# Mathematics for Technology II (Math 2131) Durham College, Mathematics
Free • 0 lessons
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• 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)

### 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 more independent variables (x and w). The three variables introduced above are related by the following equation:

• Where, as before, k is a constant of proportionality

The video below shows two examples of joint variation.

Distinguishing between joint and combined variation is sometimes confusing for students. Just like joint variation, combined variation relates two or more independent variable to the dependent variable. However, as the name implies, the variables don’t have to be directly proportional. Rather, you can combine direct, inverse, and jointly related variables. Just as before, the way they are related can be found by careful reading of the problem statement.

The last video in this lesson shows two more examples of joint and combined variation. Can you tell which of the two questions featured is joint and which is combined? Write a comment below!