Answered: The minute hand of a wall clock…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.6: Symmetry And Transformations

Problem 26E: Considering that the consecutive dials on the natural gas meter rotate in opposite directions, what...

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The minute hand of a wall clock measures 24 cm from its tip to the axis about which it rotates. The magnitude and angle of the displacement vector of the tip are to be determined for three time intervals. What are the magnitude and angle from a quarter after the hour to half past, the magnitude and angle for the next half hour, and the magnitude and angle for the hour after that? (Use a coordinate system with the origin at the clock center, +x rightward toward the "3:00" position, and +y upward toward the "12:00" position.)

(a) the magnitude from a quarter after the hour to half past
cm

(b) the angle from a quarter after the hour to half past
° (counterclockwise from the +x-axis)

(c) the magnitude for the next half hour
cm

(d) the angle for the half hour in part (c)
° (counterclockwise from the +x-axis)

(e) the magnitude for the hour after that
cm

(f) What is the angle for the hour in part (e)
° (counterclockwise from the +x-axis)

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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