tridim
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Fri Nov-24-06 08:26 PM
Response to Reply #6 |
| 17. The radius of the rope changes as the cow wraps around the silo |
| -Any Mensa DUers? 3 math/physics problems for your consideration: |
karlrschneider |
Nov-24-06 08:06 PM |
#0 |
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You're posting during a geometry exam, aren't you? |
dicksteele |
Nov-24-06 08:10 PM |
#1 |
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No. in the classic case... the attachment point at the silo |
lapfog_1 |
Nov-24-06 08:19 PM |
#7 |
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As the problem was posed |
canetoad |
Nov-24-06 08:29 PM |
#20 |
| -
Yes, I neglected to mention that, sorry! |
karlrschneider |
Nov-24-06 08:30 PM |
#21 |
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Im in MENSA |
FARAFIELD |
Nov-24-06 08:33 PM |
#24 |
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No offense, I assure you, I just find these to be fun games for some who |
karlrschneider |
Nov-24-06 08:38 PM |
#31 |
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Sounds like the "dumbing down" of MENSA, still an IQ of 144 is not |
whistle |
Nov-24-06 08:45 PM |
#39 |
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I could be in MENSA but I never needed to |
Nobody |
Nov-26-06 12:23 PM |
#101 |
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#2 - stays the same |
Viva_La_Revolution |
Nov-24-06 08:11 PM |
#2 |
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i don't think this is correct |
unblock |
Nov-24-06 08:26 PM |
#18 |
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Yes, you're right! Think Archimedes! |
karlrschneider |
Nov-24-06 08:32 PM |
# |
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For #2, there isn't quite enough information in the problem. |
Tesha |
Nov-27-06 07:00 AM |
#132 |
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ack! I didn't take into account the weight of the metal vs. the wt of the water |
Viva_La_Revolution |
Nov-24-06 08:33 PM |
#25 |
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No it is about displacement |
Toots |
Nov-25-06 07:27 AM |
#87 |
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Sorry Toots, I didn't read your reply before making mine. n/t |
greyhound1966 |
Nov-26-06 11:34 AM |
#94 |
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The mass of the metal while in the boat causes the boat to displace |
greyhound1966 |
Nov-26-06 11:33 AM |
#93 |
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Nope. Something that floats displaces a volume of water equal to |
karlrschneider |
Nov-26-06 11:50 AM |
#96 |
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But only if you assume that the scrap metal does not itself float, as someone |
greyhound1966 |
Nov-26-06 12:48 PM |
#104 |
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Yes that's true but one wouldn't ordinarily find water-tight hollow scrap |
karlrschneider |
Nov-26-06 12:54 PM |
#108 |
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Thanks, partial credit got me summa cum laude... |
greyhound1966 |
Nov-26-06 01:19 PM |
#110 |
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Wouldn't the scrap in the boat also push some air in the boat below the water's surface level? |
Bucky |
Nov-26-06 01:21 PM |
#112 |
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#1 is a bit more than 3 feet high...nt |
SidDithers |
Nov-24-06 08:12 PM |
#3 |
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nah... that can't be right |
Viva_La_Revolution |
Nov-24-06 08:15 PM |
#5 |
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Isn't it about 1.59 feet high? |
Boojatta |
Nov-24-06 08:21 PM |
#9 |
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Yeah, you're right, I buggered it up... |
SidDithers |
Nov-24-06 08:27 PM |
#19 |
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Yes, it turns out to be 5/pi feet |
karlrschneider |
Nov-24-06 08:33 PM |
#27 |
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Don't understand this question. If you have 132,000,000 (25,000 * 5280) feet of wire |
greyhound1966 |
Nov-26-06 11:47 AM |
#95 |
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You got it... |
SidDithers |
Nov-26-06 12:21 PM |
#100 |
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heh-what am I missing on #3? |
nam78_two |
Nov-24-06 08:14 PM |
#4 |
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Number three is just the area of a 200 ft. diameter circle |
A Simple Game |
Nov-24-06 08:18 PM |
#6 |
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Yeah agreed on 2 and 3 |
nam78_two |
Nov-24-06 08:22 PM |
#12 |
