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Probability of Coronavirus in the Office

What is the probability of Coronavirus in your office? This post seeks to answer that and is based on an email one of my husband’s co-workers sent out back in early March. I would have made this post back then, but two months is how long it took my husband to forward me the email. So there you go. Anyway, this post is about the probability that at least one person in their office was already…

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Physics - Traveling Lorries and Cars

Physics – Traveling Lorries and Cars

Remember those stereotypical nightmare math questions where they want you to figure out when the two trains pass each other, or when they finally get someplace? Well, this question, which was submitted to me by a reader, was so much like one of those questions I could hardly believe it. I couldn’t resist making a post out of it. Here we go!

A lorry started from town A and travelled towards…

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How to Model Draining a Conical Tank

Recently, I pulled a differential equations book off of my shelf and did a few problems for fun. I like differential equations because they are about modeling and modeling is one of my favorite topics in mathematics. This post is about modeling water draining out of a tank with a hole in the bottom.

If you follow this blog, you might be wondering, “Hey, didn’t she post on this already?” The…

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Determining the Capacity of a Tank

This post is about a fractions problem disguised in a word problem about the capacity of a tank. It’s a little tricky, but once we hash out the details, hopefully it will become clear to you, the reader. The problem is as follows:

A rectangular tank is 3/4 full of water. If you add another 320 cubic centimeters of water, the tank will be 7/8 full. What is the capacity of the tank?

First, let’s…

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#word problems

By the Laws of Transitivity...

By the Laws of Transitivity…

I work at a small software development company. Currently, we are supporting multiple systems and the owner is intent on combining them all to a single platform. There are basically 3 systems and the first step to combining them is to get them all using the same database structure. It turns out that he already did this in the past with System 1; he altered the database to get it to use the…

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5 Easy Steps for Solving Multiple Angle Trig Equations

I’m teaching Pre-Calculus this semester and one of the topics is trig equations. There are many types of trig equations, but the one that caught my interest the most was the one involving multiple angles. I guess this is because I can’t ever remember formally learning how to solve these, but I do remember coming across these in the past and not really knowing how to handle them, so it was nice to…

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#trig equations

Bacterial Growth Problem with Mutation

This post is about a bacterial growth problem, you know, those ones they made you do in your college algebra class? Only this time, we’re mixing it up a bit. This time, the bacteria MUTATES. Mwa ha ha ha… Anyway, here is the problem: In a population of bacteria with doubling time 1 hour, one bacterium underwent some mutation that changed its doubling time to 1 minute. The population doubled its…

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#population modeling

A Simple Markov Chain Example

This post features a simple example of a Markov chain. Markov chains are used in mathematical modeling to model process that “hop” from one state to the other. They are used in computer science, finance, physics, biology, you name it! A relevant example to almost all of us are the “suggestions” you get when typing a search in to Google or when typing text in your smartphone. Yep, those use Markov…

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#Markov chains #mathematical modeling

Find the Derivative of a Fraction

Derivatives. If you’re currently taking Calc 1 (which you probably are if you found yourself here), you are probably up to your elbows in derivative problems. One type is taking the derivative of a fraction, or better put, a quotient. That’s what this post is about. There is nothing special about this situation, I just needed a post for this month and this search term came up in Google Suggest so…

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#derivative #quotient rule

GRE Combinatorics Practice, Part 1

Combinatorics. When I took the Math Subject GRE, I was surprised at the number of combinatorics problems. That was a long time ago, so I don’t know if it’s still the same today, but I remember wishing I had studied combinatorics more. But the problem is that combinatorics suck. I feel like no matter how much I study it, I still get tripped up by the next combinatorics problem that comes my way.…

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#combinatorics

Test For Divergence: An Example

This post is in response to a user-submitted question. I’m going to keep it short and sweet since I just had eye surgery and am still half-blind, so computer tasks are somewhat difficult. The question gives the following infinite sum: \( \) \begin{equation*} \sum_{n=1}^{\infty} \left(1+\frac{3}{n}\right)^{-5n} \end{equation*} and says to use the Test for Divergence to show that the series…

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#infinite series

Trig Substitution and Completing the Square: An Example

This post is about another integration problem. It was submitted to the site by the same person who submitted this question. Part me wonders if this individual isn’t just getting to do their homework for them… But I will let it slide since I was struggling on coming up with posts for this month ;) Anyway, here is the problem: \( \) \begin{equation*} \int \frac{x}{x^2-4x+6} dx \end{equation*} This…

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Integration by Parts: An Example

This post is about a problem a student recently submitted to the website. I decided to answer it in post format, because to do so through email would look too messy. The question is the following:\( \) \begin{equation*} \int e^{2x}\sin(3x)dx \end{equation*} This is a challenging integration problem. Something a lot of students struggle with is simply how to get started. Direct integration and…

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#integration #integration by parts

Center of Mass Experiment

This post is about a hands-on experiment I did to explore the center of mass of an object. It’s part of my crusade to understand physics better. It was really quite fun, so I decided to make a post about it. Note that in this post I’m assuming you already have a basic understanding of the center of mass and moments. If you don’t, that’s ok, but you probably won’t understand everything I talk…

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#center of mass #physics

Related Rates: Worked Examples

This post features several related rates problems. I recently taught this section in my Calculus class and had so much fun working the problems I decided to do a blog post on it. I’m not going to waste time explaining the theory behind it, that’s your textbook’s job. Just the problems with some commentary. Hopefully it will help you, the reader, understand how to do these problems a little bit…

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Differentials Explained

Have you ever been confused about differentials? I remembering reading about these after I took Calculus and having no idea what they were. I thought maybe my teacher had skipped that section, but more likely than not, I had just forgotten. I think they can be difficult to understand because the definition is a little obscure and they involve using the derivative, so many students may just feel…

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#differentials #linear approxmations

Non-Isomorphic Finite Abelian Groups

It’s been a while since I did a post about algebra, and since keeping brushed up on algebra was one of the reasons I started this blog, I decided it was high time I did a post on the subject. Abstract algebra is among my least favorite areas of mathematics. Sure, it’s interesting, but the field is so amorphous and, well, abstract, that it is hard for me to feel like I ever have a solid footing in…

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#Abstract Algebra #groups #Sylow

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