In our series on averages, last week we introduced the idea of the weighted average (or weighted mean), where each item has a weight attached. The classic examples all involve grade averages in various ways. This time, we’ll look at how weighted averages arise when you need to average several averages together, something we touched …
(A new question of the week) Let’s look at a quick question from mid-September, that had a number of different answers. In some ways, this is an easy question; but we’ll take it a little further, so keep reading to the end.
To close out this series on the definition of the derivative, I want to look at a few questions about alternative versions of the definition, primarily the “symmetric difference quotient”. We’ll see that this leads to a slightly different result, not always equivalent to the original, and we’ll observe some associated ways that calculators can …
(A new question of the week) We have had a lot of interesting questions recently. This one involved inverse trigonometric equations that led to cubic and quartic equations. We’ll observe here one of the benefits of embedding the original discussion in a blog format where I can add information that will help you, the reader, …
Challenging Inverse Trig and Polynomial Equations Read More »
(An archive question of the week) We’ve looked at the scalar (dot) product and the vector (cross) product; but there is one answer in the Ask Dr. Math archives that was too long to fit in either post. Here we’ll see again where the two familiar products come from, while looking deeper into the math …
Having just looked at how to solve oblique triangles, let’s look at a couple “word problems” (applications) involving such triangles. We’ll be using the Law of Sines, and also exploring alternative methods of solution.
Last time, we looked at three ways to find a GCF (Greatest Common Factor). Here we’ll see the corresponding ways to find an LCM (Least Common Multiple); next time we’ll examine another method, which in its full form finds both at once. (Note that the Least Common Denominator of fractions is just the Least Common …
Last time, we looked at the basic definition of independent events. This time I want to explore some deeper questions about the concept.
Having looked at what the order of operations convention means, another common question is, why is it what it is? We’ll look at some basic ideas here, focusing on why we need a convention at all, and why the one we have makes sense; then next time we’ll dig in a little deeper, examining some …
Here is another puzzle we have received and answered many times. (I count 7 that have been archived.) It has several variations, which make it even more interesting. The story varies, too; sometimes the monkeys are the stars, other times they just get the leftovers. Someone could to an interesting folklore study on this one.