An analog clock with a minute hand and an hour hand is placed in the center of the XY plane. At 12:00 AM, the tip of the minute hand has coordinates (0, 1) and the tip of the hour hand has coordinates (0, 1/2). (a) What is the first time after 12:00 AM, if any, where the instantaneous rate of change of the x-coordinate of the tip of the minute hand with respect to time zero? Write your final answer on the line below; if there is no such time write none. (b) Let h(t) be the smallest positive angle the hour hand makes with the positive x-axis (measured clockwise) at time t minutes after 12:00 AM, and let m(t) be the smallest positive angle the minute hand makes with the positive x-axis (measured clockwise) t minutes after 12:00 AM. What is the first time after 12:00 AM is dh/dm = 4? (c) Specify the largest interval of the form [0 minutes, x minutes) on which m is invertible
An analog clock with a minute hand and an hour hand is placed in the center of the XY plane. At 12:00 AM, the tip of the minute hand has coordinates (0, 1) and the tip of the hour hand has coordinates (0, 1/2).
(a) What is the first time after 12:00 AM, if any, where the instantaneous rate of change of the x-coordinate of the tip of the minute hand with respect to time zero? Write your final answer on the line below; if there is no such time write none.
(b) Let h(t) be the smallest positive angle the hour hand makes with the positive x-axis (measured clockwise) at time t minutes after 12:00 AM, and let m(t) be the smallest positive angle the minute hand makes with the positive x-axis (measured clockwise) t minutes after 12:00 AM. What is the first time after 12:00 AM is dh/dm = 4?
(c) Specify the largest interval of the form [0 minutes, x minutes) on which m is invertible
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