Math Is Fun Forum

A little further.....
(-1/6) ln( 1-2x^3 )=
ln[1/(1-2x^3)^1/6]
MathsIsFun had done it right, I posted this
.... just to complicate things

I was first taught the difference between variables and constants.
Thereafter, the lessons were on simple operations of addition, division, multpilication, subtraction, extracting roots, exponentiation etc.
The next step was solving linear equations in one variable, simultaneous equations of two, three variables. A little later I learnt solving quadratic equations and their properties. I forgot to mention, I was also taught plotting graphs and solving equations with graphs.
The Binomial theorem was the last I was taught, and Pascal's triangle too.

It was raining cats and dogs in Chennai yesterday evening. My murderer devised a novel method of eliminating me. He connected the water supply at my home to the power. When I opened the tap, I was hit by 230 Volts, enough to kill me!
Dead!

Now you know who the murderer is!

I like Australia too.

I don't know if its allowed:-
38 - (2 x 5)

x = y + 30
y = 3z, z=y/3
Therefore, x + y + z = y + 30 + y + y/3 which is equal to 1500.
7y/3 = 1500 - 30 = 1470
y = 1470 x 3/7 = 630
y=630, x=660, z=210.

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Millie has 40 coloured shapes.

25 are circles and the rest are squares

23 of the shapes are blue and the rest are green

Therefore, 25 are circles and 15 are squares.

23 of the shapes are blue, therefore 17 are green.

The least number of blue circles is 8 and the least number of green circles is 2.

Serendipity

Osmosis

Catastrophe

Vigintillion

Connivance

Regicide

Thanatophobia

Mercenary

The proper link is
www.funcyber.com/good-fun-jokes/.

Click here

I haven't seen the contents on the website yet, I have just provided the link.

You are right Mathsy. The solution to the problem given was 81.5, which is certainly incorrect! I would solve the problem exactly the way you did
(I thought of the method of solving at the time of posting, but didn't actually solve it!)

A simple proof I can think of is
(a+b+c)²=a² + b² + c² + 2ab + 2bc + 2ac
When n=1 in your case,
a=10000, b=200, c=1
The resultant is 100000000 + 40000 + 1 + 4000000 + 400 + 20000 = 104060401.
This will continue as n increases.
For example, for n=2,
a=1000000, b=2000, c=1.
The resultant would be 1000000000000 + 4000000 + 1 + 4000000000 + 4000 + 2000000 = 1004006004001.
It can be seen that the other digits are not affected because of the number of zeros in a and b.
Hence, for any value of n, the resultant is a perfect square.
q.e.d

Problem # k + 25

Three mathematics classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.

What is the average of all the three classes?