Basic Technical Mathematics11th EditionWashington Publisher: PEARSONISBN: 9780134437705
Basic Technical Mathematics
Solutions for Basic Technical Mathematics
Problem 1PE:
|4.2| = ?Problem 2PE:
|34|=?Problem 1E:
In Exercises 14, make the given changes in the indicated examples of this section, and then answer...Problem 2E:
In Exercises 14, make the given changes in the indicated examples of this section, and then answer...Problem 3E:
In Exercises 14, make the given changes in the indicated examples of this section, and then answer...Problem 4E:
In Exercises 14, make the given changes in the indicated examples of this section, and then answer...Problem 5E:
In Exercises 58, designate each of the given numbers as being an integer, rational, irrational,...Problem 6E:
In Exercises 58, designate each of the given numbers as being an integer, rational, irrational,...Problem 7E:
In Exercises 58, designate each of the given numbers as being an integer, rational, irrational,...Problem 8E:
In Exercises 58, designate each of the given numbers as being an integer, rational, irrational,...Problem 11E:
In Exercises 1118, insert the correct sign of inequality ( or ) between the given numbers. 6 8Problem 12E:
In Exercises 1118, insert the correct sign of inequality ( or ) between the given numbers. 7 5Problem 13E:
In Exercises 1118, insert the correct sign of inequality ( or ) between the given numbers. 3.1416Problem 14E:
In Exercises 1118, insert the correct sign of inequality ( or ) between the given numbers. 4 0Problem 15E:
In Exercises 1118, insert the correct sign of inequality ( or ) between the given numbers. 4 | 3 |Problem 17E:
In Exercises 1118, insert the correct sign of inequality ( or ) between the given numbers. 23 34Problem 18E:
In Exercises 1118, insert the correct sign of inequality ( or ) between the given numbers. 0.6 0.2Problem 21E:
In Exercises 21 and 22, locate (approximately) each number on a number line as in Fig. 1.2.
21. 2.5,...Problem 22E:
In Exercises 21 and 22, locate (approximately) each number on a number line as in Fig. 1.2.
22. ,...Problem 23E:
In Exercises 2346, solve the given problems. Refer to Appendix B for units of measurement and their...Problem 24E:
In Exercises 2346, solve the given problems. Refer to Appendix B for units of measurement and their...Problem 29E:
List the following numbers in numerical order, starting with the smallest: −1, 9, π, , |−8|, −|−3|,...Problem 31E:
If a and b are positive integers and b > a, what type of number is represented by the following?
b...Problem 32E:
If a and b represent positive integers, what kind of number is represented by (a) a + b, (b) a/b,...Problem 33E:
For any positive or negative integer (a) Is its absolute value always an integer? (b) Is its...Problem 34E:
For any positive or negative rational number: (a) Is its absolute value always a rational number?...Problem 36E:
Describe the location of a number x on the number line when
(a) |x| < 1 and (b) |x| > 2.
Problem 38E:
For a number x < 0, describe the location on the number line of the number with a value of |x|.
