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Two robots in a factory move on parallel straight tracks. The two tracks are right next to each other. Engineers tested the robot control system. The graph shows the velocities, in meters per minute, of the robots A and B (functions are named for the robots) during the 10-minute test. The sign in the velocity values corresponds to direction: positive is right, negative is left. Use the graph to answer the following questions about the system test. a. How far and in what direction from the starting position is robot A after 6 minutes? Velocity b. How far and in what direction from the starting position is robot B at the end of the 10-minute test? What is the distance this robot travels during the 10-minute test? B(t) c. Use the graph to evaluate the integral , B(t) dt. Describe in words, and using the value you found, what this says about che corresponding robot.

Two robots in a factory move on parallel straight tracks. The two tracks are right next to each other. Engineers tested the robot control system. The graph shows the velocities, in meters per minute, of the robots A and B (functions are named for the robots) during the 10-minute test. The sign in the velocity values corresponds to direction: positive is right, negative is left. Use the graph to answer the following questions about the system test. a. How far and in what direction from the starting position is robot A after 6 minutes? Velocity b. How far and in what direction from the starting position is robot B at the end of the 10-minute test? What is the distance this robot travels during the 10-minute test? B(t) c. Use the graph to evaluate the integral , B(t) dt. Describe in words, and using the value you found, what this says about che corresponding robot.

Calculus: Early Transcendentals
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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**Two robots in a factory move on parallel straight tracks. The two tracks are right next to each other. Engineers tested the robot control system. The graph shows the velocities, in meters per minute, of the robots A and B (functions are named for the robots) during the 10-minute test. The sign in the velocity values corresponds to direction: positive is right, negative is left. Use the graph to answer the following questions about the system test.** **a. How far and in what direction from the starting position is robot A after 6 minutes?** **b. How far and in what direction from the starting position is robot B at the end of the 10-minute test? What is the distance this robot travels during the 10-minute test?** **c. Use the graph to evaluate the integral \(\int_{3}^{8} B(t) \, dt\). Describe in words, and using the value you found, what this says about the corresponding robot.** --- **Explanation of the Graph:** The graph displays velocity (in meters per minute) on the vertical axis and time (in minutes) on the horizontal axis, ranging from 0 to 10 minutes. - **Robot A's Velocity (A(t)):** - Starts at 0 m/min and increases linearly to 6 m/min at 3 minutes. - Remains constant at 6 m/min from 3 to 8 minutes. - Returns to 0 m/min at 10 minutes. - **Robot B's Velocity (B(t)):** - Starts at 0 m/min and decreases linearly to -4 m/min at 3 minutes. - Maintains -4 m/min from 3 to 6 minutes. - Increases linearly to 4 m/min at 9 minutes. - Returns to 0 m/min at 10 minutes.
Transcribed Image Text:**Two robots in a factory move on parallel straight tracks. The two tracks are right next to each other. Engineers tested the robot control system. The graph shows the velocities, in meters per minute, of the robots A and B (functions are named for the robots) during the 10-minute test. The sign in the velocity values corresponds to direction: positive is right, negative is left. Use the graph to answer the following questions about the system test.** **a. How far and in what direction from the starting position is robot A after 6 minutes?** **b. How far and in what direction from the starting position is robot B at the end of the 10-minute test? What is the distance this robot travels during the 10-minute test?** **c. Use the graph to evaluate the integral \(\int_{3}^{8} B(t) \, dt\). Describe in words, and using the value you found, what this says about the corresponding robot.** --- **Explanation of the Graph:** The graph displays velocity (in meters per minute) on the vertical axis and time (in minutes) on the horizontal axis, ranging from 0 to 10 minutes. - **Robot A's Velocity (A(t)):** - Starts at 0 m/min and increases linearly to 6 m/min at 3 minutes. - Remains constant at 6 m/min from 3 to 8 minutes. - Returns to 0 m/min at 10 minutes. - **Robot B's Velocity (B(t)):** - Starts at 0 m/min and decreases linearly to -4 m/min at 3 minutes. - Maintains -4 m/min from 3 to 6 minutes. - Increases linearly to 4 m/min at 9 minutes. - Returns to 0 m/min at 10 minutes.
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