Solutions for Precalculus
Problem 1SP:
Simplify. a.4z0b.-40c.23d.1n5e.3a4b9Problem 7SP:
Simplify each expression. Assume that all variables represent positive real numbers....Problem 8SP:
Multiply or divide as indicated. Assume that c,d,andy represent positive real numbers....Problem 9SP:
Add or subtract as indicated. Assume that all variables represent positive real numbers....Problem 1PE:
For a nonzero real number b, the value of b0=.Problem 2PE:
For a nonzero real number b, the value of b=1bn.Problem 3PE:
From the properties of exponents, bmbn=b.Problem 5PE:
From the properties of exponents, bmn=b.Problem 7PE:
The expression am/n can be written in radical notation as provided that an is a real number.Problem 8PE:
The expression a1/n can be written in radical notation as provided that an is a real number.Problem 15PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 18PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 21PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 24PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 25PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 27PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 29PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 33PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 36PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 37PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 40PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 41PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 42PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 44PE:
For Exercises 15-46, use the properties of exponents to simplify each expression. (See Example 2)...Problem 48PE:
For Exercises 47-52, write the numbers in scientific notation. (See Example 3) a.2710b.0.00271c.2.71Problem 49PE:
For Exercises 47-52, write the numbers in scientific notation. (See Example 3) The speed of light is...Problem 50PE:
For Exercises 47-52, write the numbers in scientific notation. (See Example 3) The mean distance...Problem 51PE:
For Exercises 47-52, write the numbers in scientific notation. (See Example 3) The size of an HIV...Problem 53PE:
For Exercises 53-58, Write the number in standard decimal notation. (see Example 3)...Problem 55PE:
For Exercises 53-58, Write the number in standard decimal notation. (see Example 3) A drop of water...Problem 56PE:
For Exercises 53-58, Write the number in standard decimal notation. (see Example 3) A computer with...Problem 58PE:
For Exercises 53-58, Write the number in standard decimal notation. (see Example 3) The blue light...Problem 59PE:
For Exercises 59-66, perform the indicates operation. Write the answer in scientific notation. (See...Problem 60PE:
For Exercises 59-66, perform the indicates operation. Write the answer in scientific notation. (See...Problem 61PE:
For Exercises 59-66, perform the indicates operation. Write the answer in scientific notation. (See...Problem 63PE:
For Exercises 59-66, perform the indicates operation. Write the answer in scientific notation. (See...Problem 64PE:
For Exercises 59-66, perform the indicates operation. Write the answer in scientific notation. (See...Problem 67PE:
Jonas has a personal music player with 80 gigabytes of memory (80 gigabytes is approximately 81010...Problem 90PE:
a. For what value of c will the statement be true? c+844=c+8 b. For what value of c will the...Problem 91PE:
For Exercises 91-100, simplify each expression. Assume that all variable expressions represent...Problem 92PE:
For Exercises 91-100, simplify each expression. Assume that all variable expressions represent...Problem 93PE:
For Exercises 91-100, simplify each expression. Assume that all variable expressions represent...Problem 94PE:
For Exercises 91-100, simplify each expression. Assume that all variable expressions represent...Problem 95PE:
For Exercises 91-100, simplify each expression. Assume that all variable expressions represent...Problem 96PE:
For Exercises 91-100, simplify each expression. Assume that all variable expressions represent...Problem 98PE:
For Exercises 91-100, simplify each expression. Assume that all variable expressions represent...Problem 103PE:
For Exercises 101-112, multiply or divide as indicated. Assume that all variable expressions...Problem 106PE:
For Exercises 101-112, multiply or divide as indicated. Assume that all variable expressions...Problem 109PE:
For Exercises 101-112, multiply or divide as indicated. Assume that all variable expressions...Problem 113PE:
For Exercises 113-120, add or subtract as indicated. Assume that all variables represent positive...Problem 114PE:
For Exercises 113-120, add or subtract as indicated. Assume that all variables represent positive...Problem 116PE:
For Exercises 113-120, add or subtract as indicated. Assume that all variables represent positive...Problem 117PE:
For Exercises 113-120, add or subtract as indicated. Assume that all variables represent positive...Problem 118PE:
For Exercises 113-120, add or subtract as indicated. Assume that all variables represent positive...Problem 121PE:
For Exercises 121-122, use the Pythagorean theorem to determine the length of the missing side....Problem 122PE:
For Exercises 121-122, use the Pythagorean theorem to determine the length of the missing side....Problem 125PE:
The depreciation rate for a car is given by r=1SC1/, where S is the value of the car after n years,...Problem 128PE:
Explain why scientific notation is used.Problem 130PE:
Explain why the given expressions cannot be simplified further. a.2x+3yb.2x+3yc.2x3+3xProblem 132PE:
