Calculation of Day of the Week

To calculate the day of the week, we need to use the concept of the Julian date. We will follow the given steps to find the day of the week for August 15th, 2010.

- We need to find the Julian date for August 15th, 2010.
- Julian date is the number of days that have elapsed since January 1st, 4713 BC.
- We will use the following formula to find the Julian date for August 15th, 2010:

JD = (1461 * (Y + 4800 + (M - 14) / 12)) / 4 + (367 * (M - 2 - 12 * ((M - 14) / 12))) / 12 - (3 * ((Y + 4900 + (M - 14) / 12) / 100)) / 4 + D - 32075

where JD is the Julian date, Y is the year, M is the month, and D is the day.

- For August 15th, 2010, Y = 2010, M = 8, and D = 15.
- Putting these values in the above formula, we get:

JD = (1461 * (2010 + 4800 + (8 - 14) / 12)) / 4 + (367 * (8 - 2 - 12 * ((8 - 14) / 12))) / 12 - (3 * ((2010 + 4900 + (8 - 14) / 12) / 100)) / 4 + 15 - 32075
JD = 2455431

- Now, we will use the following formula to find the day of the week:

Day of the week = (JD + 1) % 7

- Putting the value of JD in the above formula, we get:

Day of the week = (2455431 + 1) % 7
Day of the week = 0

- The remainder is 0, which means the day of the week is Sunday.

Therefore, the day of the week for August 15th, 2010, is Sunday.