Question 289724
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The equation you need for the clock is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{60}{5.5}h]


Where h is the hour number nearest the hour hand, noon being hour 0, and then m is the number of minutes where the hands are exactly superimposed.


For your situation, h = 1, so *[tex \Large m\ =\ \frac{60}{5.5}\ =\ 5\frac{5}{11}\ =\ 5.\overline{45}]


The equation follows from the fact that the angle between the two hands of a clock is found by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos^{-1}(\cos{5.5x})]


where *[tex \Large x] is the time of day expressed in minutes past noon, and you  have to set that expression equal to zero because when the hands are superimposed the angle between them is zero.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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