Math book 3rd Edition Front cover.pdf -- Mathematics THIRD Edition Front matter.pdf -- Mathematics -- for Business, Science, and Technology -- Third Edition -- With MATLAB®and Excel®Computations -- Steven T. Karris -- Math Book Preface.pdf -- Math book TOC All Chapters.pdf -- Mathematics THIRD Edition Chapter 01.pdf -- Chapter 1 -- Elementary Algebra -- 1.1 Introduction -- 1.2 Algebraic Equations -- 1.3 Laws of Exponents -- 1.4 Laws of Logarithms -- 1.5 Quadratic Equations -- 1.6 Cubic and Higher Degree Equations -- 1.7 Measures of Central Tendency -- 1.8 Interpolation and Extrapolation -- 1.9 Infinite Sequences and Series -- 1.10 Arithmetic Series -- 1.11 Geometric Series -- 1.12 Harmonic Series -- 1.13 Proportions -- 1.14 Summary -- 1.15 Exercises -- 1.16 Solutions to End-of-Chapter Exercises -- Mathematics THIRD Edition Chapter 02.pdf -- Chapter 2 -- Intermediate Algebra -- his chapter is a continuation of Chapter 1. It is intended for readers who need the knowl edge for more advanced topics in mathematics. It serves as a prerequisite for probability and statistics. Readers with a strong mathematical background ... -- 2.1 Systems of Two Equations -- Quite often, we are faced with problems that seem impossible to solve because they involve two or more unknowns. However, a solution can be found if we write two or more linear independent equations with the same number of unknowns, and solve... -- Example 2.1 -- Jeff Simpson plans to start his own business, manufacturing and selling bicycles. He wants to com pute the break-even point -- this is defined as the point where the revenues are equal to costs. In other words, it is the point where Jeff neithe...

Jeff estimates that his fixed costs (rent, electricity, gas, water, telephone, insurance etc.), would be around per month. Other costs such as material, production and payroll are referred to as variable costs and will increase linearly (in a... -- (2.1) -- Let us plot cost (y-axis), versus number of bicycles sold (x-axis) as shown in Figure 2.1. -- Figure 2.1. Total cost versus bicycles sold. -- In Figure 2.1, the x-axis is the abscissa and the y-axis is the ordinate. Together, these axes consti tute a Cartesian coordinate system -- it is also mentioned in Appendix A. The straight line drawn from point to point , is a graphical presen... -- In general, a straight line is represented by the equation -- (2.2) -- where is the slope, is the abscissa, is the ordinate, and is the y-intercept of the straight line, that is, the point where the straight line crosses the y-axis. -- As we indicated in Chapter 1, the slope is the rise in the vertical (y-axis) direction over the run in the abscissa (x-axis) direction. We recall from Chapter 1 that the slope is defined as -- (2.3) -- In Figure 2.1, , , and . Therefore, the slope is -- and, by inspection, the y-intercept is 1000. Then, in accordance with (2.2), the equation of the line that represents the total costs is -- (2.4) -- It is customary, and convenient, to show the unknowns of an equation on the left side and the known values on the right side. Then, (2.4) is written as -- (2.5) -- This equation has two unknowns and and thus, no unique solution exists -- that is, we can find an infinite number of and combinations that will satisfy this equation. We need a second equation, and we will find it by making use of additional fa...

