Thursday, July 23, 2009
Mathematical Proving Part 2
In case you all are wondering how to solve the maths question given by mr chow, here is the answer from the Net. Enjoy.^^
Prove that sum of all angles in a triangle is equal to 180 degrees.
Since lines a and b are parallel, <)BAC = <)B'CA and <)ABC = <)BCA'. It is obvious that <)B'CA + <)ACB + <)BCA' = 180 degrees. Thus <)ABC + <)BCA + <)CAB = 180 degrees. Prove that 9.99999[recurring forever] is equal to 10 Method 1 (chim version)
9.999999.....
= 9 + 9/10 + 9/100 + 9/1000 + ......
This is an infinite geometric series
Recall that the sum of an infinite geometric series is a/(1-r) where 'a' is the first term and 'r' is the common ratio.
In this case
a = 9
r = 1/10
Sum = 9/(1-(1/10))
= 9/(9/10)
= 10
9.99999.... = 10
Method 2 (simpler version)
x = 9.99999.....
10x = 99.99999......
10x = 90 + 9.99999.....
10x = 90 + x
9x = 90
x = 10
Method 3 (simplest version)
10/3=3.33333
3.33333*3=9.999999
10/3*3=3.333333*3
Thus, 10=9.9999[recurring forever]
Calculate sqrt(6+sqrt(6+sqrt(6+.....))))))
let x=sqrt(6+sqrt(+sqrt(6+....)))))
sqrt(6+sqrt(6+sqrt(6+....)))))=sqrt(6=Sqrt(6+sqrt(6+.....)))))
sqrt(6+x)=x6+x=x^2
x^2-x-6=0
(x-3)(x+2)=0
therefore x=3 or x=-2
Hope u enjoy it... ^^
Cheers,
-waygene=)
many hearts joined as ONE!!
7:31 PM
