15Nov 2014 by Vincent Summers No Comments

Analytic Geometry: The Parabola

Mathematics
What is a parabola, and of what use is it? If a sheet of paper is likened to an infinite plane in space, the x- and y-axes, drawn at right angles to each other, provide a means of describing each point on the plane of the paper in terms of an x and a y value. Thus the point (1, 3) tells us that beginning at the origin or center where the x-axis crosses the y-axis, if we travel one unit to the right and then three units up, we will have reached the point we seek. Introducing the Parabola Now we will pass on to describing a parabola.1 The parabola is an important mathematical "curve," inasmuch as it describes, mathematically, the behavior of a number of important actions, such…
Read More
04Mar 2014 by Vincent Summers 2 Comments

Sample High School Math Problems with Answers

Mathematics
[caption id="attachment_5578" align="alignright" width="440"] Fractal - CCA Share Alike 3.0 Unported by Wolfgang Beyer[/caption] Want some sample high school math problems with answers? Well then here you go! High School Math Problems Problem 1:     A change purse has 100 nickels and dimes. The total value of the coins is $7. How many coins of each type does the purse contain? If the number of nickels is N and the number of dimes is D, then 5N + 10D = 700 (the 5, 10 and 700 representing the number of cents) However, N + D = 100 (the number of nickels plus the number of dimes equals 100) So, solving for N for both equations, we get as the result N = – 2D + 140 and N = 100 – D…
Read More
24Feb 2014 by Vincent Summers No Comments

Math Equations for Parallel and Perpendicular Lines

Mathematics
It's fun and very instructive to figure out the math equations for parallel and perpendicular lines. The basic mathematical equation for a line is, ax + by = c Here are three examples of line equations: 2x + 3y = 6 4x – 2y = –5 –x/3 + 2.47y = √3 Slope-Intercept Form One of the most useful formats for the equation of a line is the slope-intercept form. That form is written, y = mx + b The variables here are x and y. The letters m and b are constants that represent the rise or tilt of the line (slope, m) and the point at which the line crosses the y-axis (intercept, b). So the first of the three equations for a line listed above is written in…
Read More
21Feb 2014 by Vincent Summers 1 Comment

Determining the Equation for a Line from Two Points

Mathematics
Lines can be drawn in three dimensions, but most analytical geometry courses stick to lines in two dimensions, generally using the Cartesian or XY coordinate system. The generic equation for a line may follow the form: y = mx + b where m is the slope (measure of tilt or steep-ness) of the line, while b is its intercept or intersection with the y-axis. Equation for a Line from Two Points A line can be determined and an equation derived from two points. In the Cartesian system, for instance, take two points, (2 , 3) and (– 1 , 5). The first number in each pair represents the x-value of a point and the second number in each pair represents the y-value. Writing these points into the general equation y…
Read More