# Mathematics for Technology II (Math 2131)

Durham College, Mathematics
Free
• 36 lessons
• 0 quizzes
• 14 week duration
• ##### 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.

• ##### Complex Numbers

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.

• ##### Logarithmic Functions

This chapter introduces you to exponential functions, and how they can be solved using logarithms.

• ##### Trigonometric Identities and Equations
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• ##### Analytic Geometry
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## Mathematics for Technology II (Math 2131)

### 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:

Notice how x is under a constant k.

? Don’t confuse inverse variation with inverse functions. An inverse function is one that undoes the action of the another function.

The equation y = k over x can also he written as y = k·x-1 given the negative exponent rule.

Another form is obtained by multiplying both sides of y = k over x by x, getting:

$xy=k\phantom{\rule{0ex}{0ex}}$

Each of these three forms indicate inverse variation. Inverse variation problems are solved by the same methods as for any other power function. As before, we can work these problems with or without finding the constant of proportionality (k) – question 2 in the video below.

• Part 2 and Part 3 can be accessed by following their links.
• Note that students often misread phrases like square root with square, and vice versa, of a variable as in Part 3; therefore, be cautious as you read through how the function is being modified.