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Introduction to Complex Numbers

Up to this point, we have avoided taking the square root of negative numbers, such as √(−1). We’ve simply dismissed the notion by saying an output does not exist, and rightfully so given the real number system we’ve been brought up with. In this section, we deal with them by introducing…

Combined Variation Word Problems

This section caters exclusively to word problems involving combined variation. As introduced in the previous section, combined variation is when there is both a direct (multiplication) and inverse (division) variation that occurs together. Be sure to watch all three parts as they examine different scenarios commonly found in textbooks, all of…

Joint and Combined Variation

When y varies directly as both x and w, we say that y varies jointly as x and w. When you first looked at direct variation, you focused mainly on a single dependent and independent variable (i.e. y and x, respectively). This time the equation directly depends one 2 or…

Inverse Variation

The phrase “y varies inversely as x” or “y is inversely proportional to x” means that as x gets bigger, y gets smaller, and vice versa. Inversely proportional terms can mathematically be represented as: null Notice how x is under a constant k. ? Don’t confuse inverse variation with inverse functions. An inverse function…

Direct Variation

Direct variation is when the dependent variable, y, varies according to the independent variable, x. The most generic direct variation equation is y = 1·x. If you plot this equation, you will get a diagonal line cross the origin. To generalize any direction variation equation, use the following template: null…

Introduction

This chapter introduces us to solving a system of equations. In part one of this course (Math 1131), you learned how to solve linear equations (such as, 25 = x + 5), for the unknown variables. This time you’ll learn to solve a system of linear equations with two unknowns,…

Numerical Operations

A numerical operation can be described as an action or process used to solved a numerical problem. Adding and Subtracting Signed Numbers  If you have two numbers x and y, the following rules apply when these numbers are being added or subtracted. Rule of Signs for Addition:   (x – y)…