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#42676 Re: Puzzles and Games » Trains » 2005-07-31 23:03:23
There's no inactive train at all! There is only one train!
The train passes through the tunnel, heading for the park, at 8 AM.
The same train passes through the tunnel, going away from the park, at 8 PM.
#42677 Re: Help Me ! » Has anyone seen this formula before? » 2005-07-31 22:59:05
Oh ok. But what formula would I use if i want to find the angle oposite to side 'b' if i'm only given the lengths of sides 'a' and 'b' and the angle between them?
With the help of the formula
c² = a² + b² - 2ab Cosθ,
you can find the value of c.
Now, use the formula
b² = a² + c² - 2ac Cosθ.
You know the value of a,b, and c.
You would get
Cosθ = x (some value)
The angle opposite to side 'b' would then be
θ = Cos-¹x.
Is that clear? 
#42678 Re: This is Cool » Which of the two is greater? » 2005-07-31 22:21:46
I've got as far as the yth root of y = the xth root of x, but now I'm stuck.
Interestingly, if yth root of y = xth root of x,
it does not automatically follow that x=y
For example, if x=4 and y=2,
then this is true! 
#42679 Re: Help Me ! » Has anyone seen this formula before? » 2005-07-31 22:15:20
Zmurf,
This formula is easier remembered as
a² = b² + c² - 2bc cosθ
On simplification of the equation given by you, this is what is obtained.
a,b, and c are the three sides of a triangle.
If the triangle is rightangled and θ is 90 degrees or pi/2 radians,
Cos θ = 0,
which gives us
a² = b² + c²,
the Pythogoras Theorem.
#42680 Re: Help Me ! » what u think of this problem » 2005-07-31 21:03:13
Corrected the post; thanks, Mathsyperson.
#42681 Re: Guestbook » Everyone has to like him » 2005-07-31 20:57:46
You are right, Rora! Mathsisfun is remarkable 
#42682 Re: Dark Discussions at Cafe Infinity » Be aware of my absence » 2005-07-31 20:08:39
Welcome back, Rora
#42683 Re: This is Cool » will tehre ever be a single particle that makes EVERYTHING » 2005-07-31 18:58:40
But before that read 'A Brief Histroy of Time' by Stephen Hawking
#42684 Re: This is Cool » the philosophy and science behind teleportation » 2005-07-31 18:55:51
Mathematics lovers discusing Futurology and Genetics (and Cybernetics?)
#42685 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-07-31 18:54:04
As always, you are corect, Mathsy!
I shall show how I did it.
Assume both candles are 'h' inches in height.
The height of the first candle reduces by h/4 every hour and that of the second reduces by h/3.
Lets assume in time 't' hours, the first is twice the height of the second.
Therefore,
h - t(h/4) = 2 [h - t(h/3)]
h - ht/4 = 2h - 2ht/3
h = 2ht/3 - ht/4
h = 5ht/12
Cancelling h on both sides,
1 = 5t/12
or t = 12/5
The unit we had taken was hours,
therefore, in 12/5 hours, that is 2 2/5 hours, one will be double the height of the other.
Simplified, it is 2 hours and 24 minutes.
#42686 Re: Help Me ! » what u think of this problem » 2005-07-31 18:36:24
Let's plug in some numbers just to get this started:
x=1: 3x^2 + x = 4y^2 +y becomes 5 = 4y^2 +y
When we put x=1,
3x² + x = 3(1² ) + 1 = 4
Therefore,
4y² + y - 4 = 0
y = [-1 ± √ (1 + 64)]/8 = [-1 ± √ 65 ]/8
which is an irational number.
We see that here too x-y is not the square of a natural number
#42687 Re: Help Me ! » what u think of this problem » 2005-07-31 18:21:00
x and y are two natural numbers such that 3x^2 + x = 4y^2 +y
Put x=2,
we get 4y² + y - 14 = 0, Solving,
we get y = [-1 ± √(1 + 224)] / 8
y = -2 or 1.75
Neither of them are Natural Numbers!
x - y is NOT always a square of a natural number
#42688 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-07-29 19:54:39
Two candles A and B, of equal height but different circumferences, burn for 4 hours and 3 hours respectively. If the two are lit at the same time, after what time would one candle be half the height of the other?
#42689 Re: Help Me ! » Hi » 2005-07-29 18:22:15
Nora can paint 1/6 of a house in 1 day.
Therfore, she takes 6 days to paint the house.
Meera can paint the whole house 2 days faster.
So, she can paint the house in 4 days.
In one day, Meera can paint 1/4 of the house.
