Clock Hands: 180 Degree Angle in 24 Hours

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SUMMARY

The discussion focuses on calculating the number of times the hour and minute hands of a clock form a 180-degree angle within a 24-hour period. The formula provided, ANGLE = 30H - (11/2)M, is essential for determining the angle between the hour and minute hands. By setting the equation to 180 degrees, users can solve for the values of H (hours) and M (minutes) that satisfy this condition. The solution reveals that the hands align at 180 degrees 22 times in a day.

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  • Understanding of basic clock mechanics
  • Familiarity with algebraic equations
  • Knowledge of angles and their measurement
  • Ability to solve linear equations
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  • Learn how to derive the formula for clock angles
  • Explore the concept of angular velocity in clock hands
  • Investigate the relationship between hour and minute hand movements
  • Practice solving similar problems involving angles and time
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Students, educators, and anyone interested in mathematical problem-solving related to time and angles, particularly in the context of clock mechanics.

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Homework Statement



Hi , How Many Times in A day 2 of 3 clock hands makes the angle of 180 degree with each other ?
 
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What do you think? This looks like homework, and our job as helpers and mentors is to help you do your homework rather than doing your homework for you.
 
I Just Find This Formula :

Angle BetWeen Min And Hour Is : ANGLE = 30H - (11/2)M

But I Do'nt Know how to solve it And Find the H And M That ANGLE=180 ;
 

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