For Exercises 131-132, refer to the formula F=Gm1m2d2. This gives the gravitational force F (in...Problem 133PE:
For Exercises 133-136, without the assistance of a calculator, fill in the blank with the...Problem 135PE:
For Exercises 133-136, without the assistance of a calculator, fill in the blank with the...Problem 138PE:
For Exercises 137-142, write each expression as a single radical for positive values of the...Problem 139PE:
For Exercises 137-142, write each expression as a single radical for positive values of the...Problem 143PE:
For Exercises 143-144, evaluate the expression without the use of a calculator. 8.010122.0104Browse All Chapters of This Textbook
Chapter R - Review Of PrerequisitesChapter R.1 - Sets And The Real Number LineChapter R.2 - Exponents And RadicalsChapter R.3 - Polynomials And FactoringChapter R.4 - Rational Expressions And More Operations On RadicalsChapter R.5 - Equations With Real SolutionsChapter R.6 - Complex Numbers And More Quadratic EquationsChapter R.7 - Applications Of EquationsChapter R.8 - Linear, Compound, And Absolute Value InequalitiesChapter 1 - Functions And Relations
Chapter 1.1 - The Rectangular Coordinate System And Graphing UtilitiesChapter 1.2 - CirclesChapter 1.3 - Functions And RelationsChapter 1.4 - Linear Equations In Two Variables And Linear FunctionsChapter 1.5 - Applications Of Linear Equations And ModelingChapter 1.6 - Transformations Of GraphsChapter 1.7 - Analyzing Graphs Of Functions And Piecewise-defined FunctionsChapter 1.8 - Algebra Of Functions And Function CompositionChapter 2 - Polynomial And Rational FunctionsChapter 2.1 - Quadratic Functions And ApplicationsChapter 2.2 - Introduction To Polynomial FunctionsChapter 2.3 - Division Of Polynomials And The Remainder And Factor TheoremsChapter 2.4 - Zeros Of PolynomialsChapter 2.5 - Rational FunctionsChapter 2.6 - Polynomial And Rational InequalitiesChapter 2.7 - VariationChapter 3 - Exponential And Logarithmic FunctionsChapter 3.1 - Inverse FunctionsChapter 3.2 - Exponential FunctionsChapter 3.3 - Logarithmic FunctionsChapter 3.4 - Properties Of LogarithmsChapter 3.5 - Exponential And Logarithmic Equations And ApplicationsChapter 3.6 - Modeling With Exponential And Logarithmic FunctionsChapter 4 - Trigonometric FunctionsChapter 4.1 - Angles And Their MeasureChapter 4.2 - Trigonometric Functions Defined On The Unit CircleChapter 4.3 - Right Triangle TrigonometryChapter 4.4 - Trigonometric Functions Of Any AngleChapter 4.5 - Graphs Of Sine And Cosine FunctionsChapter 4.6 - Graphs Of Other Trigonometric FunctionsChapter 4.7 - Inverse Trigonometric FunctionsChapter 5 - Analytic TrigonometryChapter 5.1 - Fundamental Trigonometric IdentitiesChapter 5.2 - Sum And Difference FormulasChapter 5.3 - Double-angle, Power-reducing, And Half-angle FormulasChapter 5.4 - Product-to-sum And Sum-to-product FormulasChapter 5.5 - Trigonometric EquationsChapter 6 - Applications Of Trigonometric FunctionsChapter 6.1 - Applications Of Right TrianglesChapter 6.2 - The Law Of SinesChapter 6.3 - The Law Of CosinesChapter 6.4 - Harmonic MotionChapter 7 - Trigonometry Applied To Polar Coordinate Systems And VectorsChapter 7.1 - Polar CoordinatesChapter 7.2 - Graphs Of Polar EquationsChapter 7.3 - Complex Numbers In Polar FormChapter 7.4 - VectorsChapter 7.5 - Dot ProductChapter 8 - Systems Of Equations And InequalitiesChapter 8.1 - Systems Of Linear Equations In Two Variables And ApplicationsChapter 8.2 - Systems Of Linear Equations In Three Variables And ApplicationsChapter 8.3 - Partial Fraction DecompositionChapter 8.4 - Systems Of Nonlinear Equations In Two VariablesChapter 8.5 - Inequalities And Systems Of Inequalities In Two VariablesChapter 8.6 - Linear ProgrammingChapter 9 - Matrices And Determinants And ApplicationsChapter 9.1 - Solving Systems Of Linear Equations Using MatricesChapter 9.2 - Inconsistent Systems And Dependent EquationsChapter 9.3 - Operations On MatricesChapter 9.4 - Inverse Matrices And Matrix EquationsChapter 9.5 - Determinants And Cramer’s RuleChapter 10 - Analytic GeometryChapter 10.1 - The EllipseChapter 10.2 - The HyperbolaChapter 10.3 - The ParabolaChapter 10.4 - Rotation Of AxesChapter 10.5 - Polar Equations Of ConicsChapter 10.6 - Plane Curves And Parametric EquationsChapter 11 - Sequences, Series, Induction, And ProbabilityChapter 11.1 - Sequences And SeriesChapter 11.2 - Arithmetic Sequences And SeriesChapter 11.3 - Geometric Sequences And SeriesChapter 11.4 - Mathematical InductionChapter 11.5 - The Binomial TheoremChapter 11.6 - Principles Of CountingChapter 11.7 - Introduction To Probability
Book Details
Julie Miller wrote her developmental math series because students were coming into her Precalculus course underprepared. They weren’t mathematically mature enough to understand the concepts of math nor were they fully engaged with the material. She began her developmental mathematics offerings with intermediate algebra to help bridge that gap. The Precalculus series is a carefully constructed end to that bridge that uses the highly effective pedagogical features from her fastest growing developmental math series. What sets Julie Miller’s series apart is that it addresses course issues through an author-created digital package that maintains a consistent voice and notation throughout the program. This consistency--in videos, PowerPoints, Lecture Notes, and Group Activities--coupled with the power of ALEKS and Connect Hosted by ALEKS, ensures that students master the skills necessary to be successful in Precalculus and can carry them through to the calculus sequence.
Sample Solutions for this Textbook
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