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You fogot that the point at which the rope is thethered varies by 50 feet... |
StraightDope |
Nov-24-06 08:22 PM |
#13 |
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Yes, the rope starts wrapping around the silo once the cow gets |
karlrschneider |
Nov-24-06 08:39 PM |
#34 |
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It would be sort of like the affect of gravity on an orbiting object around a |
whistle |
Nov-24-06 08:50 PM |
#43 |
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That changes things considerably... |
StraightDope |
Nov-25-06 03:11 PM |
#90 |
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The radius of the rope changes as the cow wraps around the silo |
tridim |
Nov-24-06 08:26 PM |
#17 |
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Exactly. That's why it's a hard problem, it's a doulbe involute |
karlrschneider |
Nov-24-06 08:42 PM |
#35 |
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It also has to be assumed the rope is attached at graze ht. |
Mr_Spock |
Nov-24-06 11:29 PM |
#84 |
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Actually, no. On #3 I forgot to mention the rope is firmly attached |
karlrschneider |
Nov-24-06 08:35 PM |
#28 |
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It's the difference of circles. 1) is an easy version of finding dD/dC |
BlooInBloo |
Nov-24-06 08:22 PM |
#11 |
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yeah |
nam78_two |
Nov-24-06 08:24 PM |
#15 |
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#3 isn't that bad... |
StraightDope |
Nov-24-06 08:21 PM |
#8 |
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ahh but |
Little Wing |
Nov-25-06 02:04 PM |
#89 |
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I win! |
stonecoldsober |
Nov-24-06 08:22 PM |
#10 |
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good answers and here is more information I need. |
uppityperson |
Nov-24-06 10:05 PM |
#69 |
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I'm busy trying to find a wire that long. Be back to you later..... |
Lastlaughin08 |
Nov-24-06 08:23 PM |
#14 |
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Uhhh. |
jayctravis |
Nov-24-06 08:24 PM |
#16 |
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Beware relying on your intuition unless it is well-developed in the subject area. |
Boojatta |
Nov-24-06 08:36 PM |
#29 |
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The question makes no sense... |
jayctravis |
Nov-24-06 08:49 PM |
#42 |
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Well, I did say "if it was evely supported above the ground..." |
karlrschneider |
Nov-24-06 08:53 PM |
#44 |
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I agree on all points |
toshirajo |
Nov-24-06 08:39 PM |
#33 |
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Welcome to DU! Unfortunately you missed all 3. |
karlrschneider |
Nov-24-06 08:44 PM |
#37 |
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Thanx Karl |
toshirajo |
Nov-24-06 09:06 PM |
#52 |
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#2 - water level drops |
unblock |
Nov-24-06 08:31 PM |
#22 |
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Does it matter if the scrap metal happens to be in the shape of a boat's hull? :) |
BlooInBloo |
Nov-24-06 08:38 PM |
#32 |
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It might. |
karlrschneider |
Nov-24-06 08:45 PM |
#38 |
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who? moi? lolol! |
BlooInBloo |
Nov-24-06 08:47 PM |
#41 |
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Exactly! |
karlrschneider |
Nov-24-06 08:42 PM |
#36 |
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Wait, wait, wait, by your logic... |
BrotherBuzz |
Nov-24-06 10:58 PM |
#80 |
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It sure would! Not much though. |
karlrschneider |
Nov-26-06 12:52 PM |
#106 |
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Ok karl... quit teasing |
Viva_La_Revolution |
Nov-24-06 08:32 PM |
#23 |
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I used to be a Mensa |
Blue_In_AK |
Nov-24-06 08:33 PM |
#26 |
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For #1 |
joe_sixpack |
Nov-24-06 08:37 PM |
#30 |
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Very close! 10 extra points to 'show your work' |
karlrschneider |
Nov-24-06 08:46 PM |
#40 |
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1 & 2 |
selfdestructive |
Nov-26-06 12:10 PM |
#98 |
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Right on #2, 1 is actually about 19 inches... |
karlrschneider |
Nov-26-06 12:49 PM |
#105 |
