ORGANON

-x. Ln(x) = (x-1) Ln (x-1)

a right angled triangle is provided all of whose sides are integers.it is required to prove that the area of the triangle is an integer which is divisible by 6.

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Clue: ORD>STEP>NULL>

Suppose you have N dots. You want to connect the dots in such a way that each dot has at least one connection to the set of other dots. A dot may have more connections -- up to N-1, I think.

You have N identical cubes in Euclidean space. Any cube can be fused face-to-face with any other cube -- at most one cube per face.

All N cubes are attached to one another, directly or indirectly. For N=1, the only possible shape is a cube. For N=2, the only possible shape is a box one unit by one unit by two units.

How many distinct shapes are possible for N=3? N=4? Higher numbers of N? Can the solution to this problem be generalized to a formula for all positive integer Ns?

Each of its digits is also a prime to the power of a prime. What is R?

1473, 2100, 3665, 4300, 5700, 6500...

. lim n^(1/n)= 1 Necesito que me ayuden a probarlo. Gracias!

x → ∞

0, 1, 2, 1, 3, 2, 4, 1, 2, 3, 5, 2, 6, 4, 3, 1, 7, 2, 8, 3, 4, 5, ?

hint: involves prime numbers.

Es una secuencia difícil, asi que les diré como pista que esta relacionada con los números primos de alguna forma.

An ant and honey are on a perfect sphere , miraculously suspended in mid-air. The radius of the sphere is 5cm.

The drop of honey is at the north pole of the sphere, moving towards the south pole at a constant speed of 1.5 cm/s (for no good reason ... gravity would neither account for the drop leaving its cosy northern spot, nor for the constant speed) and stops as soon as it arrives there (unless eaten prior to that).

The ant sits at the equator, unfortunately on the opposite side of the drop's path . It decides for the shortest intercept route and sets off immediately.

When and at which latitude will the ant catch the drop?

I forgot to mention the ants speed: 2.5 cm/ second. My apologies! :)

An ant and honey are on a perfect sphere miraculously suspended in mid-air. The radius of the sphere is 5cm.

The drop of honey is at the north pole of the sphere, moving towards the south pole at a constant speed of 1.5 cm/s (for no good reason ... gravity would neither account for the drop leaving its cosy northern spot, nor for the constant speed) and stops as soon as it arrives there (unless eaten prior to that).

The ant sits at the equator, unfortunately on the opposite side of the drop's path . It decides for the shortest intercept route and sets off immediately.

When and at which latitude will the ant catch the drop?