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

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#43752 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-07-22 21:55:17

I just remembered a question asked to me when I participated in a quiz when I was 14 :

A three digit number is written on a window glass,
the difference between the number and as it can be seen from the other side is 693,
what's the number? roll

#43753 Re: Help Me ! » Algebra problem » 2005-07-22 17:59:20

Algebra is using of variables like x,y,z etc to solve mathematical problems.
For example, if you have this problem
#1
When 53 is added to a number, you get 70. What is the number?
The solution would start this way.
Let x be the number.
Therefore, 53 + x = 70
                        x = 70 - 53 = 17

#2
25 added to the double of a number is 95. What is the number?
Solution:-
Let x be the number.
Therefore, 25 + 2x = 95
                        2x = 95 - 25 = 70
                         x = 70/2 = 35  big_smile

#43754 Re: Guestbook » Pythons » 2005-07-22 17:48:19

T R U C E !!!!!!!!!!!!!!!!

#43755 Re: Help Me ! » equations, equations... » 2005-07-22 16:55:44

GurraTedden wrote:

(three unknown x,y,z with three equations, always solvable right!? But i only want to solve this for x!!!)

There are actually six variables...x,y,z,a,b,c roll

#43756 Re: Help Me ! » Square root of 0 » 2005-07-22 16:46:51

Hi Helen,
I don't know what you mean by pie questions and pie formula.
If you mean pi, I shall explain to you.
Pi is a Greek alphabet used to represent the ratio of the circumference of a circle to its diameter, which is always a constant.
Pi is taken as 3.14 or 22/7, as an approximation,
but the actual value of pi is
3.14159265358979323846264338327950288.......it goes on and on.
The area of a circle of radius 'r' is
pi*r²  and its circumference is 2*pi*r
Similarly, the volume of a sphere of radius'r' is
4/3*pi*r³  and its area is 4*pi*r² .
Pi is also an angle of 180 degrees.
Therefore, pi/2 would be 90 degrees and pi/4 45 degrees.
If you have any specific doubt, you can post in this forum. smile

#43758 Re: Guestbook » maths » 2005-07-21 23:33:10

EveryoneTookTheGoodNames wrote:

Yup - maths is fun, expecially on this website

Great! That's a big compliment, Thank you smile

#43759 Re: Help Me ! » Square root of 0 » 2005-07-21 23:28:10

mathsyperson wrote:

e^(i*pi)=1

Of the five numbers considered important in mathematics, this number relates four.
I think this equation was given by Loenard Euler.
This, I think,  is a result of
e^(i*theta) = cos (theta) + i sin(theta)
and
Abraham de Moivre's theorem, according to which
(Cos(theta)+i*sin(theta))^n = cos n(theta) + i*sin n(theta)
which can be written as
e^(n*i*theta) = Cos n(theta) + i*sin n(theta) roll

#43760 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-07-21 22:07:33

Thank you, Admin, for the neat graph. smile

#43761 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-07-21 20:52:37

Cos(Sin A) is always greater than Sin (Cos A),
as rightly pointed out by Mathsy!
We shall test this for three values in the first quadrant, in degrees.
First, 0.01°.
Cos (Sin A) > Sin(CosA).
Next, for 45°
Again, Cos (Sin A) > Sin(CosA).
Finally, for 89.9°
Yet again, we get the same result.
I shall try to search for a proof, or prove it myself!

#43764 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-07-21 16:35:07

Which is greater?
Cos (Sin A) or Sin (Cos A)?

#43765 Re: Jokes » grand jokes » 2005-07-21 16:33:40

....and I heard the refrigerator was a washing machine! tongue

#43766 Re: Help Me ! » Square root of 0 » 2005-07-21 16:23:52

Hi, I love pi! Welcome to the forum!
Trying to find the square root of 0 using logarithms is not possible
as log 0 is not defnined. This is because any number raised to any number cannot be 0. That includes 0.
The square root, cube root, fourth root etc, of 0 IS 0.
This is because
0² = 0
0³ = 0
0^4 = 0 and so on.
Any nth root of 0 is 0, the only condition being n ≠ 0.
This follows from the fact that
if a^b = c, then bth root of c = a.
The birth of imaginary numbers is, indeed, interesting.
I had read somewhere that imaginary numbers have practical applications too!

#43767 Re: Help Me ! » Difficult question » 2005-07-20 21:21:03

There's a better one! Truly universally acceptable, but not being put into use anywhere (I think! wink )
1,0000 = Myriad
1,0000,0000 = Myllion
1,0000,0000,0000 = Byllion etc.

#43768 Re: Help Me ! » Algebra problem » 2005-07-20 21:17:54

mathsyperson wrote:

My favourite is the one with the square made up of a slightly smaller square and 4 right-angled triangles.

And thats the only one I remember! tongue

#43769 Re: Puzzles and Games » The bad coin » 2005-07-20 19:40:33

1/2
Because there's nothing special about Bill's coin!
Because the probability of getting (head, head and head),
(head, tail, and head) are the same, that is 1/8 !

#43770 Re: This is Cool » Do you think you can? » 2005-07-20 19:32:24

I would be wasting close to 33 years of my life if i did (the American Billion), assuming I don't sleep!

#43771 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-07-20 19:27:16

mathsyperson wrote:

Wow, four simultaneous equations...

There are only two:-
9x - 4y = 2,000
7x - 3y = 2,000

Solving for 'x', the annual income of the two can be calculated. They would be 9x and 7x. smile

#43772 Re: Help Me ! » Hi » 2005-07-19 22:22:44

There are two types of decimals:- Terminating and recurring.
A number like 12.5 or 1.25 or 3.75 is a terminating decimal.
On the other hand, sometimes, you have numbers like 0.33333333333333.................,
0.166666666666.....................,
1.6666666666666 etc which are called recurring decimals.
For example, 1'/2 or 1/8 is a terminating decimal.
1/3, 5/6 etc are recurring decimals.
I was talking about how recurring decimals are convereted into rational numbers (that is, fractions).
If that is clear, look at the following illustration.
How do we convert 2.166666666666.............. into a rational number?
Let x = 2.16666666666666666............
10 x = 21.66666666666666666..........  ----------(I)
100x = 216.6666666666666666.........  ----------(II)
Subtracting (I) from (II),
90x = 195,
x = 195/90 or 13/6.
Now, have I made myself clear?

#43773 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-07-19 21:58:49

#7
The ratio of annual incomes of two persons is 9:7 and the ratio of their annual expenditure is 4:3. Each of them saves $2000 yearly. Find their annual incomes.

#43774 Re: Help Me ! » Difficult question » 2005-07-19 21:56:38

As simple as that!
But you would have to remember
(1) A second is a billion (US) nanoseconds but not a billion (UK) nanoseconds.
and
(2) An American Gallon is different from a gallon in UK

#43775 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-07-19 19:25:30

31,100 = S - [500+0.04(s-10,000)]
31,100 = S -[500 + 0.04s - 400]
31,100 = S - 100 - 0.04s
31,200 = 0.96 S
S = 31,200 / 0.96
S = 32,500 smile

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