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Hope this helps with #1. |
aggiesal |
Nov-27-06 12:35 AM |
#130 |
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#3 results in an ovoid, assuming the cow can walk both |
bleever |
Nov-24-06 08:53 PM |
#45 |
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I probably should have left that one out, it actually is a very difficult |
karlrschneider |
Nov-24-06 08:59 PM |
#48 |
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Answers |
boolean |
Nov-24-06 08:54 PM |
#46 |
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Are you thinking of it as a constrained maximization problem? lol |
BlooInBloo |
Nov-24-06 08:55 PM |
#47 |
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No |
boolean |
Nov-24-06 09:06 PM |
#51 |
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Yup - just said the same in a more jackass way... |
BlooInBloo |
Nov-24-06 09:11 PM |
#56 |
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You got #1 exactly. The shape on #2 doesn't matter as long as it sinks |
karlrschneider |
Nov-24-06 09:01 PM |
#50 |
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ah - I see the problem with 3 - the poverty of available paths on the "silo side"... |
BlooInBloo |
Nov-24-06 09:09 PM |
#53 |
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What if.... |
boolean |
Nov-24-06 09:10 PM |
#55 |
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The boat wouldn't float in the first place! |
karlrschneider |
Nov-24-06 09:39 PM |
#63 |
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I believe that if the scrap iron was in the shape of sphere or cylinder |
heidler1 |
Nov-24-06 11:02 PM |
#81 |
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excellent point on #2 |
porkrind |
Nov-24-06 09:38 PM |
#62 |
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Okay you got me. If I ever pose this again I will carefully specify |
karlrschneider |
Nov-24-06 09:43 PM |
#66 |
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and now for the REAL answers: |
antifaschits |
Nov-24-06 09:00 PM |
#49 |
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Well, there you go |
toshirajo |
Nov-24-06 09:12 PM |
#57 |
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we already have faith based physicks, geology, and genetics. |
antifaschits |
Nov-24-06 09:21 PM |
#58 |
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Small boat in a swimming pool with all that scrap would sink before you |
spacelady |
Nov-24-06 09:09 PM |
#54 |
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In #3, consider the point where the rope is attached |
bleever |
Nov-24-06 09:23 PM |
#59 |
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The shape of the grazing area looks a bit like round-bottom heart with a big hole in it.. |
TahitiNut |
Nov-24-06 11:04 PM |
#82 |
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Tricky! |
porkrind |
Nov-24-06 09:28 PM |
#60 |
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oops, I assumed the rope was fixed at one point on the silo |
porkrind |
Nov-24-06 09:32 PM |
#61 |
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Nice! That #3 took me hours when I first saw it years ago! |
karlrschneider |
Nov-24-06 09:41 PM |
#65 |
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Wouldn't be the the worst Ponder This question I've ever seen.... |
BlooInBloo |
Nov-24-06 09:44 PM |
#67 |
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Thanks for the fun thread! |
porkrind |
Nov-24-06 09:58 PM |
#68 |
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Without actually pulling out a calculator... |
Gregorian |
Nov-24-06 09:40 PM |
#64 |
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#3 - 49,090 +/- |
alittlelark |
Nov-24-06 10:17 PM |
#70 |
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I Would Expect Any Teenage Schoolchild To Be AbleTo Answer Each Of Those |
ThomWV |
Nov-24-06 10:24 PM |
#71 |
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#2 - 19" (w/in 1% ) above the surace. |
alittlelark |
Nov-24-06 10:24 PM |
#72 |
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#2 goes down |
alittlelark |
Nov-24-06 10:26 PM |
#73 |
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Do you have any more problems? |
alittlelark |
Nov-24-06 10:33 PM |
#74 |
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Along the lines of (3). Citation after solution/give up - fair warning - it's a bit harder... |
BlooInBloo |
Nov-24-06 10:45 PM |
#75 |
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I'd like to see the elementary solution. |
Gregorian |
Nov-24-06 10:51 PM |
#77 |
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elementary != easy. just means doesn't use concepts beyond typical high school... |
