The minute hand turns through __________ degrees from the digit 2 to 11 on a clock
I will assume 2:00 am to 11:00 am or
2:00 pm to 11:00 pm
one rotations is 360°
The minute hand does 360° in each hour.
How many hours from 2:00 pm to 11:00 pm ?
40 to 120 degrees
rather than from 2:00 to 11:00, I read it as moving from, say 12:10 to 12:55, or 9/12 of an hour.
To find the number of degrees the minute hand turns from the digit 2 to 11 on a clock, we can use the fact that a complete revolution of a clock is 360 degrees.
We know that the digit 2 is at the 10-minute mark, and the digit 11 is at the 55-minute mark. Since there are 60 minutes on a clock, the minute hand covers 360 degrees in that time.
First, let's find the number of degrees the minute hand turns from the digit 2 to the 60-minute mark. This can be calculated by dividing the fraction of the way from 10 to 60 by 60 (the total number of minutes on a clock) and multiplying it by 360.
The fraction of the way from 10 to 60 is (60 - 10) / 60 = 50 / 60 = 5 / 6.
So, the number of degrees for this part is (5 / 6) * 360 = 300 degrees.
Next, we need to add the number of degrees the minute hand turns from the 60-minute mark to the digit 11. Since the minute hand moves uniformly, the number of degrees is directly proportional to the elapsed time.
From the 60-minute mark to the digit 11, there are 55 - 60 = -5 minutes. Since the minute hand moves 360 degrees in 60 minutes, we can find the number of degrees it moves in -5 minutes using the proportion:
(360 degrees) / (60 minutes) = x degrees / (-5 minutes).
By cross-multiplying and solving for x, we find that x = (-5 / 60) * 360 = -30 degrees.
So the total number of degrees the minute hand turns from the digit 2 to 11 on the clock is 300 degrees + (-30 degrees) = 270 degrees.