Author: Lensyl Urbano

Finding Where Two Lines Intersect: Khan Academy Lessons

Khan Academy videos on how to solve systems of linear equations:

Use a graphing calculator to double check your lines, or use WolframAlpha, or use my simple line grapher.

by Graphing

Video: Solving Linear Systems by Graphing

Most algebra texts have good problem sets for practice (Khan Academy does not – as yet).

by Substitution

Moving from the more intuitive, visual, graphical method of solution to the more exact algebraic methods, we start with solving by substitution.

Video: Solving Linear Systems by Substitution

Practice Set: Practicing Systems of equations with substitution

by Elimination

Video: Solving Systems of Equations by Elimination

Additional Video: Solving systems by elimination 2 (on YouTube).

Additional Video: Solving systems by elimination 3 (on YouTube).

Practice Set: Practicing Systems of equations with simple elimination

Exponential Growth/Decay Models (Summary)

A quick summary (more details here):

The equation that describes exponential growth is:
Exponential Growth: N = N_0 e^{rt}

where:

  • N = number of cells (or concentration of biomass);
  • N0 = the starting number of cells;
  • r = the rate constant, which determines how fast growth occurs; and
  • t = time.

You can set the r value, but that’s a bit abstract so often these models will use the doubling time – the time it takes for the population (the number of cells, or whatever, to double). The doubling time (td) can be calculated from the equation above by:

t_d = \frac{\ln 2}{r}

or if you know the doubling time you can find r using:

r = \frac{\ln 2}{t_d}

Finally, note that the only difference between a growth model and a decay model is the sign on the exponent:

Exponential Decay: N = N_0 e^{-rt}

Decay models have a half-life — the time it takes for half the population to die or change into something else.

Live Bears

Watch brown bears catch salmon in Katmai National Park on a live webcam:

Every year over a hundred Brown Bears descend on a mile long stretch of Brooks River to feast on the largest Sockeye Salmon run in the world.

— bears: brown bear & salmon cam – brooks falls on explore.org

Live video from Brooks Falls, Alaska.

Switch: Converting Audio Files for Sound Effects

Adding sound to webpages is pretty easy with HTML5’s Audio tag (as Jean-Baptiste Jung demonstrates), but since different browsers can only handle certain, different types of sound files, you’ll often need to convert your sound into .wav, .ogg, and .mp3 formats so they can work for everyone.

Switch Sound File Converter does just what it says, and is free for non-commercial use.