(A new question of the week) Since we looked at a question about economics last week, let’s examine another, which is very different, relating the supply and demand curves to the concept of variation or proportion. We are not economists, so we can’t go deeply into that subject, but it makes us think about some …
(An archive question of the week) Last week we looked at a recent question that touched on the idea of the derivative as a rate of change. Let’s look at a long discussion from a few years ago digging into what that means within calculus.
(A new question of the week) Economics can be a deeply mathematical subject; but as a separate field, it has its own terminology and notation which can sometimes be confusing. Is marginal revenue (or cost, etc.) the same as the derivative of the revenue function, or is it something different? That will be the issue …
In searching for answers about counting divisors over the last couple weeks, I found a few that are about the similar question of finding the sum of a number’s divisors. In fact, a couple questions and answers confuse the two problems. Let’s finish off the topic by looking at these. (Keep in mind that “divisor” …
(A new question of the week) Sometimes a topic you think you know looks entirely different in an unfamiliar context. Here, a returning student faces a quadratic equation where x and y are reversed, making the quadratic formula seem foreign! But this is when real learning happens, when you are forced to think through the …
A classic problem we’ve seen hundreds of times involves students opening and closing lockers. I have often told people that, believe it or not, they could find the answer by searching the Ask Dr. Math site for the word “locker”. But I prefer to give them a reference to one of the answers in which …
(A new question of the week) Last time we looked at a classic problem for which there is a nice formula, namely counting all divisors of a given number. This time, we will examine a question from last August where we have to count the number of divisors of a specific type, making it more …
How many divisors (also called factors) does a number have? We’ve answered many questions about that over the years, sometimes by just guiding a student to discover it, sometimes either deriving the formula for them or just showing and using it. Let’s look at a few.
(A new question of the week) Sometimes when we are learning a new subject, in this case calculus, a superficially simple question can be confusing. And that can be a good thing! Let’s look at a question about a derivative that, while not using very advanced concepts, gives a challenge to the learner that forces …
We’ve been celebrating a new year with some examination of dates: the fact that 2020 is a new decade (sort of) and a leap year (definitely), and now, some details about how the whole Gregorian calendar works. Some of this is collected in the Ask Dr. Math FAQ on The Calendar and the Days of …