Question is about Step Functions:(between" " are all floor functions.
The formula W=d+2m+"(3(m=1)/5)"+y+"y/4" -"y/100" + "y/400" + 2 gives the day of the month of the given date; m = the number of the month in the year with January and February regarded as the 13th and 14th months of the previous year; that is , 2/22/90 is 14/22/89. The other months are numbered 3 to 12 as usual; and y = the year as a 4-digit number.Once W is computed, divide by 7 and the remainder is the day of the week, with Saturday = 0, Sunday = 1,..., Friday = 6.
I need to find what day my birthday lies on. Everytime i try it always comes out to something different.My birthday is 4/11/1995.Somebody please help!
Was one of your answers Tuesday?
That is supposed to be the answer but i do not how to get there.
what does (m=1) mean?
Is that (m-1)?
It doesn't seem to line up with Zeller's Congruence (which google)
To find the day of the week for a given date, you can use the formula mentioned above. Let's break it down step by step.
1. Extract the values of d, m, and y from your birthday, 4/11/1995:
- d = 11 (day)
- m = 4 (April)
- y = 1995 (year)
2. Adjust the month and year as mentioned in the formula:
- If the month is January or February, subtract 1 from the year:
- Since your month is April, no adjustment is needed.
3. Substitute the values into the formula:
- W = d + 2m + "(3(m-1)/5)" + y + "y/4" - "y/100" + "y/400" + 2
Plugging in the values:
W = 11 + 2(4) + "(3(4-1)/5)" + 1995 + "1995/4" - "1995/100" + "1995/400" + 2
Simplify the expression:
W = 11 + 8 + "(3(3)/5)" + 1995 + "1995/4" - "1995/100" + "1995/400" + 2
W = 21 + "(9/5)" + 1995 + "498.75" - "19.95" + "4.9875" + 2
4. Calculate the value of W:
W = 21 + 1.8 + 1995 + 498.75 - 19.95 + 4.9875 + 2
W = 2502.7875
5. Divide W by 7 and find the remainder:
Remainder = W % 7
Remainder = 2502.7875 % 7
Remainder ≈ 1.7875
6. Round down the remainder to get the day of the week:
Since the remainder is 1.7875, we can round it down to 1.
7. Interpret the day of the week:
According to the provided convention, Sunday is represented by 1, Monday by 2, and so on. Therefore, your birthday, 4/11/1995, falls on a Tuesday.
Please note that there might be slight variations due to rounding errors in the calculations, but the overall process remains the same.