[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 371

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Mischek писал(а) >>


Question removed, I overheated.

everything works


http://blogs.pcmag.ru/node/96

:)

 
Grisha drove a 100 km long route. He has a computer in his car that provides a forecast of the time remaining before he reaches the destination. This time is calculated on the assumption that the average speed of the car on the remaining part of the route will be the same as on the already passed.

Immediately after the start the computer showed "2 hours" and all the rest of the time it showed exactly this number (the computer is good). Find x(t) - the dependence of the distance travelled by Grisha on the time since the start. Plot the graph of this dependence.

P.S. Well, you don't need to make a graph, the analytical dependence is enough.

 

For those who are brain-dead, there is a more serious problem:

There are three equal chords AB, CD and PQ in a circle with centre O (see figure). Prove that MOK is half of angle BLD.



 

Also, for lovers of problems with weights:

In physics class, the teacher set up the following experiment. He placed 16 kettlebells with weights of 1, 2, 3, ..., 16 grams on a cup scale, so that one of the cups outweighed the other. Fifteen pupils took turns leaving the classroom and taking one weight with them. As each pupil left the scale, it changed its position and the opposite end of the scale weighed. Which weight could remain on the scale?

 
Mathemat >>:

Гриша едет по маршруту длиной 100 км. ...

At first I thought it was a Perelman joke :)


P.S. I got 100*t/(2+t)

 
Yeah, right. The solution to Grisha's problem doesn't need explaining, does it? Is it clear to everyone that he'll never make it?
 
Mathemat >>:

И еще - для любителей задач с гирьками:

На физическом кружке учитель поставил следующий эксперимент. Он разложил на чашечные весы 16 гирек массами 1, 2, 3, ..., 16 грамм так, что одна из чаш перевесила. Пятнадцать учеников по очереди выходили из класса и забирали с собой по одной гирьке, причем после выхода каждого ученика весы меняли свое положение и перевешивала противоположная чаша весов. Какая гирька могла остаться на весах?

it seems that the lightest one remains: if it is removed from the outweighing cup, at the extreme, equilibrium will occur, since the sum of the weights of the weights is a natural number, but not a change in the position of the weights
 
Answer: a weight of 1 gramme remains on the scales.

Since at each moment the weights on the scales differed by at least 1 gramme, in order for the opposite scale to outweigh the other one, a weight of at least two grammes must be taken. Consequently, when leaving the classroom, no student could pick up a weight of 1 gramme.
 

Geometers and forex homers! ;)

You would offer a correct solution to the problem of drawing straight lines for Metaquotes!

Because predictions with far-reaching reference points go astray and do not come true... :(

I've already put up with it in MT4, but in MT5!

Help it get better!

;)

 

Here's a good one:

An old maths professor has put six of the most primitive locks in the door of his flat, which can be opened with a nail file. But the professor, when he leaves for work, randomly closes only three of them, three locks remain open (assuming that the key is turned in the lock anyway, i.e. it is impossible to know whether the lock is closed or not).

How many options would it take for a failing student to get to the flat to get his credit?

1...364365366367368369370371372373374375376377378...628
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