Question

Любопытный Кирилл обратил внимание, что в 16:20 угол между часовой и минутной стрелкой равен Х градусов. Немного подумав, Кирилл понял, что такое же значение угла между часовой и минутной стрелками будет в 19 часов N минут. Найдите Х. Найдите также N, если известно, что оно целое. Чему равен Х?

Answer 1

Ответ:

X=тупому углу, сейчас скажу градусы

90-180 градусов

1 час; 30градусов

30мину-15 градусов

Тогда 15минут- 7,5градусов

20 минут 10 градусов

Решение

30-15

20-?

Х=20×15:30

Ответ 130 градусов это Х

Answer 2

Problem Analysis

Kirill noticed that the angle between the hour and minute hands of a clock at 16:20 is X degrees. He also realized that the same angle between the hour and minute hands will occur at 19 hours N minutes. We need to find the value of X and determine the value of N, knowing that it is an integer.

Solution

To find the value of X, we need to calculate the angle between the hour and minute hands at 16:20.

The hour hand moves 360 degrees in 12 hours, which means it moves 30 degrees per hour. At 16:20, the hour hand has moved 16 hours * 30 degrees/hour = 480 degrees.

The minute hand moves 360 degrees in 60 minutes, which means it moves 6 degrees per minute. At 16:20, the minute hand has moved 20 minutes * 6 degrees/minute = 120 degrees.

The angle between the hour and minute hands is the absolute difference between their positions. Therefore, X = |480 degrees - 120 degrees| = 360 degrees.

Now, let's find the value of N. We know that the same angle between the hour and minute hands will occur at 19 hours N minutes. Since the angle is 360 degrees, the minute hand will be at the same position as the hour hand.

At 19 hours, the hour hand will be at 19 hours * 30 degrees/hour = 570 degrees.

To find the value of N, we need to calculate the number of minutes it takes for the minute hand to reach the same position as the hour hand. Since the minute hand moves 6 degrees per minute, we can set up the equation:

570 degrees + N minutes * 6 degrees/minute = 570 degrees

Simplifying the equation, we get:

N minutes * 6 degrees/minute = 0 degrees

Since the angle is 0 degrees, N can be any integer value.

Therefore, the value of X is 360 degrees and the value of N can be any integer.

Answer

The angle between the hour and minute hands at 16:20 is 360 degrees. The value of N can be any integer.