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Selected answers to common questions:
Solving simple linear equations.
- Using an Augmented Matrix [11/21/1999]
Solve the set of simultaneous equations x+3y+z=3, x+5y+5z=1 and 2x+6y+
3z=8 using an augmented matrix?
- Variation on Combined Work [06/13/2002]
If you run a large pipe for 4 hours, and run a small pipe for 9 hours,
you can fill 1/2 a pool. If you run both pipes together for 12 hours,
you can fill the whole pool. How long would it take to fill the pool
using each pipe by itself?
- Vectors and Linear Combinations [01/25/1999]
If vector v0 = (x0, y0, z0) and vector v1 = (x1, y1, z1) both satisfy ax
+ by + cz = d, then why does mv0 + nv1, where m + n = 1, satisfy that
- Volume by Inch of a Cone-Shaped Tank [03/03/2003]
I have a chemical tank that has a cone bottom and I need to know the
volume of each inch of the cone.
- A Way to Estimate the Square Root of Any Number [03/16/2006]
A student studying square roots discovers an interesting method of
estimating non-perfect roots and is curious why it works.
- A Way to Remember What 'm' and 'b' Mean in Slope-Intercept Form [02/01/2004]
An interesting memory trick to help you remember how to graph a linear
equation in slope-intercept form.
- What is Nonlinear Math? [10/02/1997]
What exactly is nonlinear math, and what is it used for?
- When is a Slope 0 or Undefined? [3/29/1997]
How do I know when the slope of an equation is zero or undefined (no
- Why b for Intercept? [10/16/2003]
In the slope-intercept formula, y = mx + b, why is 'b' used to
represent the y-intercept?
- Why Does Adding Equations to Solve a System Work? [02/10/2007]
I know you can add two linear equations together to eliminate one
variable as part of solving a system of equations, but I don't
understand why that works. Are you adding the lines together? What
does the resulting equation represent in terms of the original lines?
- Why Does the Slope Formula Work? [10/29/2008]
How does the slope formula (y2 - y1)/(x2 - x1), which uses subtraction
and division, come up with a slope?
- Why is 'b' Used in Slope-Intercept Form? [02/04/2004]
Why is the letter 'b' used for the y-intercept in the slope-intercept
form of a linear equation?
- Why Is Slope Rise Over Run and Not Run Over Rise? [03/05/2005]
We were wondering today in math class why slope is defined as rise
over run and why it couldn't be run over rise?
- X- and Y-Intercepts [09/15/1998]
I'm having a hard time finding out how to solve an equation and then do
the graph. The intercepts confuse me also...
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