The date December 31, 2043 can be written in the format 12/31/43. This is an example of a true mathematical statement because 12 + 31 = 43. Suppose I wanted to write dates in the 21st century for Valentine’s Day (which is always celebrated on February 14) that will also give me true mathematical statements when writing in this format. There are only two of them this century. What are these two dates? Give your answers in standard format (like 12/31/43 = December 31, 2043).
To find the two dates in the 21st century that can be written in the format 2/14/yy = February 14, yyyy, and will also give true mathematical statements, you need to determine the possible values for "yy" (the last two digits of the year).
The mathematical statement you mentioned, 12 + 31 = 43, is an example of adding the month and the day to get the last two digits of the year. Let's apply the same logic to find the two dates.
Since February is the second month of the year, its numerical value is 2. For Valentine's Day, the day is always 14. Therefore, for the last two digits of the year:
2 + 14 = 16
So, the first date in the 21st century that can be written in the format 2/14/yy and will give a true mathematical statement is February 14, 2016, written as 2/14/16 in standard format.
To find the second date, we'll add 100 years to the previous date:
2/14/16 + 100 years = 2/14/116
Again, applying the same logic:
2 + 14 = 16
So, the second date in the 21st century that can be written in the format 2/14/yy and will give a true mathematical statement is February 14, 2116, written as 2/14/116 in standard format.
Therefore, the two dates in the 21st century that satisfy the conditions are:
1. 2/14/16 = February 14, 2016
2. 2/14/116 = February 14, 2116.