Problems and Solutions

krassi_holmz · 2005-12-28 20:48:44

krassi_holmz · 2005-12-28 20:56:02

The clock:

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

krassi_holmz · 2005-12-28 20:58:08

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

Jai Ganesh · 2005-12-28 21:03:26

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

krassi_holmz · 2005-12-28 21:11:01

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

Jai Ganesh · 2005-12-28 21:29:13

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

krassi_holmz · 2005-12-28 22:31:30

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

krassi_holmz · 2005-12-28 22:38:53

Sometimes the degrees are better than the radians...

krassi_holmz · 2005-12-28 22:39:55

sqr(Phi)=1.272019650...

Jai Ganesh · 2006-01-02 16:27:23

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.

Jai Ganesh · 2006-01-02 21:34:39

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?

krassi_holmz · 2006-01-02 21:43:25

K+28-it was very simple!

But my proof is correct, too.

mathsyperson · 2006-01-02 23:11:52

Jai Ganesh · 2006-01-03 16:15:47

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?

Jai Ganesh · 2006-01-04 16:21:10

Problem # k + 79

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

krassi_holmz · 2006-01-04 23:19:37

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

Jai Ganesh · 2006-01-05 16:09:17

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

Jai Ganesh · 2006-01-05 17:42:49

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.

krassi_holmz · 2006-01-05 21:48:14

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

Jai Ganesh · 2006-01-05 22:13:31

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

mathsyperson · 2006-01-06 06:22:39

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.

Jai Ganesh · 2006-01-06 17:47:26

Probelm # k + 81

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

krassi_holmz · 2006-01-06 22:28:21

I'm not sure.

Jai Ganesh · 2006-01-07 19:00:57

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

Jai Ganesh · 2006-01-07 20:03:45

Problem # k + 82

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

Math Is Fun Forum

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