Jeff has determined that if the sells bicycles at each, he will generate a revenue of . This fact can be represented by another straight line which is added to the previous figure. It is shown in Figure 2.2. -- The new line starts at because there will be no revenue if no bicycles are sold. It ends at which represents the condition that Jeff will generate when bicycles are sold. -- The intersection of the two lines shown as a small circle, establishes the break-even point and this is what Jeff is looking for. The projection of the break-even point on the x-axis, shown as a broken line, indicates that approximately bicy... -- We will now proceed to find the so-called analytical solution. This solution will produce exact val ues. -- Figure 2.2. Graph showing the intersection of two straight lines. -- As stated above, we need a second equation. This is obtained from the straight line in Figure 2.2 which represents the revenue. To obtain the equation of this line, we start with the equation of (2.2) which is repeated here for convenience. -- (2.6) -- The slope m of the revenue line is -- (2.7) -- and, by inspection, , that is, the y-intercept, is . Therefore, the equation that describes the reve nue line is -- (2.8) -- By grouping equations (2.5) and (2.8), we get the system of equations -- (2.9) -- Now, we must solve the equations of (2.9) simultaneously. This means that we must find unique values for and , so that both equations of (2.9) will be satisfied at the same time. An easy way to solve these equations is by substitution of the ... -- (2.10) -- or -- or -- (2.11) -- To find the unknown , we substitute (2.11) into either the first, or the second equation of (2.9). Thus, by substitution into the second equation, we get -- (2.12) -- Therefore, the exact solutions for and are -- (2.13).

Since no further substitutions are needed, we simplify the values of (2.13) by division and we get and . Of course, bicycles must be expressed as whole numbers and therefore, the break-even point for Jeff's business is bicycles which, when so... -- We recall that for the break-even point, the graphical solution produced approximate values of bicycles which would generate a revenue of . Although the graphical solution is not as accurate as the analytical solution, it nevertheless provide... -- Note 2.1 -- The system of equations of (2.9) was solved by the so-called substitution method, also known as Gauss's elimination method. In Section 2.3, we will discuss this method in more detail, and two additional methods, the solution by matrix inversi... -- 2.2 Systems of Three Equations -- Systems of three or more equations also appear in practical applications. We will now consider another example consisting of three equations with three unknowns. It is imperative to remember that we must have the same number of equations as t... -- Example 2.2 -- In an automobile dealership, the most popular passenger cars are Brand A, B and C. Because buy ers normally bargain for the best price, the sales price for each brand is not the same. Table 2.1 shows the sales and revenues for a 3-month period. -- TABLE 2.1 Sales and Revenues for Example 2.2 -- 1 -- 25 -- 60 -- 50 -- 2,756,000 -- 2 -- 30 -- 40 -- 60 -- 2,695,000 -- 3 -- 45 -- 53 -- 58 -- 3,124,000 -- Compute the average sales price for each of these brands of cars. -- Solution: -- In this example, the unknowns are the average sales prices for the three brands of automobiles. Let these be denoted as for Brand A, for Brand B, and for Brand C. Then, the sales for each of the three month period can be represented by the fo... -- (2.14).

The next task is to solve these equations simultaneously, that is, find the values of the unknowns , , and at the same time. In the next section, we will discuss matrix theory and methods for solving systems of equations of this type. We digr... -- 2.3 Matrices and Simultaneous Solution of Equations -- A matrix is a rectangular array of numbers such as those shown below. -- In general form, a matrix is denoted as -- (2.15) -- The numbers are the elements of the matrix where the index indicates the row and indi cates the column in which each element is positioned. Thus, represents the element posi tioned in the fourth row and third column. -- A matrix of rows and columns is said to be of order matrix. -- If , the matrix is said to be a square matrix of order (or ). Thus, if a matrix has five rows and five columns, it is said to be a square matrix of order 5. -- In a square matrix, the elements are called the diagonal elements. Alternately, we say that the elements are located on the main diagonal. -- A matrix in which every element is zero, is called a zero matrix. -- Two matrices and are said to be equal, that is, , if, and only if for and . -- Two matrices are said to be conformable for addition (subtraction) if they are of the same order, that is, both matrices must have the same number of rows and columns. -- If and are conformable for addition (subtraction), their sum (difference) will be another matrix C with the same order as A and B, where each element of C represents the sum (difference) of the corresponding elements of A and B, that is, -- Example 2.3 -- Compute and given that -- and -- Solution: -- and -- If is any scalar (a positive or negative number) and not [] which is a matrix, then multi plication of a matrix by the scalar is the multiplication of every element of by . -- Example 2.4 -- Multiply the matrix -- by -- Solution:.

Two matrices and are said to be conformable for multiplication in that order, only when the number of columns of matrix is equal to the number of rows of matrix . The product , which is not the same as the product , is conformable for multipl...