Problem 39E:
A complex number is defined as a + b j, where a and b are real numbers and . For what values of a...Problem 40E:
A sensitive gauge measures the total weight w of a container and the water that forms in it as vapor...Problem 41E:
In an electric circuit, the reciprocal of the total capacitance of two capacitors in series is the...Problem 42E:
Alternating-current (ac) voltages change rapidly between positive and negative values. If a voltage...Problem 43E:
The memory of a certain computer has a bits in each byte. Express the number N of bits in n...Problem 44E:
The computer design of the base of a truss is x ft long. Later it is redesigned and shortened by y...Browse All Chapters of This Textbook
Chapter 1 - Basic Algebraic OperationsChapter 1.1 - NumbersChapter 1.2 - Fundamental Operations Of AlgebraChapter 1.3 - Calculators And Approximate NumbersChapter 1.4 - Exponets And Unit ConversionsChapter 1.5 - Scientific NotationChapter 1.6 - Roots And RadicalsChapter 1.7 - Addition And Subtraction Of Algebraic ExpressionsChapter 1.8 - Multiplication Of Algebraic ExpressionsChapter 1.9 - Division Of Algebraic Expressions
Chapter 1.10 - Solving EquationsChapter 1.11 - Formulas And Literal EquationsChapter 1.12 - Applied Word ProblemsChapter 2 - GeometryChapter 2.1 - Lines And AnglesChapter 2.2 - TrianglesChapter 2.3 - QuadrilateralsChapter 2.4 - CirclesChapter 2.5 - Measurement Of Irregular AreasChapter 2.6 - Solid Geometric FiguresChapter 3 - Functions And GraphsChapter 3.1 - Introduction To FunctionsChapter 3.2 - More About FunctionsChapter 3.3 - Rectangular CoordinatesChapter 3.4 - The Graph Of A FunctionChapter 3.5 - Graphs On The Graphing CalculatorChapter 3.6 - Graphs Of Functions Defined By Tables Of DataChapter 4 - The Trigonometric FunctionsChapter 4.1 - AnglesChapter 4.2 - Defining The Trigonometric FunctionsChapter 4.3 - Values Of The Trigonometric FunctionsChapter 4.4 - The Right TriangleChapter 4.5 - Applications Of Right TrianglesChapter 5 - Systems Of Linear Equations; DeterminantsChapter 5.1 - Linear Equations And Graphs Of Linear FunctionsChapter 5.2 - Systems Of Equations And Graphical SolutionsChapter 5.3 - Solving Systems Of Two Linear Equations In Two Unknowns AlgebraicallyChapter 5.4 - Solving Systems Of Two Linear Equations In Two Unknowns By DeterminantsChapter 5.5 - Solving Systems Of Three Linear Equations In Three Unknowns AlgebraicallyChapter 5.6 - Solving Systems Of Three Linear Equations In Three Unknowns By DeterminantsChapter 6 - Factoring And FractionsChapter 6.1 - Factoring: Greatest Common Factor And Difference Of SquaresChapter 6.2 - Factoring TrinomialsChapter 6.3 - The Sum And Difference Of CubesChapter 6.4 - Equivalent FractionsChapter 6.5 - Multiplication And Division Of FractionsChapter 6.6 - Addition And Subtraction Of FractionsChapter 6.7 - Equations Involving FractionsChapter 7 - Quadratic EquationsChapter 7.1 - Quadratic Equations; Solution By FactoringChapter 7.2 - Completing The SquareChapter 7.3 - The Quadratic FormulaChapter 7.4 - The Graph Of The Quadratic FunctionChapter 8 - Trigonometric Functions Of Any AngleChapter 8.1 - Signs Of The Trigonometric FunctionsChapter 8.2 - Trigonometric Functions Of Any AngleChapter 8.3 - RadiansChapter 8.4 - Applications Of Radian MeasureChapter 9 - Vectors And Oblique TrianglesChapter 9.1 - Introduction Of VectorsChapter 9.2 - Components Of VectorsChapter 9.3 - Vector Addition By ComponentsChapter 9.4 - Applications Of VectorsChapter 9.5 - Oblique Triangles, The