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

mathsyperson
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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
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Re: Problems and Solutions

mathsyperson is correct smile

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?


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

ganesh
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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.


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

krassi_holmz
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Re: Problems and Solutions

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


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

ganesh
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Re: Problems and Solutions

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


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

ganesh
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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.


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

krassi_holmz
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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
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Re: Problems and Solutions

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


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

mathsyperson
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Registered: 2005-06-22
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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. smile


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

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

ganesh
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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?


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

krassi_holmz
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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
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Re: Problems and Solutions

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


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

ganesh
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Re: Problems and Solutions

Problem # k + 82

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


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

krassi_holmz
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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
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Registered: 2005-11-24
Posts: 455

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
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Re: Problems and Solutions

krassi_holmz is right! smile
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).


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

ganesh
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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?


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

krassi_holmz
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Registered: 2005-12-02
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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
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Re: Problems and Solutions

krassi_holmz, you are given another chance.


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

Ricky
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Registered: 2005-12-04
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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
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Registered: 2005-11-24
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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
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Re: Problems and Solutions

Well done, irspow smile


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

ganesh
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Registered: 2005-06-28
Posts: 13,224

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?


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

irspow
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Registered: 2005-11-24
Posts: 455

Re: Problems and Solutions

I'll take an ill-attempted stab. 

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

ganesh
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Registered: 2005-06-28
Posts: 13,224

Re: Problems and Solutions

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


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