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#241 | |
The Blobbit
Join Date: Feb 2004
Location: Kent, England (Not Oxford! ... yet...)
Posts: 1,596
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Eep, no can do. It was part of a larger and more evil problem, that was set with the same 1950's air of can't-you-get-that-right.
Arc length needs to be found for a surface area of revolution. So that requires two processes at which I suck. Firstly the y component of the CoG of the arc has to be found, which I can't do. And then the length of arc has to be found. I was hoping to use the answer and the second soultion to get a figure for y bar and decrypt the book's explanation of how to find it. SA = 2 pi . arc length . y(bar) arc length is = integral of (1 + [dy/dx]^2 ) ^1/2 The line: y^2 = 4x 2y dy/dx = 4 dy/dx = 4 / 2y = 2 / 2 root x (dy/dx)^2 = 1 / x And so the integral is required betwix 0 and 1. If you want to solve the whole thing: Find the surface area of revolution generated by the parabola y^2 = 4x when the part between (0,0) and (1,2) revolves about the x-axis. Solution:
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Janny's Songs Janny's lyrics and random photographs Tradition means giving votes to the most obscure of all classes, our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who happen to be walking about. ~ Mercutio... erm, GK Chesterton. |
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#242 |
Fëanorophobic
Join Date: May 2004
Location: Between the pages of a book
Posts: 1,417
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Sorry, can't help much with that: our syllabus didn't cover SA of revolution.
But I can get 8 pi over 3 as the final answer (no roots, though) I don't know, but I have a feeling that the method you're using (even though I can't begin to understand it) is a bit too complicated for the problem... |
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#243 |
The Blobbit
Join Date: Feb 2004
Location: Kent, England (Not Oxford! ... yet...)
Posts: 1,596
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I perpetually have that feeling.
![]() It also says that you can integrate y w.r.t. the arc length, and multiply that by 2pi. But i have no idea how to do that.
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Janny's Songs Janny's lyrics and random photographs Tradition means giving votes to the most obscure of all classes, our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who happen to be walking about. ~ Mercutio... erm, GK Chesterton. |
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#244 |
Join Date: Nov 2003
Location: Narnia
Posts: 1,656
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I've officially started AP ("Advanced Placement") Calculus. So I may start posting in this thread more...
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Mike nodded. A sombre nod. The nod Napoleon might have given if somebody had met him in 1812 and said, "So, you're back from Moscow, eh?". Interested in C.S. Lewis? Visit the forum dedicated to one of Tolkien's greatest contemporaries. |
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#245 |
The Blobbit
Join Date: Feb 2004
Location: Kent, England (Not Oxford! ... yet...)
Posts: 1,596
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So... what's the sum of the infinite series:
1/2 + 1/4 + 2/8 + 3/16 + 5/32 + 8/64 + 13/128... How do you deal with our unspellable Italian friend's series? :S
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Janny's Songs Janny's lyrics and random photographs Tradition means giving votes to the most obscure of all classes, our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who happen to be walking about. ~ Mercutio... erm, GK Chesterton. |
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#246 |
Join Date: Nov 2003
Location: Narnia
Posts: 1,656
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Ha. We haven't gotten there yet...we did do a good bit on series last year in pre-calc though. If we learned that then I sure don't remember!
![]() I have a feeling we didn't learn it last year since it needs limits, right? That's what we've started in calculus now. EDIT: It took me a bit to realize by "unspellable Italian friend's series" you were referring to the Fibonnacci (?) Sequence! ![]() ![]() I'm still not back in the school mode.
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Mike nodded. A sombre nod. The nod Napoleon might have given if somebody had met him in 1812 and said, "So, you're back from Moscow, eh?". Interested in C.S. Lewis? Visit the forum dedicated to one of Tolkien's greatest contemporaries. Last edited by Mercutio : 09-16-2005 at 07:54 PM. |
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#247 |
The Blobbit
Join Date: Feb 2004
Location: Kent, England (Not Oxford! ... yet...)
Posts: 1,596
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You don't know how to spell Fibonacci (?) either!
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Janny's Songs Janny's lyrics and random photographs Tradition means giving votes to the most obscure of all classes, our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who happen to be walking about. ~ Mercutio... erm, GK Chesterton. |
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#248 | |
The Blobbit
Join Date: Feb 2004
Location: Kent, England (Not Oxford! ... yet...)
Posts: 1,596
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Is the answer:
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Janny's Songs Janny's lyrics and random photographs Tradition means giving votes to the most obscure of all classes, our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who happen to be walking about. ~ Mercutio... erm, GK Chesterton. Last edited by Janny : 09-19-2005 at 03:11 PM. |
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#249 |
Join Date: Nov 2003
Location: Narnia
Posts: 1,656
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I have no idea
![]() I'll come back to it once we get to that section. ![]()
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Mike nodded. A sombre nod. The nod Napoleon might have given if somebody had met him in 1812 and said, "So, you're back from Moscow, eh?". Interested in C.S. Lewis? Visit the forum dedicated to one of Tolkien's greatest contemporaries. |
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#250 |
Hobbit in the Music
Join Date: Nov 1999
Location: Westmarch
Posts: 1,111
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Here's the infamous 3x+1 problem:
First pick a positive integer. if it's even, divide it by 2. if it's odd, multiply it by 3 and add 1. Repeat this process until you get 1, then stop. For example: 10 5 16 8 4 2 1 But will you always get 1, or will some numbers just keep getting bigger and never terminate? Actually, I've tested this (by writing a simple program) on every positive integer from 1 to about 200000000, and it's terminated every time. But can you prove that it always will? |
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#251 | |
Fëanorophobic
Join Date: May 2004
Location: Between the pages of a book
Posts: 1,417
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Quote:
Do you have the answer to it? I mean, if I reach a proof would you be able to tell me if it's wrong or right? |
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#252 |
Hobbit in the Music
Join Date: Nov 1999
Location: Westmarch
Posts: 1,111
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My Computer Science teacher said it's been tested up to something like 10^16 (though my computer couldn't go that high without overflowing), and it's terminated every time.