Law Of SinesChapter 9.6 - The Law Of CosinesChapter 10 - Graphs Of The Trigonometric FunctionsChapter 10.1 - Graphs Of Y = A Sin X And Y = A Cos XChapter 10.2 - Graphs Of Y = A Sin Bx And Y = A Cos BxChapter 10.3 - Graphs Of Y = A Sin (bx + C) And Y = Csc (bx + C)Chapter 10.4 - Graphs Of Y = Tan X, Y = Cot X, Y = Sec X, Y = Csc XChapter 10.5 - Applications Of The Trigonometric GraphsChapter 10.6 - Composite Trigonometric CurvesChapter 11 - Exponents And RadicalsChapter 11.1 - Simplifying Expressions With Integer ExponentsChapter 11.2 - Fractional ExponentsChapter 11.3 - Simplest Radical FormChapter 11.4 - Addition And Subtraction Of RadicalsChapter 11.5 - Multiplication And Division Of RadicalsChapter 12 - Complex NumbersChapter 12.1 - Basic DefinitionsChapter 12.2 - Basic Operations With Complex NumbersChapter 12.3 - Graphical Representation Of Complex NumbersChapter 12.4 - Polar Form Of A Complex NumberChapter 12.5 - Exponential Form Of A Complex NumberChapter 12.6 - Products, Quotients, Powers, And Roots Of Complex NumbersChapter 12.7 - An Application To Alternating-current (ac) CircuitsChapter 13 - Exponential And Logarithmic FunctionsChapter 13.1 - Exponential FunctionsChapter 13.2 - Logarithmic FunctionsChapter 13.3 - Properties Of LogarithmsChapter 13.4 - Logarithms To The Base 10Chapter 13.5 - Natural LogarithmsChapter 13.6 - Exponential And Logarithmic EquationsChapter 13.7 - Graphs On Logarithmic And Semilogarithmic PaperChapter 14 - Additional Types Of Equations And Systems Of EquationsChapter 14.1 - Graphical Solution Of Systems Of EquationsChapter 14.2 - Algebraic Solution Of Systems Of EquationsChapter 14.3 - Equations In Quadratic FormChapter 14.4 - Equations With RadicalsChapter 15 - Equations Of Higher DegreeChapter 15.1 - The Remainder And Factor Theorems; Synthetic DivisionChapter 15.2 - The Roots Of An EquationChapter 15.3 - Rational And Irrational RootsChapter 16 - Matrices; Systmes Of Linear EquationsChapter 16.1 - Matrices: Definitions And Basic OperationsChapter 16.2 - Multiplication Of MatricesChapter 16.3 - Finding The Inverse Of A MatrixChapter 16.4 - Matrices And Linear EquationsChapter 16.5 - Gaussian EliminationChapter 16.6 - Higher-order DeterminantsChapter 17 - InequalitiesChapter 17.1 - Properties Of InequalitiesChapter 17.2 - Solving Linear InequalitiesChapter 17.3 - Solving Nonlinear InequalitiesChapter 17.4 - Inequalities Involving Absolute ValuesChapter 17.5 - Graphical Solution Of Inequalities With Two VariablesChapter 17.6 - Linear ProgrammingChapter 18 - VariationChapter 18.1 - Ratio And ProportionChapter 18.2 - VariationChapter 19 - Sequences And The Binomial TheoremChapter 19.1 - Arithmetic SequencesChapter 19.2 - Geometric SequencesChapter 19.3 - Infinite Geometric SeriesChapter 19.4 - The Binomial TheoremChapter 20 - Additional Topics In TrigonometryChapter 20.1 - Fundamental Trigonometric IdentitiesChapter 20.2 - The Sum And Difference FormulasChapter 20.3 - Double-angle FormulasChapter 20.4 - Half-angle FormulasChapter 20.5 - Solving Trigonometric EquationsChapter 20.6 - The Inverse Trigonometric FunctionsChapter 21 - Plane Analytic GeometryChapter 21.1 - Basic DefinitionsChapter 21.2 - The Straight LineChapter 21.3 - The CircleChapter 21.4 - The ParabolaChapter 21.5 - The EllipseChapter 21.6 - The HyperbolaChapter 21.7 - Translation Of AxesChapter 21.8 - The Second-degree EquationChapter 21.9 - Rotation Of AxesChapter 21.10 - Polar CoordinatesChapter 21.11 - Curves In Polar CoordinatesChapter 22 - Introduction To StatisticsChapter 22.1 - Graphical Displays Of DataChapter 22.2 - Measures Of Central TendencyChapter 22.3 - Standard DeviationChapter 22.4 - Normal DistributionChapter 22.5 - Statistical Process ControlChapter 22.6 - Linear RegressionChapter 22.7 - Nonlinear RegressionChapter 23 - The DerivativeChapter 23.1 - LimitsChapter 23.2 - The Slope Of A Tangent To A CurveChapter 23.3 - The DerivativeChapter 23.4 - The Derivative As An Instantaneous Rate Of ChangeChapter 23.5 - Derivatives Of PolynomialsChapter 23.6 - Derivatives Of Products And Quotients Of FunctionsChapter 23.7 - The Derivative Of A Power Of A FunctionChapter 23.8 - Differentiation Of Implicit FunctionChapter 23.9 - Higher DerivativesChapter 24 - Applications Of The DerivativeChapter 24.1 - Tangents And NormalsChapter 24.2 - Newton's Method For Solving EquationsChapter 24.3 - Curvilinear MotionChapter 24.4 - Related RatesChapter 24.5 - Using Derivatives In Curve SketchingChapter 24.6 - More On Curve SketchingChapter 24.7 - Applied Maximum And Minimum ProblemsChapter 24.8 - Differentials And Linear ApproximationsChapter 25 - IntegrationChapter 25.1 - AntiderivativesChapter 25.2 - The Definite IntegralChapter 25.3 - The Area Under A CurveChapter 25.4 - The Definite IntegralChapter 25.5 - Numerical Integration: The Trapezoidal RuleChapter 25.6 - Simpson's RuleChapter 26 - Applications Of IntegrationChapter 26.1 - Applications Of The Definite IntegrationChapter 26.2 - Areas By IntegrationChapter 26.3 - Volumes By IntegrationChapter 26.4 - CentroidsChapter 26.5 - Moments Of InertiaChapter 26.6 - Other ApplicationsChapter 27 - Differentiation Of Transcendental FunctionsChapter 27.1 - Derivative Of The Sine And Cosine FunctionsChapter 27.2 - Derivatives Of The Other Trigonometric FunctionsChapter 27.3 - Derivatives Of The Inverse Trigonometric FunctionsChapter 27.4 - ApplicationsChapter 27.5 - Derivative Of The Logarithmic FunctionChapter 27.6 - Derivative Of The Exponential FunctionChapter 27.7 - L'hospital's RuleChapter 27.8 - ApplicationChapter 28 - Methods Of IntegrationChapter 28.1 - The Power Rule For IntegrationChapter 28.2 - The Basic Logarithmic FormChapter 28.3 - The Exponential FormChapter 28.4 - Basic Trigonometric FormsChapter 28.5 - Other Trigonometric FormsChapter 28.6 - Inverse Trigonometric FormsChapter 28.7 - Integration By PartsChapter 28.8 - Integration By Trigonometric SubstitutionChapter 28.9 - Integration By Partial Fractions: Nonrepeated Linear FractionsChapter 28.10 - Integration By Partial Fractions: Other CasesChapter 28.11 - Integration By Use Of TablesChapter 29 - Partial Derivatives And Double IntegralsChapter 29.1 - Functions Of Two VariablesChapter 29.2 - Curves And Surfaces In Three DimensionsChapter 29.3 - Partial DerivativesChapter 29.4 - Double IntegralsChapter 30 - Expansion Of Functions In SeriesChapter 30.1 - Infinite SeriesChapter 30.2 - Maclaurin SeriesChapter 30.3 - Operations With SeriesChapter 30.4 - Computations By Use Of Series ExpansionsChapter 30.5 - Taylor SeriesChapter 30.6 - Introduction To Fourier SeriesChapter 30.7 - More About Fourier SeriesChapter 31 - Differential EquationsChapter 31.1 - Solutions Of Differential EquationsChapter 31.2 - Separation Of VariablesChapter 31.3 - Integrating CombinationsChapter 31.4 - The Linear Differential Equation Of The First OrderChapter 31.5 - Numerical Solutions Of First-order EquationsChapter 31.6 - Elementary ApplicationsChapter 31.7 - Higher-order Homogeneous EquationsChapter 31.8 - Auxillary Equation With Repeated Or Complex RootsChapter 31.9 - Solutions Of Nonhomogeneous EquationsChapter 31.10 - Applications Of Higher-order EquationsChapter 31.11 - Laplace TransformsChapter 31.12 - Solving Differential Equations By Laplace Transforms
