Math Is Fun Forum

Mathsy, if you didn't know this earlier, Chennai is between the Equator and the Tropic of Cancer, and the people here are far more comfortable with Summer than winter! Many have respiratory syndromes and the winter is not too conducive. Again, if you didn't know that before, Chennai is one of the hottest cities in the world! A bonus is the fact that it is one of the cheapest metropoloitans with population of 5 million plus in the world!

its winter in chennai....its raining cats and dogs...yesterday we had 25 cm of rain...and temp is between 20 and 25 degrees Centigrade....very very cold......
I am very comfortable at 40 degrees Centigrade !

Yes, the shortest......
and do you know the worst tongue twister in English language?
'The sixth sick Sheik's sixt sheep's sick.'
I ain't sure 'bout that!

I think 4^^^6^^^8^^^9 is a much bigger number. You can use any number of '^' and keep increasing the number. There's no end to it.
If you are interested in knowing what x^^^y or x^^^^y is, go to this page.

Correct!

Problem # k + 52

Thereare a number of rabbits in a room. A leopard enters the room and eats a certain number of rabbits. The remaining rabbits run towards the next room. As they move from the first room to the second, the number of rabbits doubles. The leopard then enters the second room and eats the same number of rabbits as it did in the first room. The remaining rabbits run towards the third room. As they land in the third room, the number of rabbits multiplies by 3. Then the leopard comes and eats the same number of rabbits as it did in the first and the second. The remaining rabbits run to the fourth room and as they go from the third to the fourth room, the numbers or rabbits multiplies by 4. When the leopard comes to the fourth room, and eats the same number of rabbits as it did in the first, second and the third, there are no rabbits left.

How many rabbits were there in the first room before the leopard went and how many did the leopard eat in each room?

Mathsyperson's solution to problem # k + 50 is correct. Wanna be math wiz, thanks for your post.

Problem # k + 51

What would be the coefficient of the middle term of (a+b)^10?

You are right! Well done!
However, instead of finding a common denominator, a much simpler method exists.
If you have to tell which of the fractions a/b or c/d is greater,
multiply a and d, and b and c. ad represents the first fraction, bc the second.
If ad>bc, the first fraction is higher. If ad<bc, the second fraction is higher.
When comparing three or more fractions, rule out the options by choosing the higher or lower of the two, whichever is required.
For example,
to tell which of 3/7, 4/11, 5/13 is highest,
first compare 3/7 and 4/11. 33 represents the first fraction and 28 the second. Now, compare the first and the third. 39 represents the first fraction and 35 the third. Therefore, 3/7 is the highest of the three. Simple, isn't it?

A lemniscate is a curve with the cartesian equation
(x²  + y²)²  = a² (x²  - y²)
It is like this :- ∞
The polar equation is
r²=a²Cos2θ

Thanks to the teacher!

A = 88L² /7
When L=12.5 cm,
A= (88*12.5*12.5)/7 = 1964.28571 cm² rounded off to
A=1964 cm²