Math Is Fun Forum

Hi Shelly,
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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!

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

I got killed when I was riding a bike, and I was shot at a short range with a pistol in the head

The world record holder remembers 100,000 places

Thanks, Mathsisfun,
I am on the verge of post # 200
and this an occassion for me to celebrate,
I shall take a big chunk of thhat

We would be missing you all......
Do join us at the earliest........

MaTHEMATICS IS THE HIGHEST DEGREE OF LOGIC
AND IF YOU THINK RIGHT, MATHEMATICS IS WITH YOU

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?

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

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.