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## #401 2006-02-15 12:53:51

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

### Re: Problems and Solutions

I think my and irspow's methods are pretty much the same, just worded differently. We get the same answer, anyway.

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

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## #402 2006-02-15 13:04:42

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: Problems and Solutions

Sorry, I didn't mean to jump in your spot.  The wording of this problem is what had me scratching though.  I wasn't sure if ganesh wanted the over-all probability of drawing a defective bolt from B or the probability that I (or should I say we?) calculated.

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## #403 2006-02-15 13:54:23

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

### Re: Problems and Solutions

Don't worry, you're in your own spot. Our spots just happen to look similar.
Anyway, I think we're right. Ganesh told us that the bolt was defective, and wanted to know tha probability of it being from B.

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

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## #404 2006-02-16 00:21:55

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### Re: Problems and Solutions

Both mathsyperson and irspow are correct. Well done.

Problem # k + 90

Find the formula for sum of n terms of
(1*2*3), (2*3*4), (3*4*5), (4*5*6),................. Prove that the formula is correct by Mathematical Induction.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #405 2006-02-16 05:03:04

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

### Re: Problems and Solutions

k+90's formula is:

Anybody want to try their hand at an induction proof, or should I?

"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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## #406 2006-02-16 16:32:01

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### Re: Problems and Solutions

Ricky is correct. I shall wait for someone to post a proof.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #407 2006-02-16 16:51:11

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### Re: Problems and Solutions

Problem # k + 91

Find three consecutive terms in Geometric Progression such that their sum is 21 and the sum of their squares is 189.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #408 2006-02-17 00:11:28

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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## #409 2006-02-17 00:36:45

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### Re: Problems and Solutions

mathsyperson's solution to problem # k + 91 is correct. I shall post the method if none of the others are able to give a proper solution with the steps.

Problem # k + 92

If x=9 + 4√5, find the value of √x - 1/√x.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #410 2006-02-17 08:21:57

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

### Re: Problems and Solutions

I have the induction proof written up on paper, but I'm a bit too lazy to type it all up now.  Maybe later tonight.

"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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## #411 2006-02-17 11:17:34

irspow
Member
Registered: 2005-11-24
Posts: 457

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## #412 2006-02-17 20:47:57

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### Re: Problems and Solutions

Ricky and irspow are correct!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #413 2006-02-17 21:35:43

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### Re: Problems and Solutions

Problem # k + 93

A right ciruclar cone is cut by two planes parallel to the base, trisecting the altitude. What is the ratio of the volumes of the three parts, the top, middle and the bottom respectively?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #414 2006-02-18 01:48:50

mathsyperson
Moderator
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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## #415 2006-02-18 02:33:13

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### Re: Problems and Solutions

Well done, mathsyperson!

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #416 2006-02-18 03:06:10

irspow
Member
Registered: 2005-11-24
Posts: 457

### 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.

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## #417 2006-02-18 05:00:24

irspow
Member
Registered: 2005-11-24
Posts: 457

### 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)

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## #418 2006-02-18 19:13:54

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### Re: Problems and Solutions

irspow, please check the solution you posted again

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #419 2006-02-18 19:36:18

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### 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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #420 2006-02-18 22:07:26

krassi_holmz
Real Member
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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## #421 2006-02-18 22:31:02

krassi_holmz
Real Member
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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## #422 2006-02-19 01:22:20

irspow
Member
Registered: 2005-11-24
Posts: 457

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## #423 2006-02-19 02:24:03

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

### Re: Problems and Solutions

Yeah

IPBLE:  Increasing Performance By Lowering Expectations.

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## #424 2006-02-19 02:25:03

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### Re: Problems and Solutions

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #425 2006-02-19 03:48:19

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### 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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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