Posted: 9/2/2010 7:48:03 AM EDT
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I was working on a math problem for my college Trigonometry class for more than an hour last night and I kept coming up with the same answer, which is different from the books answer.
ETA - THIS IS NOT AN ASSIGNED HOMEWORK PROBLEM. THIS IS ONE OF THE UNASSIGNED PROBLEMS THAT I AM WORKING FOR STUDY PURPOSES ONLY. The problem is this: 2200 years ago, this guy named Eratosthenes read in the Alexandria library that at noon on June 21st a vertical stick in Syene cast no shadow. So, on June the 21st he put a vertical stick up in Alexandria and found that it did cast a shadow. He then figured out that the Earth was round and that there was a 7 degree difference in the position of Syene and Alexandria on the Earth. So then he pays a guy to walk off the distance between Syene and Alexandria and finds that it is 800km. So he calculates the circumference of the Earth. The problem asks us to calculate the circumference of the Earth using the information that he had back then, and then calculate it again with the currently accepted radius of 6378 km. OK, so here's what I'm doing: IF: s = arc length a= measure of angle alpha r = radius AND: s = ar THEN: s = 800km a = 7 degrees r = s/a So, the first thing to do is to convert my angle from degrees to radian: 7 * pi/180 = .122 (three decimal places are sufficient for this class) So, now I plug my numbers in: r = 800km/.122 radians = 6557.377 km So the radius of the Earth, according to this ancient guy is 6557.377 km Now if Circumference = Diameter * pi and if Diameter = 2 Radius Then Circumference = 2 Radius * pi So then I get circumference = 2(6557.377) * 3.142 = 41,206.557 km Rounded this would be 41,207 km. Books says he came up with 41,143 km I say he must have forgotten to carry the 1. 
Anyone see where I fucked this up? |
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Instead of using 3 decimal places, use 3 significant figures for all of your intermediate results. Ugh. OK, here's what the book is doing: they're not being consistent with significant figures. To get the book's result: 7 * 3.14 / 180 = 0.1221111 800 / 0.1221111 = 6551.411 6551.411 * 2 * 3.14 = 41143. |
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360 / 7 * 800 = 41142.857142857142857142857142857 Or that.
Yeah, but this problem is from the section on radians, and converting degrees to radians, so I kinda need to do it the hard way. Not that it ever even crossed my mind to do it his way or anything though. 
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Instead of using 3 decimal places, use 3 significant figures for all of your intermediate results. Ugh. OK, here's what the book is doing: they're not being consistent with significant figures. To get the book's result: 7 * 3.14 / 180 = 0.1221111 800 / 0.1221111 = 6551.411 6551.411 * 2 * 3.14 = 41143. Calculator fucked me. I set it to 3 decimal points because he said that's all we needed for this class. That said, the professor did warn us that we will be tricked in this class. Then again, I would have to use two decimal places for pi, which wouldn't have worked out either. Hmmm...whoever wrote that problem is a real asshole. |
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Quoted: Quoted: Quoted: If Mary has 5 apples and John has 3 apples. How many babannas does Kelly have if she gives Adam 3 apples on Friday. Wait. How fast was the train going again? What does it matter? He turned his homework in late and now were ALL getting a zero MOTHERFUCKER |
| OP: In my experience when a prof says that 3 decimal places will be sufficient for the class, what they really mean is it is ok for the answer to be in 3 decimal places. If you have a multiple step problem with large numbers, then it is very easy for one rounded number early in the problem to fuck up your answer. |
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Circumference = pi *R squared FYI AREA= pi * r squared Circumference=pi * r * 2=pi*diameter Dear GOD in heaven. What in the FUCK are you people talking about? Circumstance, circumscision. perimeter, time WTF? Third grade called. It's for you.
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Quoted: Quoted: Quoted: If Mary has 5 apples and John has 3 apples. How many babannas does Kelly have if she gives Adam 3 apples on Friday. Wait. How fast was the train going again? What does it matter? He turned his homework in late and now were ALL getting a zero I read that thread....  |
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Quoted: See me after class.Quoted: Quoted: If Mary has 5 apples and John has 3 apples. How many babannas does Kelly have if she gives Adam 3 apples on Friday. Wait. How fast was the train going again? What does it matter? He turned his homework in late and now were ALL getting a zero |
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See me after class.
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If Mary has 5 apples and John has 3 apples. How many babannas does Kelly have if she gives Adam 3 apples on Friday. Wait. How fast was the train going again? What does it matter? He turned his homework in late and now were ALL getting a zero 
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Quoted: Quoted: See me after class.Quoted: Quoted: If Mary has 5 apples and John has 3 apples. How many babannas does Kelly have if she gives Adam 3 apples on Friday. Wait. How fast was the train going again? What does it matter? He turned his homework in late and now were ALL getting a zero I thought our "private arrangement" was only between us.  |
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Quoted: Quoted: Instead of using 3 decimal places, use 3 significant figures for all of your intermediate results. Ugh. OK, here's what the book is doing: they're not being consistent with significant figures. To get the book's result: 7 * 3.14 / 180 = 0.1221111 800 / 0.1221111 = 6551.411 6551.411 * 2 * 3.14 = 41143. Calculator fucked me. I set it to 3 decimal points because he said that's all we needed for this class. That said, the professor did warn us that we will be tricked in this class. Then again, I would have to use two decimal places for pi, which wouldn't have worked out either. Hmmm...whoever wrote that problem is a real asshole.  |