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#426 2006-02-19 06:01:50

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Problems and Solutions

I don't know if it was appropriate to say QED in that, but it's just really cool to say. ^_^


Why did the vector cross the road?
It wanted to be normal.

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#427 2006-02-19 16:39:00

ganesh
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Registered: 2005-06-28
Posts: 15,209

Re: Problems and Solutions

mathsyperson, you are correct! roflolwave up


Character is who you are when no one is looking.

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#428 2006-02-19 17:52:50

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Problems and Solutions

By mathimatical law, you can only say QED when you start out with "Pf" or "Proof".  But we'll let you go with a warning this time.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#429 2006-02-19 18:37:08

ganesh
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Registered: 2005-06-28
Posts: 15,209

Re: Problems and Solutions

Problem # k + 97


Two men set out at the same time to walk towards
each other from points A and B, 72 km apart. The first man
walks at the constant rate of 4 km/hr. The second man walks
1 km the first hour, 2 km the second hour, 3 km the third hour
and so on. When will  the two men meet?


Character is who you are when no one is looking.

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#430 2006-02-20 02:49:11

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Problems and Solutions


Why did the vector cross the road?
It wanted to be normal.

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#431 2006-02-20 11:56:23

John E. Franklin
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Registered: 2005-08-29
Posts: 3,582

Re: Problems and Solutions

On k + 89, I meant to multiply by 3, but then I still would be wrong.
I wish there was a theorum to get the number that is close to this 3.
I'll have to work on that.  The 3 multiplier would be like having 4 + 4 + 4 in the numerator.
I know it is wrong, but I feel the need to research this further.


igloo myrtilles fourmis

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#432 2006-02-20 13:07:51

John E. Franklin
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Registered: 2005-08-29
Posts: 3,582

Re: Problems and Solutions

On k + 89, I was below with this 3 times correction still by factor of 1.062801932.
So with the new correction factor, it's kind of dumb, but, you'll laugh, but...
percentage that it was from machine B knowing first that the piece is
defective = 35% ((4 x 3)/(5 + 4 + 2)) * correction factor, where correction factor = (5 + 4 + 2)/(3*(.35 x 4 + .25 x 5 + .40 x 2))


igloo myrtilles fourmis

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#433 2006-02-20 14:32:25

irspow
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Registered: 2005-11-24
Posts: 455

Re: Problems and Solutions

Last edited by irspow (2006-02-20 16:00:28)

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#434 2006-02-20 17:20:59

ganesh
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Registered: 2005-06-28
Posts: 15,209

Re: Problems and Solutions

Solution to Problem # k + 97

After 8 hours, the first man has walked (8x4) kilometers, i.e. 32 kilometers.
After 8 hours, the second man has walked (1+2+3+4+5+6+7+8) kilometers, i.e. 36 kilometers. In the ninth hour, the first man is walking at 4 km/hr and the second is walking at 9 km/hr. Let them meet after time t hours. 
Hence, 4t+9t=4, 13t=4, t=4/13 hours = 18.46 minutes approximately.
Hence, they would meet after 8 hours and 18.46 minutes approximately.

mathsyperson is correct smile smile smile


Character is who you are when no one is looking.

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#435 2006-02-20 18:13:40

ganesh
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Registered: 2005-06-28
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Re: Problems and Solutions

Problem # k + 98

A and B are two stations 300 km apart. Two trains T1
and T2 start from A and B respectively, towards each other at
the same time. T1 reaches B nine hours and T2 reaches A four
hours after they meet. Find the difference between the speeds
of T1 and T2.


Character is who you are when no one is looking.

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#436 2006-02-21 03:37:38

irspow
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Registered: 2005-11-24
Posts: 455

Re: Problems and Solutions

lol. You love this instantaneous velocity.  I stand by my k+97 solution(s).  There was nothing in the question that required the solution agreed upon.  Distance travelled does not prove constant velocity during a time period.  I have yet to see an instance of infinite acceleration either.  My equations describe the motion of both people as correctly as your assumptions.

  I am not trying to dispute your solution, just pointing out that the wording of a problem is just as vitally important as the mathematics that lead to a solution.  Your solution and mine are equally valid given the way in which it was worded.  More details would be needed to invalidate either one.
 
