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brainTeaser[0]
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Norway tr1sth3t
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PostPosted: Fri Mar 19, 2010 7:59 pm   Post subject: brainTeaser[0] Reply with quote


I have decided to start a specific kind of trivia for fun. This game will be specific so that you can not simply go to Google and look this up. I will say that you can find the concepts used for these trivia(s) on Google and even YouTube. Here goes the zeroth one for DFM.

Q: Suppose that the radius and height of a right circular cylinder is measured to be 10m and 15m with maximum possible absolute error(s) in measurement of positive or negative 1.2m and positive or negative 2.4m, respectively. Use the method of differentials to estimate (a) the maximum possible absolute error in the calculated volume and (b) the maximum possible relative (percentage) error in the calculated volume.

Hints:
  • Volume of cylinder: V=(pi)*r^2*h.
  • r = 10m, derivative of r (dr = +-1.2m)
  • h = 15m, derivative of h (dh = +-2.4m)
The answer will be posted with the next trivia question, or when someone posts the correct 2-part answer. (a & b)
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Norway tr1sth3t
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PostPosted: Fri Mar 19, 2010 8:02 pm   Post subject: Reply with quote


Good luck to everyone. If you need a lecture on wtf I'm talking about, go here.
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PostPosted: Sat Mar 20, 2010 6:00 am   Post subject: Reply with quote


Are you wanting someone to resolve a difficult math question for you?

Anyway, the answer is here:

Jefferson State Community College

Wink
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PostPosted: Sat Mar 20, 2010 6:32 am   Post subject: Reply with quote


Pesadelo wrote:
Are you wanting someone to resolve a difficult math question for you?

Anyway, the answer is here:

Jefferson State Community College

Wink


Mr. Green Prof. Pesa Cool

I still didnt understand why both meanderings get added in the ▲V and are not taken together in one formula for V, which means 2pi*dr*dr*hr as the absolute mess that could happen to the cylinder?? Instead its mixed and added hmm or shouldnt it be the real volume V ▲V???

erhmm I hope he has A as grade .. Depressed Math my massgrave ..nice wordplay Mr. Green
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PostPosted: Sat Mar 20, 2010 6:45 am   Post subject: Reply with quote


I don't know if I well understood your doubt.

Given the 2 errors ranges, the V function must be seen as a function of 2 variables, named r and h.

So remember that the derivative of a product of 2 variables (keeping the previous ones) would be: r.dh + h.dr
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PostPosted: Sat Mar 20, 2010 8:01 am   Post subject: Reply with quote


Im absolutely untalented on maths i nearly failed the endexam. But u made it plausible for me thnx Yes
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Last edited by SeclusionSolution on Sat Mar 20, 2010 5:05 pm; edited 1 time in total
Norway tr1sth3t
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PostPosted: Sat Mar 20, 2010 4:47 pm   Post subject: Reply with quote


Pesadelo wrote:
Are you wanting someone to resolve a difficult math question for you?

Anyway, the answer is here:

Jefferson State Community College

Wink


No, I was starting a math trivia. You did find an answer.
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PostPosted: Sat Mar 20, 2010 11:46 pm   Post subject: Reply with quote


I got a maximum error of 2144.59 cubic metres, for a 31.28% of error. Grin

I also used 3.1415 for pi.

Last edited by irule on Sun Mar 21, 2010 12:55 am; edited 3 times in total
Pakistan lunarstrain88
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PostPosted: Sun Mar 21, 2010 12:24 am   Post subject: Reply with quote


Is there some way that I can remove this post?

Last edited by lunarstrain88 on Tue Mar 23, 2010 12:12 am; edited 4 times in total
Canada irule
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PostPosted: Sun Mar 21, 2010 12:27 am   Post subject: Reply with quote


I failed calculus... I just went with the highest possible volume, and subtracted the measured value.
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PostPosted: Sun Mar 21, 2010 11:09 am   Post subject: Reply with quote


,,|,, no comment on some comment

Lunar i read your PM after this, I think it should be visible for you. Thnx
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Last edited by SeclusionSolution on Sun Mar 21, 2010 11:30 am; edited 1 time in total
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PostPosted: Sun Mar 21, 2010 11:27 am   Post subject: Reply with quote


The result is equal to the sum of the square root of all the beers I have drunk in my life minus the tonelage of shit my ass has released to the power of negative whatever amont of months I have existed, all devided by the cubic meters of cum I have released on the universe to the power of the number of cunts squared I have nailed thus far in my pathetic life. Thnx,

Mr. Green Silly
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PostPosted: Sun Mar 21, 2010 3:54 pm   Post subject: Reply with quote


spinemaggot wrote:
The result is equal to the sum of the square root of all the beers I have drunk in my life minus the tonelage of shit my ass has released to the power of negative whatever amont of months I have existed, all devided by the cubic meters of cum I have released on the universe to the power of the number of cunts squared I have nailed thus far in my pathetic life. Thnx,

Mr. Green Silly


At least I can understand that.. OK!
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PostPosted: Sun Mar 21, 2010 4:25 pm   Post subject: Reply with quote


sorry Seclu Sad Peace

Last edited by lunarstrain88 on Mon Apr 05, 2010 12:54 pm; edited 2 times in total
Norway tr1sth3t
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PostPosted: Mon Mar 22, 2010 6:36 pm   Post subject: Reply with quote


Okay, so it seems this answer was findable on the internet. The next one will not be. In which case I guess I will post the answer.


r = 10m, Δr = 1.2m
h = 15m, Δh = 2.4m


If we logically think about these changes (Δr and Δh) in r and h they are simple the limits on the instrument.

ΔV ≈ dV = (dπr)
= πrdh + hd(πr)
= πrdh + h2πrdr
= πrdh + 2πrhdr


|ΔV| ≈ |dV| = |πrdh + 2πrhdr|
≤ |πrdh| + |2πrhdr|
= |π(10)(2.4)| + |2π(10)(15)(1.2m)|
= 240π + 360π = 600πm1,884.66m


Now we need to compute the relative error.
V = πrh = (10)(15)π = 1500π ≈ 4,712.4m
|ΔV V| ≈ |dV V| = 600πm 1500πm


Here the units cancel along with the symbol π (pi) leaving:
600 1500 = 0.40 or a 40% relative error.

(a) The maximum possible absolute error in the calculated volume is 1,884.66m
(b) The maximum possible relative (percentage) error in the calculated volume is 40%.


So this instrument sucks and a new one needs to be bought.
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