Question

Турист за первый час пешего пути поднялся в гору на 500м, а каждый следующий час поднимался на 25метров меньше, чем в предыдущий. За сколько часов он достигнет высоты 3300метров?

Answer 1

За первый час турист поднялся на 500м
за второй час 500-25=475 м 

мы получаем арифметическую прогрессию, где 
а₁=500, d= -25

Сумма n членов прогрессии равна 3300м

вспомним формулу суммы




теперь подставим наши данные и найдем n





выбираем наименьший корень 

n=8

Значит через 8 часов поднимется на высоту 3300м

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почему выбираем наименьший корень

наше уравнение парабола и в двух точках у нее будут одинаковые значение

т.е. при 8 часов будет высота 3300м и при 33 час 
но при этом через 33 часа возможно турист будет уже спускаться) 

Answer 2

Problem Analysis

We are given that a tourist climbed a mountain and in the first hour, they climbed 500 meters. Each subsequent hour, they climbed 25 meters less than the previous hour. We need to determine how many hours it will take for the tourist to reach a height of 3300 meters.

Solution

To solve this problem, we can set up an equation to represent the height climbed by the tourist at each hour. Let's assume that the number of hours the tourist has climbed is represented by h.

In the first hour, the tourist climbed 500 meters. From the second hour onwards, the tourist climbed 25 meters less than the previous hour. Therefore, the height climbed in the second hour would be 500 - 25, in the third hour would be 500 - 2 * 25, and so on.

We can represent the height climbed at each hour using the following equation:

Height climbed at hour h = 500 - 25 * (h - 1)

We need to find the value of h for which the height climbed is equal to 3300 meters. Let's set up the equation and solve for h:

500 - 25 * (h - 1) = 3300

Simplifying the equation:

500 - 25h + 25 = 3300

-25h + 525 = 3300

-25h = 3300 - 525

-25h = 2775

h = 2775 / -25

h = -111

Since the number of hours cannot be negative, we can conclude that it is not possible for the tourist to reach a height of 3300 meters using the given conditions.

Therefore, the tourist will not be able to reach a height of 3300 meters based on the given information.

Conclusion

Based on the given information, the tourist will not be able to reach a height of 3300 meters.