Chapter 5 Algebra Fundamentals: Algebraic Terms, Roots, and Powers.
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Transcript of Chapter 5 Algebra Fundamentals: Algebraic Terms, Roots, and Powers.
Chapter 5Algebra Fundamentals:
Algebraic Terms, Roots, and Powers
Numbers, Expressions, and Terms
• Literal and Real Numbers Real Numbers
•Always have the same value. Never can have other values. Aka. Constants
•Examples: 6, 7, 27,1024, etc.
Literal Numbers•Take on different values
Can represent constants or variables
•Examples: E= I * R
Numbers, Expressions, and Terms
• Algebraic Expressions and Terms Expressions contain Real, Literal, or both types of numbers
Terms are numbers separated by ‘+’ and ‘-’ •2ab + 4c – 5ac
Three terms: 2ab, 4c, 5ac
•Expression with one term – monomial•Expression w/two + terms - polynomial
Numbers, Expressions, and Terms
• Coefficients Of Algebraic term is real number part of term•6 is coefficient of 6xy•Coefficient of ax is ‘1’
• Exponents 53 = 5 * 5 * 5 = 125 X3 = X * X * X = depends on value of X
Finding Values of Algebraic Expressions
• When expression has real and literal numbers Need value of literals to find value 6X2 yields different values for different X’s•If X =3 => 6 * 32 = 6 * 9 = 54•If X =4 => 6 * 42 = 6 * 16 = 96•If X =1 => 6 * 12 = 6 * 1 = 6
If x = 3 and y = 4 Find:•xy = 3 * 4 = 12•x2y = 32 * 4 = 9 * 4 = 36
Finding Values of Algebraic Expressions
• When expression has real and literal numbers If x = 3 and y = 4 Find:
•x2y2 = 32 * 42 = 9 * 16 = 144•4x3y2 = 4 * 33 * 42 = 1730•(xy) 2 = (3 * 4) 2 = 12 2 = 144•(xy) 2 = x 2 y 2 = 3 2 * 4 2 = 9 * 16 = 144
•3x 2 y – xy 2 = 3 * 3 2 *4 – 3 * 4 2 = 108 -48 = 60
Roots
Roots
DC Circuit Examples• In Electronics Literal number in equations represent relationships between variables in electrical circuits. Ohm’s Law E = I * R
•Voltage across a component = Current through the component time resistance of the component
•Example problems 5-7 through 5-11 on page 116
Practice exercises – Practice Problems 5-5 on page 117
AC Circuit Examples
AC Circuit Examples• Impedance of a circuit
Includes resistance and any reactance• Resistance and reactance are orthogonal • i.e. an impedance of circuit with 5 ohms resistance and 5 ohms reactance in series has an impedance of the vector sum of the two elements
Z = (52 +52)1/2 = 501/2 = 7.07 (rounded to 3 places)
Z = 21/2 * 5
• Example 5-14 on page 119
Work Practice problems
• For this and all the chapters Odd number ones have answers in back of book
WORK THEM UNTIL YOU UNDERSTAND THE PROBLEMS