Question

В какое время между 5 ч и 6 ч угол между минутной и часовой стрелками будетсоставлять 40 впервые за этот час?А. В 5 ч 40 мин. Б. В 5 ч 34 мин. В. В 5 ч 25 мин. Г. В 5 ч 20 мин.

Answer 1

Угол между соседними цифрами на часах равен 360° : 12 = 30°
40° - это 1 час и еще 1/3 часа.
Значит, минутная стрелка должна указывать на 4, а часовая сдвинуться на
1/3 часа = 20 мин.
То есть в 5 часов 20 мин.
Или наоборот, минутная стоит на 7, а часовая на 1/3 часа не доходит до 6.
Значит, в 5 часов 30 мин угол меньше 40°, а в 5 часов 35 мин - больше.
То есть примерно в 5 часов 33-34 минут.
Ответ: 5 часов 20 мин - точный ответ, 5 часов 34 мин - примерный.

Answer 2

Finding the Angle Between the Minute and Hour Hands

To determine the time at which the angle between the minute and hour hands is 40 degrees for the first time within the hour, we need to calculate the angle at each minute interval between 5:00 and 6:00.

The angle between the minute and hour hands can be calculated using the following formula:

Angle = |(30 * H) - (11/2 * M)|

Where: - H is the hour (in 12-hour format) - M is the minute

We will calculate the angle at each minute interval and check when it first reaches 40 degrees.

Calculation:

Let's calculate the angle at each minute interval between 5:00 and 6:00:

- At 5:00, the angle is |(30 * 5) - (11/2 * 0)| = 150 degrees. - At 5:01, the angle is |(30 * 5) - (11/2 * 1)| = 145.5 degrees. - At 5:02, the angle is |(30 * 5) - (11/2 * 2)| = 141 degrees. - At 5:03, the angle is |(30 * 5) - (11/2 * 3)| = 136.5 degrees. - At 5:04, the angle is |(30 * 5) - (11/2 * 4)| = 132 degrees. - At 5:05, the angle is |(30 * 5) - (11/2 * 5)| = 127.5 degrees. - At 5:06, the angle is |(30 * 5) - (11/2 * 6)| = 123 degrees. - At 5:07, the angle is |(30 * 5) - (11/2 * 7)| = 118.5 degrees. - At 5:08, the angle is |(30 * 5) - (11/2 * 8)| = 114 degrees. - At 5:09, the angle is |(30 * 5) - (11/2 * 9)| = 109.5 degrees. - At 5:10, the angle is |(30 * 5) - (11/2 * 10)| = 105 degrees. - At 5:11, the angle is |(30 * 5) - (11/2 * 11)| = 100.5 degrees. - At 5:12, the angle is |(30 * 5) - (11/2 * 12)| = 96 degrees. - At 5:13, the angle is |(30 * 5) - (11/2 * 13)| = 91.5 degrees. - At 5:14, the angle is |(30 * 5) - (11/2 * 14)| = 87 degrees. - At 5:15, the angle is |(30 * 5) - (11/2 * 15)| = 82.5 degrees. - At 5:16, the angle is |(30 * 5) - (11/2 * 16)| = 78 degrees. - At 5:17, the angle is |(30 * 5) - (11/2 * 17)| = 73.5 degrees. - At 5:18, the angle is |(30 * 5) - (11/2 * 18)| = 69 degrees. - At 5:19, the angle is |(30 * 5) - (11/2 * 19)| = 64.5 degrees. - At 5:20, the angle is |(30 * 5) - (11/2 * 20)| = 60 degrees. - At 5:21, the angle is |(30 * 5) - (11/2 * 21)| = 55.5 degrees. - At 5:22, the angle is |(30 * 5) - (11/2 * 22)| = 51 degrees. - At 5:23, the angle is |(30 * 5) - (11/2 * 23)| = 46.5 degrees. - At 5:24, the angle is |(30 * 5) - (11/2 * 24)| = 42 degrees. - At 5:25, the angle is |(30 * 5) - (11/2 * 25)| = 37.5 degrees. - At 5:26, the angle is |(30 * 5) - (11/2 * 26)| = 33 degrees. - At 5:27, the angle is |(30 * 5) - (11/2 * 27)| = 28.5 degrees. - At 5:28, the angle is |(30 * 5) - (11/2 * 28)| = 24 degrees. - At 5:29, the angle is |(30 * 5) - (11/2 * 29)| = 19.5 degrees. - At 5:30, the angle is |(30 * 5) - (11/2 * 30)| = 15 degrees. - At 5:31, the angle is |(30 * 5) - (11/2 * 31)| = 10.5 degrees. - At 5:32, the angle is |(30 * 5) - (11/2 * 32)| = 6 degrees. - At 5:33, the angle is |(30 * 5) - (11/2 * 33)| = 1.5 degrees. - At 5:34, the angle is |(30 * 5) - (11/2 * 34)| = 3 degrees. - At 5:35, the angle is |(30 * 5) - (11/2 * 35)| = 7.5 degrees. - At 5:36, the angle is |(30 * 5) - (11/2 * 36)| = 12 degrees. - At 5:37, the angle is |(30 * 5) - (11/2 * 37)| = 16.5 degrees. - At 5:38, the angle is |(30 * 5) - (11/2 * 38)| = 21 degrees. - At 5:39, the angle is |(30 * 5) - (11/2 * 39)| = 25.5 degrees. - At 5:40, the angle is |(30 * 5) - (11/2 * 40)| = 30 degrees.

Based on the calculations, the angle between the minute and hour hands will first reach 40 degrees at 5:40.

Therefore, the correct answer is A. В 5 ч 40 мин.

Please note that the calculations were made using the formula mentioned above, and the sources provided did not contain specific information about this particular question.