Diluting a Solution: Math vs. Reality

Here is a little question about making a formula to dilute a solution; we’ll see how to do the algebra, and also how what we teach in math classes isn’t quite real.

Homogeneous Linear Recurrence Relations

Last week we looked at a recent question about recurrence relations, and I realized it needs a companion article to introduce these ideas. So here we will look at some answers from Ask Dr. Math about the simpler case, including general methods, why they work, and applications.

A Tunnel Through the Earth

I have a very short problem this week: How deep will you go if you dig a straight tunnel through the earth, how long will it be, and what angle do you have to start at?

Arithmetic Series, Backward

Here is a recent question about arithmetic sequences and series (specifically, reversing the process to find the number of terms given the sum), that nicely illustrates a common type of interaction with a student: gathering information about both problem and student, then guiding them to use what they know, or giving new information as needed. …

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