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#401 2006-02-18 01:48:50

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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#402 2006-02-18 02:33:13

Jai Ganesh
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Registered: 2005-06-28
Posts: 47,110

Re: Problems and Solutions

Well done, mathsyperson!

neat_work_a.jpg

Problem # k + 94

If 1/a + 1/b + 1/c = 1/(a+b+c); a+b+c≠0 and abc≠0, what is the value of (a+b)(b+c)(c+a)?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#403 2006-02-18 03:06:10

irspow
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Registered: 2005-11-24
Posts: 1,055

Re: Problems and Solutions

Nice job, Mathsyperson!  I spent like twenty minutes to come up with the same answer using the disk method of integration.


I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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#404 2006-02-18 05:00:24

irspow
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Registered: 2005-11-24
Posts: 1,055

Re: Problems and Solutions

This is not my type of problem, but here goes nothing.

*edit

  Duh!  I forgot to subtract abc from both sides of the equation.

Last edited by irspow (2006-02-19 01:14:16)


I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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#405 2006-02-18 19:13:54

Jai Ganesh
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Registered: 2005-06-28
Posts: 47,110

Re: Problems and Solutions

irspow, please check the solution you posted again wink


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#406 2006-02-18 19:36:18

Jai Ganesh
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Registered: 2005-06-28
Posts: 47,110

Re: Problems and Solutions

Problem # k + 95

1 man or 2 women or three boys can do a work in 55 days. In how many days can 1 man, 1 woman and 1 boy do the same work?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#407 2006-02-18 22:07:26

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: Problems and Solutions











So a=-c or a=-b and

Last edited by krassi_holmz (2006-02-18 22:26:54)


IPBLE:  Increasing Performance By Lowering Expectations.

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#408 2006-02-18 22:31:02

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: Problems and Solutions

k+95:
1m-1/55 per day
1w-1/110 per day
1b-1/165 per day
t-the numbers of days:
t(1/55+1/110+1/165) = 1;
t(1/30)=1;
t=30 days.


IPBLE:  Increasing Performance By Lowering Expectations.

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#409 2006-02-19 01:22:20

irspow
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Registered: 2005-11-24
Posts: 1,055

Re: Problems and Solutions


I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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#410 2006-02-19 02:24:03

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: Problems and Solutions

Yeah


IPBLE:  Increasing Performance By Lowering Expectations.

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#411 2006-02-19 02:25:03

Jai Ganesh
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Registered: 2005-06-28
Posts: 47,110

Re: Problems and Solutions

24805BP~The-Simpsons-Mr-Burns-Excellent.jpg


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#412 2006-02-19 03:48:19

Jai Ganesh
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Registered: 2005-06-28
Posts: 47,110

Re: Problems and Solutions

Problem # k + 96

Can a majority of the numbers from 1 to a million be represented as the sum of a square and a (non-negative) cube?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#413 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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#414 2006-02-19 16:39:00

Jai Ganesh
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Registered: 2005-06-28
Posts: 47,110

Re: Problems and Solutions

mathsyperson, you are correct! roflolwave up


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#415 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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#416 2006-02-19 18:37:08

Jai Ganesh
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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?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#417 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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#418 2006-02-20 11:56:23

John E. Franklin
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Registered: 2005-08-29
Posts: 3,588

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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#419 2006-02-20 13:07:51

John E. Franklin
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Registered: 2005-08-29
Posts: 3,588

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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#420 2006-02-20 14:32:25

irspow
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Registered: 2005-11-24
Posts: 1,055

Re: Problems and Solutions

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


I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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#421 2006-02-20 17:20:59

Jai Ganesh
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Registered: 2005-06-28
Posts: 47,110

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


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#422 2006-02-20 18:13:40

Jai Ganesh
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Registered: 2005-06-28
Posts: 47,110

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.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#423 2006-02-21 03:37:38

irspow
Member
Registered: 2005-11-24
Posts: 1,055

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)


I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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#424 2006-02-21 03:46:47

Jai Ganesh
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Registered: 2005-06-28
Posts: 47,110

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


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#425 2006-02-21 03:49:19

irspow
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Registered: 2005-11-24
Posts: 1,055

Re: Problems and Solutions

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


I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

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