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Topic: Clock Angles (Read 728 times) |
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Benoit_Mandelbrot
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Clock Angles
« on: Apr 28th, 2004, 9:30am » |
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This is about analog clocks.
a) The time is 3:10. What is the smaller angle between the two hands?
b) Develop a formula to find the angle at any given time.
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towr
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Re: Clock Angles
« Reply #1 on: Apr 28th, 2004, 9:58am » |
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::
for time XX:YY
angle = min( |30 XX - 5.5 YY| , 360-|30 XX - 5.5 YY| )
so 35 degrees for 3:10
::
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Wikipedia, Google, Mathworld, Integer sequence DB
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Icarus
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Re: Clock Angles
« Reply #2 on: Apr 28th, 2004, 6:57pm » |
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I don't think so! ::Since it is 10 after, the minute hand is pointing exactly at 2. The hour hand should be 1/6 of the way from 3 to 4. Each division is 20o, so the separation should be (20+20/6) degrees = 23o20'.::
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ThudnBlunder
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Re: Clock Angles
« Reply #3 on: Apr 28th, 2004, 9:52pm » |
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Quote:
Hmm...
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rmsgrey
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Re: Clock Angles
« Reply #4 on: Apr 29th, 2004, 3:48am » |
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Obviously Icarus uses the well known 18 hour clock!
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Sameer
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Re: Clock Angles
« Reply #5 on: Apr 29th, 2004, 8:13am » |
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on Apr 29th, 2004, 3:48am, rmsgrey wrote:| Obviously Icarus uses the well known 18 hour clock! |
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Hehe 
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jtrook
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Re: Clock Angles
« Reply #6 on: Apr 29th, 2004, 10:08am » |
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Towr, your solution is excellent. I searched for another formula to find the angle and every attempt lead me back to the same thing - the formula you posted.
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Benoit_Mandelbrot
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Re: Clock Angles
« Reply #7 on: Apr 29th, 2004, 10:24am » |
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Towr's solution is the correct one. The answer is ::35 degrees::.
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Icarus
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Re: Clock Angles
« Reply #8 on: Apr 29th, 2004, 3:15pm » |
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Sheesh! I had a rough day yesterday, but I didn't think I'd sunk that low! 
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"Pi goes on and on and on ...
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I wonder: Which is larger
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Sir Col
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Re: Clock Angles
« Reply #9 on: Apr 29th, 2004, 4:43pm » |
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Oh well, I'm sure that your low day indirectly lifted many of our mediocre days with a bit of a chuckle. I hope this day was better for you.
I feel like I could do with one of those 18 hour clocks somedays; imagine what I could do with an extra 12 hours per day! Then it would be just the small matter of slowing the earth's rotation to coincide.
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Icarus
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Re: Clock Angles
« Reply #10 on: Apr 29th, 2004, 6:16pm » |
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Certain days (such as I have been having all week), do not need extended! Shortening would be much more appropriate! 
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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Sir Col
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Re: Clock Angles
« Reply #11 on: Apr 30th, 2004, 4:55am » |
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Good point!
Perhaps we could maintain the average of 24 hours per day, but make Monday to Friday last 4 hours 48 minutes each (24 hours in total), and split Saturday and Sunday equally between the remaining 144 hours. As we normally work around 8 hours of a 24 hour cycle, we could excuse the fact that we didn't turn up to work until late on "Tuesday" by boasting about working all through "Wednesay" and most of "Thursday" with only an hour lunch break. Surely that would entitle us to take the rest of the week off?
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ljoynich
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Re: Clock Angles
« Reply #12 on: May 6th, 2005, 12:23pm » |
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Re analog clock angle for 3:10.
Every 5 minutes represents 30 degrees.
so when it's 10 minutes after the hour that = 30 degrees.
The hour hand will also move 1/12 of 30 degrees each 5 minutes.
So 2/12 x 30 = 5 degrees plus the 30 degrees = a total of 35 degrees. (A solution by one of my seventh grade students)
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