BlooInBloo |
Nov-24-06 10:53 PM |
#78 |
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Yes. Please. |
Gregorian |
Nov-24-06 10:57 PM |
#79 |
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The tether attached to the silo does not say it is fixed |
alittlelark |
Nov-24-06 11:12 PM |
#83 |
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Do you mean the 'elementary' solution is an approximate one |
muriel_volestrangler |
Nov-25-06 07:08 AM |
#86 |
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A solution gets the right answer by definition... |
BlooInBloo |
Nov-25-06 01:59 PM |
#88 |
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In that case, I'll give up |
muriel_volestrangler |
Nov-25-06 03:27 PM |
#91 |
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:) |
Gregorian |
Nov-26-06 11:10 AM |
#92 |
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I found a fairly simple integral that should calculate |
BrewerJohn |
Nov-26-06 12:44 PM |
#103 |
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Haha. |
Gregorian |
Nov-26-06 01:41 PM |
#115 |
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#3 is the area of the silo |
ChaoticSilly |
Nov-24-06 10:47 PM |
#76 |
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1,2,3 |
Mr_Spock |
Nov-24-06 11:42 PM |
#85 |
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#2 is Down |
stepnw1f |
Nov-26-06 12:06 PM |
#97 |
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1 & 2 |
selfdestructive |
Nov-26-06 12:10 PM |
#99 |
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Geometry & simple algebra solution to #1: |
karlrschneider |
Nov-26-06 12:26 PM |
#102 |
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*shakes fist* |
selfdestructive |
Nov-26-06 01:01 PM |
#109 |
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Right, another way... |
IMModerate |
Nov-26-06 01:41 PM |
#114 |
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Very good! |
karlrschneider |
Nov-26-06 02:27 PM |
#118 |
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I think you mean... |
IMModerate |
Nov-26-06 03:25 PM |
#119 |
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Well, there are actually 2 involutes |
karlrschneider |
Nov-26-06 03:47 PM |
#121 |
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#3 is the rope fixed to a single point on the silo? If so, how far above the ground is |
greyhound1966 |
Nov-26-06 12:52 PM |
#107 |
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I think it is really indicative that this thread has generated so many |
greyhound1966 |
Nov-26-06 01:20 PM |
#111 |
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I wish I could join Mensa, but I am very stopid |
Bucky |
Nov-26-06 01:24 PM |
#113 |
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In other words, you're a "moran". |
StraightDope |
Nov-26-06 02:00 PM |
#116 |
| -
let's just say |
selfdestructive |
Nov-26-06 02:04 PM |
#117 |
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Question 1: 23.097744 nanometers |
Cookie wookie |
Nov-26-06 03:44 PM |
#120 |
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Question 2. Stays the same |
Cookie wookie |
Nov-26-06 03:49 PM |
#122 |
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Ha! You forgot the water displaced by the air in the boat. |
Bucky |
Nov-26-06 08:57 PM |
#126 |
| -
well, I'm not a Mensa, but what the hey |
Cookie wookie |
Nov-27-06 10:08 PM |
#134 |
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I've never joined Mensa, but I'll try. |
porphyrian |
Nov-26-06 04:00 PM |
#123 |
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Here's what I settled on as a solution to (3) |
BrewerJohn |
Nov-26-06 05:18 PM |
#124 |
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You have the right approach but your region 3 is actually part of region 2! |
karlrschneider |
Nov-26-06 11:42 PM |
#128 |
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Uh, if the cow can go there, I need to calculate it, no? |
BrewerJohn |
Nov-27-06 12:02 AM |
#129 |
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Okay I see what you're saying but my solution considered all area alements |
karlrschneider |
Nov-27-06 01:06 AM |
#131 |
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Here's the approach to answering #3 |
Gregorian |
Nov-26-06 08:53 PM |
#125 |
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I think my solution reduces to Wolfram's |
BrewerJohn |
Nov-26-06 10:06 PM |
#127 |
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I'm not going to try to answer the first one. |
Sentinel Chicken |
Nov-27-06 07:35 AM |
#133 |
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