 100
Figure 1.5.1: The graph of y = s(t), the position of the car along highway 46, which
tells its distance in miles from Gackle, ND, at time t in minutes.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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