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.

#51 Re: Help Me ! » Hep with Trig. please :) » 2005-08-23 22:41:28

wcy

1=cos^2 x+sin^2 x
then, group all the sin terms...

2 sinx cosx +cos^2x=cos^2x +sin^2 x
2 sinx cosx=sin^2 x
sin^2 x-2 sinx cos x=0
sin x(sin x-2 cos x)=0
sin x=0 or sin x=2 cos x
x=0,etc..
or tan x=2
x=...

#52 Re: This is Cool » 0x∞=-1 ??? » 2005-08-22 21:00:47

wcy

since i²=-1,
then 0x∞=i²
hmm...

#53 Re: Help Me ! » Integration. Where is the 2 coming from? » 2005-08-22 20:56:37

wcy

maybe it is the power half "brought down", as in

0.5 ln x=ln (x^0.5)

#54 Puzzles and Games » Tunnel Conundrum » 2005-08-15 23:02:45

wcy
Replies: 8

If a hole was drilled from one end of the earth to the other through the centre, and a ball was dropped into it, what will happen to the ball?

#55 Re: This is Cool » 0x∞=-1 ??? » 2005-08-15 22:56:45

wcy

Proof of following "theorem" using vectors method.

Let the first line be a vector (x,y) (vertical matrix)
Let the 2nd line be a perpendicular vector (p,q)

cos 90=0=(x,y).(p,q)=xp+yq (dot product)
yq=-xp

Therefore, gradient1xgradient2=(y/x)(q/p)=yq/xp=-xp/xp=-1

#56 This is Cool » 0x∞=-1 ??? » 2005-08-15 22:40:04

wcy
Replies: 8

Under the topic of linear graphs, we are taught that if two straight lines are perpendicular to each other, then their product of gradients is equal to -1.

Since a line with gradient 0 (horizontal line)is perpendicular to a line with gradient ∞ (vertical line), isn't 0x∞=-1 ??

#59 Re: This is Cool » Remembering sin and cos values » 2005-08-15 00:48:41

wcy

another way of remembering sin/cos 45 and sin/cos 60 or 30 is to draw some triangles.
For 45 degrees, draw an isosceles right angled triangle, with sides 1,1,√2
For 60 degrees, draw an equilateral triangle with sides 2 by 2 by 2 and divide it into 2 equal triangles by bisecting one of the 60 degree angles
for sin 0, cos 0, just imagine a triangle with an angle so small that it is almost 0

#60 Re: Help Me ! » doubling » 2005-08-15 00:45:15

wcy

doubling is in fact a subset of multiplication; you just multiply by 2 each time

#61 Re: Jokes » funny one » 2005-08-15 00:39:36

wcy

why is a newspaper red??

#62 Re: This is Cool » 0.9999....(recurring) = 1? » 2005-08-13 19:08:54

wcy

This proof will probably prove once and for all that 0.999..=1

0.9999...=0.9+0.09+0.009+0.0009+...
This is clearly a Geometric Progression, so we can use the formula Sum to infinity=a/(1-r), where a is the first term and r is the common ratio (0.1)

Hence, the sum to infinity=0.9/(1-0.1)=0.9/0.9=1 !!!

Proof of GP formula:
(1-r)(a+ar+ar^2+ar^3+...)=a
Therefore, a+ar+ar^2+ar^3+...=a/(1-r)

#63 Re: Help Me ! » Vectors question » 2005-08-12 23:08:40

wcy

can someone pls help me with this question, i am stuck at it for weeks

#64 Re: This is Cool » 0.9999....(recurring) = 1? » 2005-08-12 23:03:18

wcy

actually this problem is only relevant to mathematics.

In physics and chemistry, 1+a=1 if a is small.

#65 Re: Help Me ! » Hi » 2005-08-12 23:00:25

wcy

yeah 2nd is school is really good

#67 Re: Jokes » Mnemonics » 2005-08-12 22:34:33

wcy

mnemonics are really useful, but no much use for maths. Maths is not so much about memorising. Mnemonics are really useful for subjects like Biology, though

#69 This is Cool » interesting numbers » 2005-08-12 22:31:40

wcy
Replies: 4

i found this in a book:

11826²=139854276

30384²=923187456

which are all the digits from 1 to 9

#70 Re: Help Me ! » Constrain proportions » 2005-08-12 22:22:56

wcy

visit http://www.geocities.com/chengyuanwu
it has a shrinking thingy that is similar

i used this code:
var shrinkspeed=0.99;
document.gate.height*=shrinkspeed
document.gate.width*=shrinkspeed
gateheight*=shrinkspeed
gatewidth*=shrinkspeed
document.gate.style.posLeft+=6
document.gate.style.posTop+=3
shrinkspeed-=0.001

so basically, it shrinks less and less as time progresses

#71 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-11 21:01:53

wcy

for quadratic equations, you can make use of the symmetry of the graphs to find the minimum point, which is halfway in between the two x-intercepts

#72 Re: This is Cool » 0.9999....(recurring) = 1? » 2005-08-11 20:59:54

wcy

no matter what, 0.99999999999... is really close to 1

here is another "proof" thought of by me
Let
a=1
b=0.0000000000000000...1
a-b=0.99999999....
a²-b²=1²-0.000000....1=0.99999999...
(a+b)(a-b)=a²-b²
a+b = (a²-b²)/(a-b)=0.9999.../0.9999...=1
a=1
therefore b=0 !!!!
therefore a-b=0.999999...=1-0=1  !!!!!

#73 Maths Is Fun - Suggestions and Comments » Online poll for website » 2005-08-10 12:51:00

wcy
Replies: 14

Maybe the website could add an online poll or something like that. That would be fun

#74 Re: Introductions » hello im jamie » 2005-08-10 12:49:19

wcy

why 444 or 777?
what is so special abt these numbers?

Board footer

Powered by FluxBB