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In the last two sections of this chapter we desire to discuss solving equations & inequalities that have absolute values. We will look at equations along with absolute value in them in this section.
However, before solving first we must have a brief discussion of just what absolute value is.
The notation for the absolute value of p is |p|. Note as well that the absolute value bars are not parentheses and in several cases don't act as parentheses so be careful with them.
There are two ways to describe absolute value. There is geometric definition & a mathematical definition. We will look at both.
In this definition we will think of |p| as the distance of p from the origin onto a number line. Also we will always employ a positive value for distance. Assume the following num
In this section we are going to look at equations which are called quadratic in form or reducible to quadratic in form . What it means is that we will be looking at equations th
Solve out the following system of equations by using augmented matrices. 3x - 3 y - 6 z = -3 2x - 2 y - 4 z = -2 -2x + 3 y + z = 7 Solution Notice that this system
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Maximise, p =168x+161y+158z+132w 475x+450y+440z+438w 250x+230y+220z+210w 119x+115.5y+114.8z+112.25w 160x+50y+120z+50w 12x+8.8y+7.4z+5.3w x >=4
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Example: Sketch the graph of ellipses. (x +2) 2 /9 + ( y - 4) 2 /25 =1 Solution So, the center of this ellipse is ( -2, 4) and as usua
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