Question 1117661
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It takes the minute hand one hour to complete an entire circle, i.e. it is moving at 360 degrees per hour or 6 degrees per minute.  Since there are 12 hours on the clock, and 360 divided by 12 is 30, the hour hand moves at a rate of 30 degrees per hour, or one-half degree per minute.


At exactly 8 o'clock, the hour hand points exactly to the 8 which is at a position of 240 degrees measured clockwise from 0 (i.e. 12).  The minute hand points to 12, which is 0 degrees.


So the function that describes the motion of the hour hand during the interval from 8 to 9 o'clock is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ h(x)\ =\ 0.5x\ +\ 240]


And the function that describes the motion of the minute hand during the interval from 8 to 9 is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m(x)\ =\ 6x]


Where *[tex \Large x] is the number of minutes past 8.  When these two functions are equal, the hands point to the same place.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6x\ =\ 0.5\ +\ 240]


Solve for *[tex \Large x]


Straight up, this will give you the number of minutes with a decimal fraction.  If you want the answer in minutes and seconds, take just the decimal fraction part and multiply it by 60.


Don't forget to add the minutes to 8 o'clock to get the time of day this occurs.  Alternatively, you can specify that your answer represents minutes after 8 o'clock.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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