But no one has ever been able to prove that it always will... even really freaky genius mathematicians. In class we figured out that if 3x+1 will always get to a power of 2 at some point, it will terminate by the x/2 rule, but will 3x+1 always reach a power of 2? Someone in the class proved that 4^n = 3x+1 by induction: Base: 4^1 = 3(1) + 1 Inductive Hypothesis: 4^k = 3x+1 Prove: 4^(k+1) = 3y+1 4^(k+1) = 4 * 4^k = 4(3x+1) by Inductive Hypothesis = 12x+4 = 12x + 3 + 1 = 3(4x+1) +1 = 3y+1 ... This doesn't prove that the 3x+1 problem always terminates, but it might help as a step along the way. But apparently Paul Erdos said, "Mathematics is not yet ready for these kinds of questions," or something like that. |
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#253 |
Fenway Ranger, Lord of Red Sox Nation
Join Date: Aug 2005
Location: College!
Posts: 1,976
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Has this already been posted?
a=b+c
b+c=a 5a=5b+5c 4b+4c=4a Add 4b+4c=4a to 5a=5b+5c: 5a+4b+4c=4a+5b+5c Subtract 9a: 4b+4c-4a=5b+5c-5a 4(b+c-a)=5(b+c-a) 4=5 Tell me what's wrong. ![]() ![]()
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Adventure...betrayal...heroism... Atharon: where heroes are born. My wife once said to me—when I'd been writing for ten or fifteen years—that I could always go back to being a nuclear engineer. And I said to her, 'Harriet, would you let someone who quit his job to go write fantasy anywhere near your nuclear reactor? I wouldn't!' (Robert Jordan) |
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#254 | |||
Fëanorophobic
Join Date: May 2004
Location: Between the pages of a book
Posts: 1,417
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Quote:
![]() Quote:
and I think it has been posted before... Last edited by Beren3000 : 09-20-2005 at 03:58 AM. |
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#255 | |
Hobbit in the Music
Join Date: Nov 1999
Location: Westmarch
Posts: 1,111
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Quote:
I know-- it feels right, and I certainly believe that it will always terminate, but I guess for mathematicians it's not good enough. I guess the point is that you can't prove everything with the tools of mathematics we use today. |
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#256 | ||
Fenway Ranger, Lord of Red Sox Nation
Join Date: Aug 2005
Location: College!
Posts: 1,976
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Quote:
__________________
Adventure...betrayal...heroism... Atharon: where heroes are born. My wife once said to me—when I'd been writing for ten or fifteen years—that I could always go back to being a nuclear engineer. And I said to her, 'Harriet, would you let someone who quit his job to go write fantasy anywhere near your nuclear reactor? I wouldn't!' (Robert Jordan) |
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#257 |
The Blobbit
Join Date: Feb 2004
Location: Kent, England (Not Oxford! ... yet...)
Posts: 1,596
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It's one of those tricks maths people have to learn. If someone is proving something that doesn't work, look for the algebra that equals zero and find where they divided using it.
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__________________
Janny's Songs Janny's lyrics and random photographs Tradition means giving votes to the most obscure of all classes, our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who happen to be walking about. ~ Mercutio... erm, GK Chesterton. |
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#258 |
Fenway Ranger, Lord of Red Sox Nation
Join Date: Aug 2005
Location: College!
Posts: 1,976
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And don't forget it's dangerous to divide/multiply by a variable. This creates extraneous roots. For example:
x=1-->x^2=1 Where there was one solution, now there are two (-1, +1)
__________________
Adventure...betrayal...heroism... Atharon: where heroes are born. My wife once said to me—when I'd been writing for ten or fifteen years—that I could always go back to being a nuclear engineer. And I said to her, 'Harriet, would you let someone who quit his job to go write fantasy anywhere near your nuclear reactor? I wouldn't!' (Robert Jordan) |
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#259 |
Fëanorophobic
Join Date: May 2004
Location: Between the pages of a book
Posts: 1,417
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Here's a nice one (don't know if this has been posted before):
A certain room has no windows whatsoever. It only has a light bulb on the inside. When you're outside the room, the door is closed so that you can't see whether the light bulb is on or not. Outside the room, there are 3 switches; you know that 1 of these switches turns the lamp on: the other two are not connected to anything. The trick is, you only get to enter the room once. How can you find out for certain which switch controls the lamp? |
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#260 | |
Fenway Ranger, Lord of Red Sox Nation
Join Date: Aug 2005
Location: College!
Posts: 1,976
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Oh, that's a classic
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Here's a twist: there are 3 switches and 3 lights. Can you match them up with the same parameters? (I saw this on The Scholar)
__________________
Adventure...betrayal...heroism... Atharon: where heroes are born. My wife once said to me—when I'd been writing for ten or fifteen years—that I could always go back to being a nuclear engineer. And I said to her, 'Harriet, would you let someone who quit his job to go write fantasy anywhere near your nuclear reactor? I wouldn't!' (Robert Jordan) |
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