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.

Function Transformations as Composition

(A new question of the week) We have discussed transformations of functions and their graphs at length, but a recent question suggested a slightly different way to think about them.

Clarifying Definitions: Triangle, Rectangle, Circle

(A new question of the week) Several recent questions involved details about definitions of geometrical objects, so I thought I’d group them together, because each is relatively short. We’ll be looking at the definitions of triangles (do we need to say “exactly three sides”?), rectangles (did Euclid use an exclusive definition?), and circles (can the …

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Three Trigonometric Inequalities

(A new question of the week) We often solve basic trigonometric equations; but a recent set of questions dealt with challenging trigonometric inequalities, which bring with them a new set of issues. We’ll look at several of those here, which combine trig with polynomials, rational functions, and more. Each will illustrate something new to watch …

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