[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 199
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Вопрос: можно ли 3-мя оборотами открутить болт, не сломав его, на котором 27 ниток (оборотов) резьбы, если этот болт
был закручен полностью на 27 ниток (оборотов)?
You can if the thread is 1. tapered, 2. sagged 3. fine-pitch.
Вопрос: можно ли 3-мя оборотами открутить болт, не сломав его, на котором 27 ниток (оборотов) резьбы, если этот болт
был закручен полностью на 27 ниток (оборотов)?
you can if the thread has 9 starts :))))))))
it is possible if the temperature of the jet is more than 850 degrees Celsius.
The answer is absolutely correct. Diamond in hot air burns by turning into carbon dioxide.
Question: is it possible to cut a diamond with a jet of clean air at no more than 3 atmospheres?
>> Slowly :)
you can if the thread has 9 starts :))))))))
It is possible if the thread is 1. tapered, 2. sagged 3. fine-pitch.
Slowly :)
That would probably be too slow :)
2 alsu - по поводу построения треуга по сторонам и биссектрисе: вижу, что прямое построение геометрических мест становится тут популярным методом решения задач :)
When I was a kid, pure geometry was somehow worse for me than combining it with abstract methods. But they gave me half a point for such solutions at the Olympiads :))))
By the way, at our oblast schools we didn't have a 60-people capacity lot in the 2nd round, a maximum of 10-15 best in the district and town ones.
One more thing about the muzik.
We were given it at the institute before the examination. I remember solving it in a slightly different way - I made a marginal transition from discrete to continuous case and made a diphener, its solution gave an analytical expression for the distance from the mucik to the end of the rubber product.
Question:
Vladimirovich flew from Moscow to Peter in a helicopter. The helicopter flew 600 km and consumed 3000 litres of fuel.
When Vladimirovich flew back in the same helicopter, the helicopter used 2800 litres of fuel. Explain why the helicopter
used 200 litres less fuel on the way back?
PS:
There was no wind in both cases. The helicopter flew on exactly the same trajectories, for exactly the same time, with similar speeds
and accelerations, at the same altitudes. The load on the helicopter was exactly the same. The helicopter in both cases was perfectly
in perfect working order. The number of passengers and crew members were the same in both cases. The fuel in both cases was exactly
identical.
Bortach, as always, has written off the excess to the stash :)
On the subject: the movement (rotation) of the Earth.
Mathemat писал(а) >>
1. Criterion circles by the very nature of their construction have radii equal to the radius of our Y.
1a. Their centres are constructed even more simply by intersecting the arcs of the circles from A and O with the radii of A.
2. It is not obvious that these geometrical places are exactly circles. But it is very easy to prove them analytically.
1. Seems to be true. Somehow I didn't think of that.
1а. Well, if I had understood 1, maybe I would have been able to do that too. :)
2. Right. Unobvious. I still have these doubts (about the ellipse), and I could not quickly find a formula to check it.
(And even now I hardly know how to model it.) So I relied on intuition, which actively voted for the circle... :)))