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Solving Systems of Equations
This unit introduces how to systematically solve a system of equations, namely linear equations. Examples of non-linear systems, including systems of 3 unknowns will be of emphasis.
Graphs of Trigonometric Functions
The unit focuses primarily on how to graph periodic sinusoidal functions, and how to identify features of a waveform to produce an equation by inspection.
Polar Coordinate Functions
An introduction to the polar coordinate system.
Exponents and Radicals
This unit is an extension of what was introduced in Math 1131. To learn how to work with radicals, knowing your exponent laws in crucial. Hence, this unit begins with a thorough review.
This chapter introduces you to exponential functions, and how they can be solved using logarithms.
Trigonometric Identities and Equations
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:
Where k is the constant of proportionality. The constant of proportionality is the constant value that relates the two variables or the factor that keeps the variables proportional. To find the constant k, as demonstrated in the video below, you substitute the given information into the template formula, such as y and x, then solve.
Summary of steps
1) Substitute the known pair of x and y values into the formula, and solve for k.
2) Rewrite the formula with the value for k.
3) Substitute the single x value, and solve for y.
Now that you’ve covered a few easy examples pertaining to direct variation, the next set video shows how applicable this concept is to real-life problems involving force and electricity.
The independent variable, x, doesn’t always have to be of first degree. The next video shows two examples where the powers are ½ (square root) and 3/2. The relationship is direct variation as long as k is being directly multiplied to the independent variable.
You may encounter questions where one or more variable experiences an increases or decreases by a specified amount, as you’ll find in question 2 below. Generally, if there’s a percentage decrease, it’s represented by a factor less than 1. For example, a decrease of 15% is presented as 0.85. The opposite is true with a percent increase; so if there’s a 15% increase, you write a factor of 1.15. Similarly, a 100% increase is represented by the factor 2 (i.e. 1 + 1). One last thing you should discover in question 2 is you can work problems with or without finding the constant of proportionality. Let’s have a look:
More applications pertaining to direct variation can be found in the links below:
- Part 5
- Part 6