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## #351 2006-01-02 23:11:52

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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## #352 2006-01-03 16:15:47

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

mathsyperson is correct

Problem # k + 78

A, B, and C are partners in a business. Their shares of capital are 1/2:1/3:1/4. A withdraws half of his capital after 15 months. After 15 months more,the profit of \$ 4340 is divided between them propotional to their capital. What is C's share of the profit?

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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## #353 2006-01-04 16:21:10

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

Problem # k + 79

Show that the set (1, 11, 101, 1001,......10^n+1) where n≥10 has more non-prime numbers than primes.

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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## #354 2006-01-04 23:19:37

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

### Re: Problems and Solutions

Last edited by krassi_holmz (2006-01-04 23:30:18)

IPBLE:  Increasing Performance By Lowering Expectations.

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## #355 2006-01-05 16:09:17

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

Outstanding! krassi_holmz, you deserve to be complimented for that!

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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## #356 2006-01-05 17:42:49

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

Probelm # k + 80

A line 2x + 3y + 1 = 0 tocuhes a circle C at (1, -1). Another circle cuts circle C orthogonally and the end points of its diameter are (0, -1), (-2, 3). Find the equation of the circle C.

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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## #357 2006-01-05 21:48:14

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

### Re: Problems and Solutions

Thank you. For the next problem I'll leave it to somebody else.

IPBLE:  Increasing Performance By Lowering Expectations.

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## #358 2006-01-05 22:13:31

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

Interestingly, none has replied to Problem # k + 78, which I thought was relatively simple

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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## #359 2006-01-06 06:22:39

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

### Re: Problems and Solutions

krassi_holmz wrote:

Thank you. For the next problem I'll leave it to somebody else.

Me too. I've answered far too many of these, so let's give someone else a turn.

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

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## #360 2006-01-06 17:47:26

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

Probelm # k + 81

If [{(sinθ)/(1+cosθ)} + {(1+cosθ)/(sinθ)}]= 4, what is the value of θ if
0 degrees≤θ≤90 degrees?

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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## #361 2006-01-06 22:28:21

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

### Re: Problems and Solutions

I'm not sure.

IPBLE:  Increasing Performance By Lowering Expectations.

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## #362 2006-01-07 19:00:57

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

krassi_holmz, you are correct! Why are you uncertain about a correct answer? Well done, krassi_holmz.

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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## #363 2006-01-07 20:03:45

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

Problem # k + 82

If x^4 + y^4 = 17 and x + y =1, what is the value of x²y²-2xy?

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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## #364 2006-01-07 23:18:08

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

### Re: Problems and Solutions

x^2+y^2=x^2+y^2+2xy-2xy=(x+y)^2-2xy=1-2xy.
x^4+y^4=17=x^2^2+y^2^2+2x^2y^2-2x^2y^2=(x^2+y^2)^2-2x^2y^2=(1-2xy)^2-2x^2y^2 = 1-4xy+4x^2y^2-2x^2y^2=1-4xy+2x^2y^2 =>
2x^2y^2-4xy=17-1=16
x^2y^2-2xy=16/2=8

IPBLE:  Increasing Performance By Lowering Expectations.

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## #365 2006-01-08 04:51:53

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

### Re: Problems and Solutions

I might be missing something obvious, but...

1/2 + 1/3 + 1/4 = 13/12?  Doesn't one of the partners in k+78 own a 1/12 imaginary share?

I think that this problem could only be solved if we knew who was holding the fake share.

Last edited by irspow (2006-01-08 04:54:55)

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## #366 2006-01-08 16:22:43

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

krassi_holmz is right!
To irspow : In problem # k + 78, when it is stated that the shares are in the ration a:b:c, it need not be true that a+b+c be equal to 1. a's share of the total would be a/(a+b+c), b's share would be b/(a+b+c) and c's c/(a+b+c).

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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## #367 2006-01-08 17:28:19

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

Problem # k + 83

Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. What is the area left ungrazed by the horses?

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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## #368 2006-01-08 17:45:49

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

### Re: Problems and Solutions

70^2 - 45^2 Pi ?

IPBLE:  Increasing Performance By Lowering Expectations.

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## #369 2006-01-08 22:50:51

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

krassi_holmz, you are given another chance.

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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## #370 2006-01-09 03:36:33

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

### Re: Problems and Solutions

Last edited by Ricky (2006-01-09 03:40:26)

"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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## #371 2006-01-09 13:06:26

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

### Re: Problems and Solutions

Last edited by irspow (2006-01-09 13:39:29)

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## #372 2006-01-09 16:16:22

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

Well done, irspow

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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## #373 2006-01-09 16:39:06

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

Problem # k + 84

Two spheres of radii 6 cm and 1 cm are inscribed in a right circular cone. The bigger sphere touches the smaller sphere and also the base of the cone. What is the height of the cone?

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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## #374 2006-01-10 11:21:02

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

### Re: Problems and Solutions

I'll take an ill-attempted stab.

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## #375 2006-01-10 21:54:50

ganesh
Registered: 2005-06-28
Posts: 23,359

### Re: Problems and Solutions

irspow is correct! Although the actual solution is arrived at differently!

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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