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.

• 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.

• 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)

There are several rules of radicals, which are similar to the laws of exponents and, in fact, are derived from them. The first rule is for products.

Root of a Product

Take, for example, (x·y)ⁿ. In the past, you learned that any monomial (i.e. x·y) raised to a single power can be represented as a product of its factors individually raised to that power. Therefore, (x·y)ⁿ is the same as xⁿ·yⁿ. If ⁿ were a fraction, the same rules would apply; remember that fractional exponents can be represented as radicals:

Example 1:

${\left(xy\right)}^{1}{2}}={x}^{1}{2}}{y}^{1}{2}}=\sqrt{x}\sqrt{y}=\overline{)\sqrt{x·y}}\phantom{\rule{0ex}{0ex}}$

Example 2:

${\left(9x\right)}^{1}{2}}={9}^{1}{2}}{x}^{1}{2}}=\sqrt{9}\sqrt{x}=\overline{)3\sqrt{x}}\phantom{\rule{0ex}{0ex}}$

Generally:

${\left(ab\right)}^{1}{n}}={a}^{1}{n}}{b}^{1}{n}}=\sqrt[n]{a}\sqrt[n]{b}\phantom{\rule{0ex}{0ex}}$

Rooting of a Quotient

To root a fraction, follow the pattern shown below:

$\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\frac{{a}^{1}{n}}}{{b}^{1}{n}}}={\left(\frac{a}{b}\right)}^{1}{n}}\phantom{\rule{0ex}{0ex}}$

Example:

$\sqrt{\frac{w}{25}}=\frac{\sqrt{w}}{\sqrt{25}}=±\frac{\sqrt{w}}{5}$