A day can be evenly divided into 86,400 periods of 1 second; 43,200 periods of each 2 seconds; or in many other ways. In total, how many ways are there to divide a day into periods of seconds, where and are positive integers

96 ways

Step-by-step explanation:

Given

Required

Ways to divide it into period of seconds

What this question implies is to determine the total number of factors of 86400

To start with, we determine the prime factorization of 86400

To do this, we continually divide 86400 by 2; when it can not be further divided, we divide by 3, then 7, then 11...

This implies that:

The number of factors d is the solved by:

Where

By comparison:

So:

Hence, there are 96 total ways

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s