Question

2. В школе 1 октября узнали новость. Каждый день число знающих новость увеличивалось в 3 раза. 21 октября новость узнали все в школе. В какой день новость знали 1/9 часть учащихся?

Answer 1

Ответ:

19 октября.

Пошаговое объяснение:

21=9/9

9/3=3=20октября

3/3=1=19 октября

Answer 2

Problem Analysis

We are given the following information: - On October 1st, the number of people who knew the news increased by 3 times every day. - On October 21st, everyone in the school knew the news. - We need to determine on which day 1/9 of the students knew the news.

Solution

To solve this problem, we can work backwards from the day when everyone in the school knew the news (October 21st) and calculate the number of people who knew the news on each previous day.

Let's assume that on October 21st, the number of people who knew the news was "x". Since everyone in the school knew the news on that day, "x" represents the total number of students in the school.

On October 20th, the number of people who knew the news would be 1/3 of "x" because the number of people who knew the news increased by 3 times every day. Therefore, the number of people who knew the news on October 20th would be "x/3".

Similarly, on October 19th, the number of people who knew the news would be 1/3 of the number of people who knew the news on October 20th, which is "(x/3)/3" or "x/9".

We can continue this pattern until we find the day when 1/9 of the students knew the news.

Let's calculate the number of people who knew the news on each day:

- October 21st: "x" (everyone in the school) - October 20th: "x/3" - October 19th: "x/9" - October 18th: "x/27" - October 17th: "x/81" - October 16th: "x/243" - October 15th: "x/729" - October 14th: "x/2187" - October 13th: "x/6561" - October 12th: "x/19683" - October 11th: "x/59049" - October 10th: "x/177147" - October 9th: "x/531441" - October 8th: "x/1594323" - October 7th: "x/4782969" - October 6th: "x/14348907" - October 5th: "x/43046721" - October 4th: "x/129140163" - October 3rd: "x/387420489" - October 2nd: "x/1162261467" - October 1st: "x/3486784401"

Since we know that on October 1st, the number of people who knew the news increased by 3 times every day, we can set up the following equation:

(x/3486784401) * 3^20 = x/9

Simplifying the equation:

3^20 = 3486784401/9

Now we can solve for "x" to find the total number of students in the school.

Let's calculate the value of "x":

3^20 = 3486784401/9

x = (3486784401/9) * (1/3^20)

x ≈ 1.2345679012345679 * 10^8

Therefore, the total number of students in the school is approximately 123,456,790.

To find the day when 1/9 of the students knew the news, we need to calculate (1/9) * x:

(1/9) * 1.2345679012345679 * 10^8 ≈ 1.371742112

So, approximately 1.37 million students knew the news on the day when 1/9 of the students knew the news.

Answer

Therefore, approximately 1.37 million students knew the news on the day when 1/9 of the students knew the news.

Please note that the above calculations are based on the given information and assumptions made.