Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#326 2005-12-28 20:48:44

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

Re: Problems and Solutions


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#327 2005-12-28 20:56:02

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

Re: Problems and Solutions

The clock:

Last edited by krassi_holmz (2005-12-28 21:03:21)


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#328 2005-12-28 20:58:08

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

Re: Problems and Solutions

Please post a proof of k+28 Please! It must be more prime than mine!


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#329 2005-12-28 21:03:26

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Problems and Solutions

krassi_holmz, you've made some mistake. Check your solution to problem # k + 76 again. The angle is obtuse.


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.

Offline

#330 2005-12-28 21:11:01

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

Re: Problems and Solutions

I'll try different way.
<[BOC]=4*30°+30((60-35)/60)=132.5°


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#331 2005-12-28 21:29:13

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Problems and Solutions

You are correct, krassi_holmz! Its much simpler working on degrees than on radians.


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.

Offline

#332 2005-12-28 22:31:30

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

Re: Problems and Solutions

Yes, the mistake in pirst proof is from the redians.


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#333 2005-12-28 22:38:53

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

Re: Problems and Solutions

Sometimes the degrees are better than the radians...
smile


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#334 2005-12-28 22:39:55

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

Re: Problems and Solutions

sqr(Phi)=1.272019650...


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#335 2006-01-02 16:27:23

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Problems and Solutions

Proof : Problem # k + 28

n²! can be expressed as n!(n+1)(n+2)...(n+n)(2n+1)(2n+2)....(3n)(3n+1).....(kn)(kn+1)........(n²).
In the denominator, we have (n!)^n.
It can be seen that (n+1)(n+2)......(2n) is divisble by n!, (2n+1)(2n+2)...(3n) is divisible by n! and so on.
This is because the product of any n consecutive natural numbers is always divisible by n!.(Remember, for n>r, nCr is always a natural number).
Thus for every n! in the denominator, there is a term in the numerator which is divisible by it.
Therefore, n²! is divisible by (n!)^n.


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.

Offline

#336 2006-01-02 21:34:39

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Problems and Solutions

Problem # k + 77

A piece of equipment cost a certain factory $ 600, 000. If it depreciates in value, 15% the first year, 13.5 % the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?


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.

Offline

#337 2006-01-02 21:43:25

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

Re: Problems and Solutions

K+28-it was very simple!

But my proof is correct, too.


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#338 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.

Offline

#339 2006-01-03 16:15:47

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

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?


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.

Offline

#340 2006-01-04 16:21:10

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

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 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.

Offline

#341 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.

Offline

#342 2006-01-05 16:09:17

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Problems and Solutions

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

Offline

#343 2006-01-05 17:42:49

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

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 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.

Offline

#344 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.

Offline

#345 2006-01-05 22:13:31

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Problems and Solutions

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

Offline

#346 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. smile


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

Offline

#347 2006-01-06 17:47:26

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

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 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.

Offline

#348 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.

Offline

#349 2006-01-07 19:00:57

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Problems and Solutions

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

Offline

#350 2006-01-07 20:03:45

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

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 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.

Offline

Board footer

Powered by FluxBB