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 tr1sth3t
Lieutenant Commander
Joined: Feb 27, 2007
Member#: 3130
Posts: 279
Location: Bergen
    
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 Posted:
Fri Mar 19, 2010 7:59 pm Post subject: brainTeaser[0] |
 
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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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It is more likely that a brain randomly forms out of the chaos with false memories of its life than that the universe around us would have billions of self-aware brains. |
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tr1sth3t
Lieutenant Commander
Joined: Feb 27, 2007
Member#: 3130
Posts: 279
Location: Bergen
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Posted:
Fri Mar 19, 2010 8:02 pm Post subject: |
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Good luck to everyone. If you need a lecture on wtf I'm talking about, go here.
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It is more likely that a brain randomly forms out of the chaos with false memories of its life than that the universe around us would have billions of self-aware brains. |
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 Pesadelo 
Admiral (Administrator)
Joined: Feb 18, 2007
Member#: 3090
Posts: 1955
Location: Rio de Janeiro, Brazil
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Posted:
Sat Mar 20, 2010 6:00 am Post subject: |
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Are you wanting someone to resolve a difficult math question for you?
Anyway, the answer is here:
Jefferson State Community College
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 SeclusionSolution
Commodore
Joined: Jun 22, 2006
Member#: 2031
Posts: 3596
Location: Papua New Guinea
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Sat Mar 20, 2010 6:32 am Post subject: |
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 Prof. Pesa 
I still didn´t 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 it´s mixed and added hmm or shouldn´t it be the real volume V ± ▲V???
erhmm I hope he has A as grade ..  Math my massgrave ..nice wordplay
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Pesadelo
Admiral (Administrator)
Joined: Feb 18, 2007
Member#: 3090
Posts: 1955
Location: Rio de Janeiro, Brazil
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Posted:
Sat Mar 20, 2010 6:45 am Post subject: |
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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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SeclusionSolution
Commodore
Joined: Jun 22, 2006
Member#: 2031
Posts: 3596
Location: Papua New Guinea
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Posted:
Sat Mar 20, 2010 8:01 am Post subject: |
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Im absolutely untalented on maths i nearly failed the endexam. But u made it plausible for me thnx 
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Last edited by SeclusionSolution on Sat Mar 20, 2010 5:05 pm; edited 1 time in total |
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tr1sth3t
Lieutenant Commander
Joined: Feb 27, 2007
Member#: 3130
Posts: 279
Location: Bergen
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Posted:
Sat Mar 20, 2010 4:47 pm Post subject: |
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No, I was starting a math trivia. You did find an answer.
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It is more likely that a brain randomly forms out of the chaos with false memories of its life than that the universe around us would have billions of self-aware brains. |
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 irule
Captain
Joined: Sep 20, 2006
Member#: 2410
Posts: 1379
Location: Canada
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Sat Mar 20, 2010 11:46 pm Post subject: |
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I got a maximum error of 2144.59 cubic metres, for a 31.28% of error. 
I also used 3.1415 for pi.
Last edited by irule on Sun Mar 21, 2010 12:55 am; edited 3 times in total |
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 lunarstrain88
Captain
Joined: Dec 25, 2009
Member#: 9680
Posts: 2403
Location: Karachi, Pakistan
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Posted:
Sun Mar 21, 2010 12:24 am Post subject: |
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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 |
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irule
Captain
Joined: Sep 20, 2006
Member#: 2410
Posts: 1379
Location: Canada
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Posted:
Sun Mar 21, 2010 12:27 am Post subject: |
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I failed calculus... I just went with the highest possible volume, and subtracted the measured value.
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SeclusionSolution
Commodore
Joined: Jun 22, 2006
Member#: 2031
Posts: 3596
Location: Papua New Guinea
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Posted:
Sun Mar 21, 2010 11:09 am Post subject: |
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,,|,, 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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 spinemaggot
Commander
Joined: Sep 27, 2007
Member#: 4007
Posts: 855
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Posted:
Sun Mar 21, 2010 11:27 am Post subject: |
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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,
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 Necrotten
Cadet 2
Joined: Mar 21, 2010
Member#: 10334
Posts: 5
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Posted:
Sun Mar 21, 2010 3:54 pm Post subject: |
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| 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,
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At least I can understand that..  |
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lunarstrain88
Captain
Joined: Dec 25, 2009
Member#: 9680
Posts: 2403
Location: Karachi, Pakistan
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Posted:
Sun Mar 21, 2010 4:25 pm Post subject: |
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sorry Seclu  
Last edited by lunarstrain88 on Mon Apr 05, 2010 12:54 pm; edited 2 times in total |
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tr1sth3t
Lieutenant Commander
Joined: Feb 27, 2007
Member#: 3130
Posts: 279
Location: Bergen
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Posted:
Mon Mar 22, 2010 6:36 pm Post subject: |
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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 = (dπr²)
= πr²dh + hd(πr²)
= πr²dh + h2πrdr
= πr²dh + 2πrhdr
|ΔV| ≈ |dV| = |πr²dh + 2πrhdr|
≤ |πr²dh| + |2πrhdr|
= |π(10)²(±2.4)| + |2π(10)(15)(±1.2m)|
= 240π + 360π = 600πm³ ≈ 1,884.66m³
Now we need to compute the relative error.
V = πr²h = (10)²(15)π = 1500π ≈ 4,712.4m³
|ΔV ÷ V| ≈ |dV ÷ V| = 600πm³ ÷ 1500πm³
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 1,884.66m³
(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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It is more likely that a brain randomly forms out of the chaos with false memories of its life than that the universe around us would have billions of self-aware brains. |
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