If both of them paint the house together, in one day,
they can paint (1/6+1/4) of th house. That is,
10/24 or 5/12. Therefore, the whole house can be painted
by them in 12/5 days, that is 2 2/5 days.
#42690 Re: This is Cool » the philosophy and science behind teleportation » 2005-07-28 18:27:54
We are discussing this 2.500 years ahead of mankind
Maybe in 4,500 AD, brain and the body could be digitized,
maybe then the DNA pattern would be
010100101011100101011001011100011010100010110001.........................
and not
AGCTGGCTAACGTTACTGTTACACGTACGGAATCAGTTAAGCTAAGCT..........
#42691 Re: Dark Discussions at Cafe Infinity » do fish have a personality » 2005-07-28 16:51:29
i don't think fish have real process of their mind, it is proven that they don't feel pain.
It is wrong to assume fish don't feel pain. Any member of the animal kingdom that reacts to touch does feel pain (I think )
#42692 Re: This is Cool » will tehre ever be a single particle that makes EVERYTHING » 2005-07-28 16:36:40
......or will it just keep getting smaller, if we do we will have gotten to the smallest possible thing,.....
Atoms were considered to be the building blocks, then the subatomic particles were discovered....and now, it is said that the subatomic particles like neutrons, protons, electorns etc are made up of quarks;
but I am not sure whether that is true for neutrinos, mesons, muons, positrons etc.
#42693 Re: Help Me ! » Relation between: inv, arc, co, arcco?? » 2005-07-28 16:31:30
That is neatly explained.
Both Sin-¹x and Arcsin x are one and the same, and both are in use in Mathematics Textbooks.
To make things simple, if Sin x = 1/2,
it follows that Sin -¹(1/2) = x
or ArcSin(1/2) = x
#42694 Re: Dark Discussions at Cafe Infinity » Serious Discussion! » 2005-07-27 00:09:01
An eye for an eye, a tooth for a tooth....
Extrapolated,
a life for a life
It takes the society nowhere.
But what do we do with criminals involved in
Homicide / Terrorism / Drug trafficking / Adultery / Molesting ?
Forgive them?
Award a lesser sentence like life imprisonment??
Banish them ???
#42695 Re: Help Me ! » Integration... » 2005-07-27 00:01:50
dx=asin(y)dt
(a is a constant value)
where y=y(t)
∫dx = ∫ asinyt dt
∫dx = a ∫sinyt dt
x = a(-cosyt/y) + Constant ???????????
#42696 Re: Guestbook » maths » 2005-07-26 23:03:07
what is your name
from shelly
Hi Shelly,
There are 909 registered users in this forum.
#42697 Re: This is Cool » One divided by Infinity » 2005-07-25 20:32:22
The logic seems acceptable.
It is easy to say 1/∞ is 0 because 1/0 is ∞,
just as 1/(a/b) = b/a.
If 1/a=b, it follows that 1/b=a
Indeterminate forms are only when both a and b are equal to zero,
or both a and b are equal to infinity.
Abishek, you missed another indeterminate form.
That is 0^0
#42698 Re: Help Me ! » . » 2005-07-25 19:33:58
The binomial expansion of the Left Hand Side
contains two terms, among many, which are
a^a*n and b^a*n which appear to make the LHS greater than the RHS,
but when we assign arbitrary values,
say a=10, b=1,000,000,000 and n=100
the LHS is (1,000,000,010)^1000, which would contain 9,001 digits;
the RHS becomes
100 x (100^1,000,000,000) which would contain more than 2 billion digits!
This happened because we assumed b>>n.
Otherwise, the LHS may be greater.
Say, when a=10, b=100, n=1000.
LHS would be 110^10,000 containing 20,414 digits and the RHS would be much smaller, viz. 100*(1000^100), containing approximately 300 digits!
#42699 Re: Help Me ! » As easy as it seems? » 2005-07-25 16:29:36
You may also remember, given the roots of a quadratic equation, the equation can be got thus:-
x² -(Sum of the roots)x + (products of the root) = 0
#42700 Re: Help Me ! » Substitution Method (where two lines cross) » 2005-07-25 16:26:05
Solving the two equations, you get
x = -5/2, y = -1/6
Hence, the two lines cross at
(-5/2, -1/6)
How the two equations are solved:-
First equation can be written as x+3y = -3
The second equation can be written as x - 3y = -2
Adding the two, we get 2x = -5, or x = -5/2
Substituting this value in equation (1) -5/2 + 3y = -3
3y = -3 + 5/2
3y = -1/2
y = -1/6