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# Solutions for Chapter 12-4: THE DOT PRODUCT

## Full solutions for Functions Modeling Change: A Preparation for Calculus | 4th Edition

ISBN: 9780470484753

Solutions for Chapter 12-4: THE DOT PRODUCT

Solutions for Chapter 12-4
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##### ISBN: 9780470484753

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 12-4: THE DOT PRODUCT includes 29 full step-by-step solutions. This textbook survival guide was created for the textbook: Functions Modeling Change: A Preparation for Calculus , edition: 4. Since 29 problems in chapter 12-4: THE DOT PRODUCT have been answered, more than 25140 students have viewed full step-by-step solutions from this chapter. Functions Modeling Change: A Preparation for Calculus was written by and is associated to the ISBN: 9780470484753.

Key Calculus Terms and definitions covered in this textbook
• Binomial probability

In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n - k2!pk11 - p) n-k where p is the probability of the outcome occurring once

• Convergence of a series

A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S

• Exponential growth function

Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

• Factor

In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

• Fundamental

Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).

• Head minus tail (HMT) rule

An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2 - x 1, y2 - y19>

• Invertible linear system

A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

• nth root

See Principal nth root

• One-to-one function

A function in which each element of the range corresponds to exactly one element in the domain

• Ordered set

A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

• Partial fractions

The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

• Pie chart

See Circle graph.

• Positive numbers

Real numbers shown to the right of the origin on a number line.

• Power-reducing identity

A trigonometric identity that reduces the power to which the trigonometric functions are raised.

• Principle of mathematical induction

A principle related to mathematical induction.

• Scientific notation

A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

• Subtraction

a - b = a + (-b)

• Sum of complex numbers

(a + bi) + (c + di) = (a + c) + (b + d)i

• y-intercept

A point that lies on both the graph and the y-axis.

• Zero factorial

See n factorial.

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