We started by looking at one of the more difficult problems on her assignment that had to do with the changing area of the section swept out by the minute hand of the clock. Her teacher had made the simplification of disregarding the movement of the hour hand (but I think that to be more accurate, you would want to take that into account since I think on most clocks the hour hand does move slowly as the minutes progress, it would change the result by about 2%).

The approach for a problem like that is to figure out what things change, the variable, and what is constant. At first she thought that the radius of the minute hand was a variable, but since it does not change in this problem, it is also constant, just like numbers. Using the variable theta to describe the angle swept out by the minute hand helped solve the problem, though that variable was not mentioned explicitly in the directions.

She was a bit unfamiliar with the natural number e. It functions like any other constant in most of the problems and is related to the natural log function.

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