  My answers are more correct though!  Just kidding.  Why quibble over less than 30 seconds?

Last edited by irspow (2006-02-21 03:42:33)

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#437 2006-02-21 03:46:47

ganesh
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Registered: 2005-06-28
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Re: Problems and Solutions

I concede you're correct too, irspow! The time given to solve the problem was about a minute! I thought the best way to do that was the way I solved cool


Character is who you are when no one is looking.

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#438 2006-02-21 03:49:19

irspow
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Registered: 2005-11-24
Posts: 455

Re: Problems and Solutions

Thanks for the concession. lol.  Interesting how both are correct and yet different with a problem stated as such, no?

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#439 2006-02-21 05:06:44

irspow
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Registered: 2005-11-24
Posts: 455

Re: Problems and Solutions

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#440 2006-02-21 17:09:37

ganesh
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Registered: 2005-06-28
Posts: 15,209

Re: Problems and Solutions

clap.gif


Character is who you are when no one is looking.

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#441 2006-02-21 17:14:09

ganesh
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Registered: 2005-06-28
Posts: 15,209

Re: Problems and Solutions

Problem # k + 99

If y + 1/z = 1 and x + 1/y = 1, what is the value of xyz?


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#442 2006-02-22 02:40:00

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Problems and Solutions

I love that kind of problems.


IPBLE:  Increasing Performance By Lowering Expectations.

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#443 2006-02-22 03:29:04

ganesh
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Registered: 2005-06-28
Posts: 15,209

Re: Problems and Solutions

dart.jpg


Character is who you are when no one is looking.

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#444 2006-02-22 09:44:22

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Problems and Solutions

You're right, irspow, it would be more natural to model the man as having a constant acceleration like that, but ganesh did say that the men were moving towards each other, so the second part of your k+97 solution was not needed.


Why did the vector cross the road?
It wanted to be normal.

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#445 2006-02-22 10:13:42

irspow
Member
Registered: 2005-11-24
Posts: 455

Re: Problems and Solutions

I agree mathsyperson.  I nit-pick too much sometimes.  I wasn't trying to imply anything other than the real problems I was having with the solution and nothing more.  I will admit it is a little bit of a pet-peeve of mine that velocities are vectors and rarely treated as such.  I guess it's my physics background.  All I could think about for k+98 was all of the other real considerations that would be needed to solve such a problem in real life versus the friction free, force free, instantaneous velocity, infinite acceleration capable trains in question.  Please excuse me for these faults, I meant no harm.

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#446 2006-02-22 16:55:22

ganesh
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Registered: 2005-06-28
Posts: 15,209

Re: Problems and Solutions

Problem # k + hundred.jpg

From 3 men and 4 women, three persons are to be selected
in such a way that at least one woman is selected. In how many
different ways can they be selected?


Character is who you are when no one is looking.

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#447 2006-02-22 17:16:31

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Problems and Solutions


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#448 2006-02-22 18:59:02

ganesh
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Registered: 2005-06-28
Posts: 15,209

Re: Problems and Solutions

Ricky, try again!

Problem # k + 101

Prove that n! + 1 is composite for infinitely many values of n where n is a positive integer.


Character is who you are when no one is looking.

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#449 2006-02-22 19:22:48

rimi
Member
Registered: 2006-02-21
Posts: 17

Re: Problems and Solutions

For the problem K+100 the answer should be 34..
(4C1*3C2)+(4C2*3C1)+(4C3*3C0)=12+18+4=34

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#450 2006-02-22 19:23:24

ganesh
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Registered: 2005-06-28
Posts: 15,209

Re: Problems and Solutions

After a long time, here's solution to Problem # k + 42

Problem # k + 42

On a deserted island live five people and a monkey. One day everybody gathers coconuts and puts them together in a community pile, to be divided the next day. During the night one person decides to take his share himself. He divides the coconuts into five equal piles, with one coconut left over. He gives the extra coconut to the monkey, hides his pile, and puts the other four piles back into a single pile. The other four islanders then do the same thing, one at a time, each giving one coconut to the monkey to make the piles divide equally. What is the smallest possible number of coconuts in the original pile?

The smallest solution is 3121 coconuts in the pile.


Character is who you are when no one is looking.

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