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

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

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

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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,621

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

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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,621

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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,621

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

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,621

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.

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

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

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,621

Ricky and irspow are correct!

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,621

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?

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

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

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,621

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)?

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

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

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

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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,621

irspow, please check the solution you posted again

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,621

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?

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

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

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

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

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

Yeah

IPBLE: Increasing Performance By Lowering Expectations.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,621

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

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,621

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?

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

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