To calculate the number of degrees the hour hand rotates on the clock between 8 o'clock in the morning and 2 o'clock in the afternoon, we can use the following formula:
Degrees rotated by the hour hand = (Hour hand's movement per hour) * (Number of hours elapsed)
In a standard 12-hour clock, the hour hand completes a full circle, 360 degrees, in 12 hours. So, the hour hand's movement per hour is:
Hour hand's movement per hour = 360 degrees / 12 hours = 30 degrees per hour
The number of hours elapsed between 8 in the morning and 2 o'clock in the afternoon is 6 hours.
Now, let's calculate the degrees rotated by the hour hand:
Degrees rotated by the hour hand = 30 degrees/hour * 6 hours = 180 degrees
So, the hour hand will rotate 180 degrees between 8 o'clock in the morning and 2 o'clock in the afternoon when an accurate clock is being used.
Let's first find out what day of the week the seventh day of the month is.
If the seventh day of the month is three days earlier than Friday, then:
Friday - 3 days = Tuesday
So, the seventh day of the month is Tuesday.
Now, we need to determine the day of the week on the nineteenth day of the month, which is 12 days later than the seventh day.
Starting from Tuesday and counting 12 days forward:
Tuesday + 1 day = Wednesday
Wednesday + 1 day = Thursday
Thursday + 1 day = Friday
Friday + 1 day = Saturday
Saturday + 1 day = Sunday
Sunday + 1 day = Monday
Monday + 1 day = Tuesday
Therefore, the nineteenth day of the month will be Tuesday.
A clock's hands are straight twice a day.
At 12:00 (midnight and noon), the hour and minute hands align perfectly, making a straight line. Thus, the clock's hands are straight twice in a 24-hour day.
The minute hand moves 360 degrees in one hour because there are 60 minutes on a clock face and 360° divided by 60 minutes is 6° per minute.
So, the minute hand moves 6° per minute.
If the second hand moves 4800 degrees in the same amount of time, we can calculate the number of minutes that have passed by dividing the total number of degrees moved by the second hand (4800°) by the degrees moved by the minute hand per minute (6°):
Number of minutes = 4800° ÷ 6° per minute = 800 minutes
Therefore, in the same amount of time that the second hand moves 4800 degrees, the minute hand moves 80 degrees (800 minutes * 6° per minute).
To determine the day of the week for January 1, 2008, we can use the fact that 2007 was not a leap year, so there are 365 days in that year.
Since January 1, 2007, was a Monday, we know that January 1, 2008, will be one day after that since 2008 is a leap year, adding an extra day. So:
Monday + 1 day = Tuesday
Therefore, January 1, 2008, was a Tuesday.
To calculate the number of degrees the hour hand rotates on the clock between 6 in the morning and 11 o'clock in the morning, we can use the following formula:
Degrees rotated by the hour hand = (Hour hand's movement per hour) * (Number of hours elapsed)
In a standard 12-hour clock, the hour hand completes a full circle, 360 degrees, in 12 hours. So, the hour hand's movement per hour is:
Hour hand's movement per hour = 360 degrees / 12 hours = 30 degrees per hour
The number of hours elapsed between 6 in the morning and 11 o'clock is 5 hours.
Now, let's calculate the degrees rotated by the hour hand:
Degrees rotated by the hour hand = 30 degrees/hour * 5 hours = 150 degrees
So, the hour hand will rotate 150 degrees between 6 in the morning and 11 o'clock in the morning.
To determine the day of the week for August 16, 1947, we can use a technique called the "Doomsday Algorithm," which helps find the day of the week for any given date. The algorithm was developed by mathematician John Horton Conway.
Step 1: Extract the last two digits of the year (47 for 1947).
Step 2: Divide the two-digit year by 12 and find the remainder (47 ÷ 12 = 3, remainder 11).
Step 3: Find the number of 12s in the remainder (11 ÷ 4 = 2, remainder 3).
Step 4: Add the day of the month (16) to the number of 12s (2) and the remainder (3).
Step 5: Find the day of the week using the following key:
0 - Sunday
1 - Monday
2 - Tuesday
3 - Wednesday
4 - Thursday
5 - Friday
6 - Saturday
16 + 2 + 3 = 21
Since 21 corresponds to the day of the week Saturday, August 16, 1947, was a Saturday.
To determine the day of the week that will be 61 days later from Monday, we need to consider that there are seven days in a week. Since 61 is not evenly divisible by 7, we need to find the remainder when dividing 61 by 7.
61 ÷ 7 = 8 with a remainder of 5
So, 61 days later will be equivalent to 8 weeks and 5 days later.
Starting from Monday, if we add 8 weeks (56 days), we will reach the same day of the week, which is Monday.
Now, adding the remaining 5 days to Monday:
Monday + 1 day = Tuesday
Tuesday + 1 day = Wednesday
Wednesday + 1 day = Thursday
Thursday + 1 day = Friday
Friday + 1 day = Saturday
Therefore, 61 days later from Monday will be a Saturday.
On December 8, 2006, it was a Friday.
1. At 7 am on Monday, the clock is set to display the right time.
2. The clock is off by 15 minutes in 24 hours. This means the clock loses 15 minutes every 24 hours.
3. The next Friday, the clock reads 6 am.
Since the clock loses 15 minutes every 24 hours, in 24 hours, it will be 15 minutes behind the correct time. So, the time between 6 am on Friday and 6 am on Saturday will actually be 23 hours and 45 minutes.
Since the clock is 15 minutes behind the correct time at 6 am on Friday, it will catch up 15 minutes by 6 am on Saturday. So, at 7 am on Friday, the clock will display the correct time.
Therefore, at 7 am on the next Friday, the hour displayed by the clock will be 7 am, and it will be the correct time.
To determine the day of the week for December 8, 2006, we can use a calendar or calculate it using algorithms like the Zeller's Congruence. Here's a simple way to calculate it manually:
Step 1: Identify the day of the week for January 1, 2006
January 1, 2006, was a Sunday.
Step 2: Count the number of days between January 1, 2006, and December 8, 2006
From January 1 to December 7, there are 341 days (31 days in January + 28 days in February + 31 days in March + 30 days in April + 31 days in May + 30 days in June + 31 days in July + 31 days in August + 30 days in September + 31 days in October + 30 days in November + 7 days in December).
Step 3: Add the number of days from Step 2 to the day of the week for January 1, 2006
Since January 1, 2006, was a Sunday, we add 341 days to Sunday:
341 mod 7 = 2
So, December 8, 2006, was two days after Sunday, which makes it a Friday.
Therefore, on December 8, 2006, it was a Friday.
To determine the day of the week for March 6, 2004, we can use the fact that March 6, 2005, was a Sunday.
Since 2004 was a leap year, it had 366 days. So, March 6, 2004, is one day before March 6, 2005.
Sunday - 1 day = Saturday
Therefore, on March 6, 2004, it was a Saturday.
