[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 222
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Для оживления ветки:
Кто какие знает доказательства теоремы Пифагора? Если знаете - выкладывайте идею и само краткое доказательство. Я был знаком с уникумом, знавшим не менее 10 доказательств.
Классическое школьное доказательство не рассматриваем.
I respect your knowledge, honestly. Do you trade in real life yourself?
As you know, our legislators are about to ban incandescent bulbs.
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Problem: there are 2 bulbs which give the same luminous flux:
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1. Incandescent bulb: power - 100 W, price - 8 rubles, lifetime - 1000 hours, disposal cost of the bulb - 0.1 rubles
(we throw it away in a trash box);
2. Compact fluorescent lamp: power - 25 W, price - 210 rubles, lifetime - 2000 hours (average real, not according to the certificate),
disposal cost of the lamp - 20 rubles (it contains mercury);
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electricity cost - 3 rubles/kWh.
Question: which lamp is more cost-effective to use?
Тут какое-то несоответствие. Если коза с гусем едят как корова, то корова так-же прокормится на этом пастбище 90 дней. значит 2 коровы 45 дней, значит коза ест как корова по второму условию а гусь ничего не ест, но это противоречит третьему условию. С другой стороны нигде не сказано, что они смогут пастись дольше, чем указано, тогда животные смогут пастись пока Гансу не надоест молочница.
You were close...!
"In the pasture conundrum, the daily growth of grass must be taken into account. We know that a cow eats as much as a goat and a goose. Hence, if a cow and a goat eat all the grass in 45 days, it is clear that two goats and a goose will eat the same amount of grass in the same amount of time. Since a goat and a goose eat all the grass in twice the time, we see that one goat will eat all the grass in 90 days and that a goose can eat only the growth of the grass. Consequently, if a cow eats 1/60 of the original supply of grass per day and a goose 1/90, together they will eat 1/36. Thus, the cow and goat will eat the original supply of grass in 36 days, while the goose will take care of its growth in the meantime."
// I solved it too, but with an ass... equation. Took me a long time, man.
:)
Mathemat писал(а) >> 2 MetaDriver:
1) Lloyd's problem really got to you. When you take integrals, call me.
2) By the way, here's another thing: I faintly looked up the solution of the problem about numbers between consecutive squares. Surprisingly, there's nothing at all about divisibility. But the properties of natural numbers are, of course, used. The whole reasoning is based only on "greater than/less than" evaluations.
Nope, not by myself. Write it out in formulas, it's easier to understand. Just be sure to say what the relevant variable is.
1) There are no integrals there. But if grass could no longer grow on bald spots... then we'd have to call. :)
2) I was surprised to find a hole in my solution. It may be plugged, but it's very difficult somehow. I abandoned that path.
I'll try another way of doing it.
Как вы знаете, скоро наши законодатели собираются запретить лампы накаливания.
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Задача: есть 2 лампочки, которые дают одинаковый световой поток:
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1. Лампа накаливания: мощность- 100 Вт, цена - 8 рублей, срок службы - 1000 часов, стоимость утилизации лампы - 0,1 рублей
(выкидываем в помойный ящик);
2. Лампа компактная люминесцентная: мощность - 25 Вт, цена - 210 рублей, срок службы - 2000 часов (средний реальный, а не по паспорту),
стоимость утилизации лампы - 20 рублей (в ней - ртуть);
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Стоимость электроэнергии - 3 рубля\кВт*ч.
Вопрос: какую лампу использовать более экономически выгодно?
It is not about the economic benefits of use - this is of course bullshit from the zombie TV - but about the benefits of the introduction itself into production. Calculate for yourself what gross product is created by the incandescent light bulb plant and the energy-saving light bulb plant. Plus assess the structure of the product in terms of scientific and technological saturation - it is incomparably higher in Novolampamp bulb factory and it creates more qualified jobs. Therefore, if there is a need to stimulate innovative development, transition to more sophisticated technologies, even if they are less profitable at the first stage, is justified. Of course, a prerequisite for efficiency of such measures is production of light bulbs in the country where the ban is introduced: so far we feed the Chinese who rivet those very light bulbs that burn for only 2,000 hours. But there is an opinion that if at least some All-Union light bulb factory is formed in our native country, its products will still be closer to the passport data in terms of performance.
Alsu, we have our own factories that produce these bulbs, but their quality leaves a lot to be desired.
However, banning them, in my opinion, is a stupid thing, and also mean. And who will dispose of them? We will breathe mercury.
Откуда прирост травы? Мне тоже такой травы!
Ask Richie. He knows everything, even how to make quid out of snow.
Ask Richie. He knows everything, even how to make quid out of snow.
I'm not an herbalist, I'm confused about your problem. Give me a nuclear reactor, or at least a multivibrator.)
The forum is tense: where does the herb come from, where to collect it, how to infuse it, what phase of the moon to brew it in?
And if you're on the dime, how much of a discount?