Boba Rhett Posted December 1, 2007 Share Posted December 1, 2007 Do you know how many exams I would have failed without trial and error? Heck, do you know how many unfinished work projects I'd have without trial and error? Link to comment Share on other sites More sharing options...
tk102 Posted December 1, 2007 Author Share Posted December 1, 2007 I'd say trial and error is where math leaves off and engineering begins. Part of being an engineer is knowing how precise you have to be in any given context and then adjusting your problem-solving accordingly to minimize costs in terms of money or, in this case, time. Link to comment Share on other sites More sharing options...
tk102 Posted January 30, 2008 Author Share Posted January 30, 2008 What values of x (besides 0) satisfy this series: x = x^3/3! - x^5/5! + x^7/7! - x^9/9! ... Link to comment Share on other sites More sharing options...
tk102 Posted January 31, 2008 Author Share Posted January 31, 2008 Nobody recognized the sine series? sin(x) = x - x^3/3! + x^5/5! - x^7/7! + x^9/9! ... In the previous post, the equation could be rewritten: x - x^3/3! + x^5/5! - x^7/7! + x^9/9! ... = 0 by position then, sin(x) =0 therefore x is a multiple of pi Trying it on the calculator with 5 terms: pi^3/6 - pi^5/120 + pi^7/5040 - pi^9/362880 + pi^11/39916800 = 5.1677 - 2.5502 + 0.5993 - 0.0821 + 0.0074 = 3.1421 (3 decimal place accuracy) At 12 terms (i.e. up to pi^25/25!), you get 11 decimal places. At 20 terms (i.e. up to pi^33/33!), you get 21 decimal places though I really don't trust MS Excel beyond 16 digits. Definitely not the fastest convergence. Link to comment Share on other sites More sharing options...
tk102 Posted July 30, 2008 Author Share Posted July 30, 2008 If you have a clock that represents time as hexadecimal (that is 16 hours per day), how much "normal" time would have to pass for the minute hand to travel from one hexdigit to the next? Link to comment Share on other sites More sharing options...
JCarter426 Posted July 30, 2008 Share Posted July 30, 2008 24*60=1440; 1440/16=90 --> 90 minutes per hour Judging from the picture, that's a 16 hour clock, so... 90/16=5.265 --> 5.625 minutes...I think. Link to comment Share on other sites More sharing options...
tk102 Posted July 30, 2008 Author Share Posted July 30, 2008 5.6255 minutes You are correct! Two follow-ups: 1. If there are 16 divisions per number, and the second hand and the minute hand "tick" on these divisions, how long is a hex-minute in real time? How long is a hex-second in real time? 2. What time is it on the clock above (A_D9_00)? Link to comment Share on other sites More sharing options...
tk102 Posted July 31, 2008 Author Share Posted July 31, 2008 1. If there are 16 divisions per number, and the second hand and the minute hand "tick" on these divisions, how long is a hex-minute in real time? How long is a hex-second in real time? If there are 16 divisions per number, and 16 numbers per revolution, there 256 divisions per revolution. If the hex-minute hand travels 16 divisions in 5.6255 minutes as JCarter426 deduced, then one 1 hex-minute = 5.6255/16 = 21.09 seconds. A hex-second then is 21.09/256 = 0.0824 seconds. Alternative solution: 1 day = 16 hex-hours 1 hex-hour = 256 hex-minutes 1 hex-minute = 256 hex-seconds 1 day = 256*256*16 = 1048576 hex-seconds = 86400 normal seconds 1 hex second * 86400 sec/104876 hex-sec = 0.8238 seconds 2. What time is it on the clock above (A_D9_00)? Using a hexadecimal calculator to translate the hexclock time 0xAD900 = 710912 (hex-seconds) Then 710912 hexseconds since midnight = 58577 normal seconds = 16 hours 16 minutes 17 seconds or 4:16:17pm Link to comment Share on other sites More sharing options...
JCarter426 Posted August 1, 2008 Share Posted August 1, 2008 ...5.6255 minutes as JCarter426 deduced It's actually just 5.625; I made a bit of a typo. Link to comment Share on other sites More sharing options...
tk102 Posted August 1, 2008 Author Share Posted August 1, 2008 The spamfest in this thread has been moved here Link to comment Share on other sites More sharing options...
ForeverNight Posted October 8, 2008 Share Posted October 8, 2008 Hmmm... Well, here's one! Since nobody seems to be putting forward any new math. 2X+1=2X-1 Believe it or not, this actually does work out! Oh, and X!=0 Link to comment Share on other sites More sharing options...
tk102 Posted October 8, 2008 Author Share Posted October 8, 2008 Hmm.... maybe: X = sqrt (1/4) which has two answers: X₁ = +1/2 X₂ = -1/2 2X₂ + 1 = 0 2X₁ - 1 = 0 2X₂ + 1 = 2X₁ - 1 Link to comment Share on other sites More sharing options...
Tupac Amaru Posted October 8, 2008 Share Posted October 8, 2008 Hmm.... maybe: X = sqrt (1/4) which has two answers: I know this is very nit-picky, but X^2 = 1/4 has two answers. x = sqrt (1/4) only has the answer sqrt (1/4) = 1/2. Link to comment Share on other sites More sharing options...
Boba Rhett Posted October 8, 2008 Share Posted October 8, 2008 Ooooooooooh snap, tk. Link to comment Share on other sites More sharing options...
tk102 Posted October 8, 2008 Author Share Posted October 8, 2008 Not sure how else to express the principal and non-principal square roots within the context of a single variable. I'm interested in ForeverNight's answer. Link to comment Share on other sites More sharing options...
Istorian Posted October 9, 2008 Share Posted October 9, 2008 Hello, guys! Ok, here's a math trick. It's not exactly a problem, though it will cause some headaches: 1) Put any number in your mind 2) Add 20 3) Subtract 15 4) Multiply by 3 5) Add 40 6) Add the digits until you have an one-digit number (e.g. if you have 185, you add 1 with 8 and 5, which equals 14, and then you add 4 with 1 which equals 5.) 7) Multiply by 4 8) Divide by 2 9) Add the digits again (exactly as Command 6 told you to do.) 10) Multiply by 9 11) Add the digits again (teh same boring way...) 12) Add 40 13) Subtract 12 Click this hidden to see what you have...expect to be surprised!! Show spoiler (hidden content - requires Javascript to show) If done correctly you should have 37! Tricky, eh? That's it, there you go! EDIT: (Answering to tk) Exactly...The whole point is that every number who is multiplied by 9, if you add his digits, you get 9, but why make it plain when we can make it beautiful and complicated? |I| Link to comment Share on other sites More sharing options...
tk102 Posted October 9, 2008 Author Share Posted October 9, 2008 You can also skip over steps 1-9 and get the same answer. Link to comment Share on other sites More sharing options...
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