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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=...
since i²=-1,
then 0x∞=i²
hmm...
maybe it is the power half "brought down", as in
0.5 ln x=ln (x^0.5)
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?
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
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 ??
i dun get it
is e a variable or is it the constant e?
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
doubling is in fact a subset of multiplication; you just multiply by 2 each time
why is a newspaper red??
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)
can someone pls help me with this question, i am stuck at it for weeks
actually this problem is only relevant to mathematics.
In physics and chemistry, 1+a=1 if a is small.
yeah 2nd is school is really good
how to differentiate log x ?
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
what is dh00m?can someone enlighten me?
i found this in a book:
11826²=139854276
30384²=923187456
which are all the digits from 1 to 9
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
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
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 !!!!!
Maybe the website could add an online poll or something like that. That would be fun
why 444 or 777?
what is so special abt these numbers?
a can only be 0