alking along a straight path has her velocity in miles per hour at time t given by the function v(t) = 0.25t– 1.5t2 + 3t + 0.25, for times in the interval 0

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.1: Quadratic Functions And Models
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A person walking along a straight path has her velocity in miles per hour at time t given by the function v(t) = 0.25t – 1.5t2 + 3t + 0.25, for times in the interval 0 <t< 2. The
graph of this function is also given in each of the three diagrams below.
mph
mph
3-
mph
3-
y = v(1)
y=v(r)
y=v(t)
2-
2-
2
1.
1.
A4
A3
A2
B4
B3
B2
hrs
B1
hrs
hrs
A1
1
2
1
Note that in each diagram, we use four rectangles to estimate the area under y = v(t) on the interval [0, 2], but the method by which the four rectangles' respective heights are
decided varies among the three individual graphs.
Think about how the heights of the rectangles in the left-most diagram are being chosen. Determine the value of S = Aj + A2 + A3 + A4 by evaluating the function y = v(t) at
appropriately-chosen values and observing the width of each rectangle. Note, for example, that A3 = v(1) = 2. =1
S =
Use the rectangles in the middle diagram to find the value of T = B, + B2 + B3 + B4.
Т-
Use the rectangles in the right-most diagram to find the value of U = C, + C2 + C3 + C4
U =
Which estimate do you think is the best approximation of D, the total distance the person traveled on [0, 2|? Why?
Transcribed Image Text:A person walking along a straight path has her velocity in miles per hour at time t given by the function v(t) = 0.25t – 1.5t2 + 3t + 0.25, for times in the interval 0 <t< 2. The graph of this function is also given in each of the three diagrams below. mph mph 3- mph 3- y = v(1) y=v(r) y=v(t) 2- 2- 2 1. 1. A4 A3 A2 B4 B3 B2 hrs B1 hrs hrs A1 1 2 1 Note that in each diagram, we use four rectangles to estimate the area under y = v(t) on the interval [0, 2], but the method by which the four rectangles' respective heights are decided varies among the three individual graphs. Think about how the heights of the rectangles in the left-most diagram are being chosen. Determine the value of S = Aj + A2 + A3 + A4 by evaluating the function y = v(t) at appropriately-chosen values and observing the width of each rectangle. Note, for example, that A3 = v(1) = 2. =1 S = Use the rectangles in the middle diagram to find the value of T = B, + B2 + B3 + B4. Т- Use the rectangles in the right-most diagram to find the value of U = C, + C2 + C3 + C4 U = Which estimate do you think is the best approximation of D, the total distance the person traveled on [0, 2|? Why?
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