Question

На озере начали распускаться кувшинки. Каждый день количество кувшинок возрастало в двое. На двадцатый день кувшинками заросла вся поверхность озера. На какой день половина озера была покрыта кувшинками?два ответа: или на 10й день,или на 19день. решение задачи точное напишите

Answer 1

20:2=10(дн)-половина озера была покрыта кувшинками

Answer 2

Problem Analysis

We are given that the number of water lilies (кувшинки) on a lake doubles every day. On the twentieth day, the entire surface of the lake is covered with water lilies. We need to determine on which day half of the lake's surface was covered with water lilies.

Solution

To solve this problem, we can work backwards from the twentieth day and divide the number of water lilies by 2 until we find the day when half of the lake's surface was covered.

Let's start with the twentieth day, where the entire surface of the lake is covered with water lilies. On the nineteenth day, the number of water lilies would have been half of what it was on the twentieth day. We can continue this process until we find the day when half of the lake's surface was covered.

Let's calculate the number of water lilies on each day:

- On the twentieth day, the entire surface of the lake is covered with water lilies. - On the nineteenth day, the number of water lilies is half of what it was on the twentieth day. - On the eighteenth day, the number of water lilies is half of what it was on the nineteenth day. - ... - On the first day, the number of water lilies is half of what it was on the second day.

We can see that the number of water lilies on each day is halved compared to the previous day. Therefore, the day when half of the lake's surface was covered with water lilies is the day before the entire surface was covered, which is the nineteenth day.

Therefore, the correct answer is the nineteenth day.

Conclusion

The day when half of the lake's surface was covered with water lilies is the nineteenth day.