Sample Solutions for this Textbook
We offer sample solutions for Basic Technical Mathematics homework problems. See examples below:
The given statement is “The absolute value of any real number is positive”. The distance between the...From the given figure it is observed that, the angle ∠AOC and ∠COB makes a straight line. That is,...Calculation: The given statement is f(−x)=−f(x) for any function f(x)”. Consider the function...Definition: Third quadrant angle: “An angle is called third quadrant angle, if the angle lies in...Definition used: The solution of the linear equation ax+by=c is a pair of numbers, one for each...Expand the expression (2a−3)2 as, (2a−3)2=(2a)2−2(2a)(3)+(3)2 (∵(a−b)2=a2−2ab+b2)=4a2−12a+9 Thus,...Given: The given statement is “The solution of the equation x2−2x=0 is x=2”. Calculation: Consider...It is a known fact that all trigonometric ratios are positive in the first quadrant (0° to 90°). The...A vector should have magnitude and direction. Let A and B are two vectors of magnitudes A and B...
The given function is, y=2cosx and the point is (π,−2). Substitute x=π and y=−2 in y=2cosx....Rule used: The exponent rule: a0=1 where a≠0. Calculation: Given that, the equation is 2x0=1....Result used: The imaginary unit −1 is denoted by the symbol j. In other words, j=−1 and j2=−1....Definition used: The exponential function is defined as y=bx, where b>0,b≠1 and x is any real...The given statement is, “To get the calculator display of the equation 2x2+y2=4, let y1=4−2x2.” Note...Procedure used: Procedure for Synthetic Division: “1. Write the coefficients of f(x). Be certain...Check the matrix operation as follows: 2[3−102]=[6−202][6−204]≠[6−202]LHS≠RHS Hence,...Consider the inequality 1<x<−3. The given inequality 1<x<−3 can be written as 1<x and...The ratio of 25 cm to 50 mm is computed as, 25 cm50 mm=250 mm50 mm=5 That is, the ratio of 25 cm to...Definition used: n terms: The nth term of the arithmetic sequence is given by an=a1+(n−1)d, where an...Formula used: The Basic Trigonometric Identity: tanθ=sinθcosθ. Calculation: The given identity is...Formula used: The formula for distance between any two points d=(x2−x1)2−(y2−y1)2. Calculation: Find...Definition used: The relative frequency of a given data is found by dividing the frequency by the...Formula used: The limit of a function f(x) is that value of the limit of the function approaches as...Differentiate y with respect to the x. y=ddx(3x2−5)dydx=3(2x)−5=6x−5 Slope of tangent of the curve...Given that the equation is ∫(3x2+1)5dx=16(3x2+1)6+C. Evaluate the left hand side of the given...Consider the give statement. Let the initial velocity of an object be v0. Since the horizontal...Formula used: The derivative of sinu is d(sinu)dx=cosududx. Calculation: Evaluate the derivative of...Formula used: Log rule for integration: ∫duu=ln|u|+C Calculation: The given integral is ∫dx1+2x....It is given that if the function is f(x,y)=2x2y−y22xy, then f(y2,x)=2xy4−x22x2y . Replace x=y2 and...Result used: Let ∑n=0∞a1rn be a geometric series of terms, the partial sums Sn represents the sum...Definition used: “A solution of a differential equation is a relation between the variables that...
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