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03-02-2013, 08:51 PM | #16 |
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My youngest son took first overall in the state for the individual portion (his team took 2nd for the team part) when he was in 5th grade /proud papa
I went up through Differential Equations in college and look at these questions now and feel stupid. |
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03-02-2013, 08:55 PM | #17 |
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03-02-2013, 08:58 PM | #18 |
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Is there an explanation for it or it just a pattern to remember? The "10's " are trivial and I remembered the "9's" trick from school but explaining the pairs was trickier other than "it just is".
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03-02-2013, 09:09 PM | #19 |
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What trick? That any 2 digit number whose digits add up to 9 is also divisible by 9?
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03-02-2013, 09:16 PM | #20 |
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The relationship in the pairs is:
(2a*10+a)/3a = 7 and (a*10+2a)/3a = 4 for a = 1,2,3,4 That's the why, but the way you would "just know it" would be playing with numbers all the time. |
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03-02-2013, 09:17 PM | #21 |
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More like the digits of the multiples of 9 from 1 to 10 add up to 9. Not really a trick, I guess. I think the back of my mind was also thinking about how transposed numbers are divisible by 9 when I wrote "trick".
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03-02-2013, 09:34 PM | #22 |
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03-02-2013, 09:58 PM | #23 |
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03-02-2013, 10:02 PM | #24 |
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03-02-2013, 10:21 PM | #25 | |
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Quote:
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03-03-2013, 05:10 PM | #26 | |
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I have a new one. It's driving us nuts because it seems straightforward but we are not getting the answer they give so we must be missing something.
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03-03-2013, 05:34 PM | #27 |
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Drinking does not make this easier.
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03-03-2013, 07:38 PM | #28 |
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Are you getting 1+sqrt(2) ?
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03-03-2013, 07:47 PM | #29 |
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03-03-2013, 07:54 PM | #30 |
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Let a be the speed of the column, b the speed of the officer, and x be the the length of the column. Let t' be the time for the officer to reach the front of the column and t be the total time. We then get the following relationships:
at = x bt' = at' + x bt = 2at' + x Do a bunch of algebra and get b/a = 1+sqrt(2) Let me know if it isn't working out. |
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