By Soo T. Tan
Combining the easiest of conventional insurance with smooth instruments, market-leading Applied Calculus for the Managerial, existence, and Social Sciences: a short Approach, 8th version, applies math on your international. It supplies simply the perfect stability of functions, pedagogy, and expertise that will help you achieve the direction. instructing via program, the textual content is full of real-life examples that encourage and enlighten you. Its intuitive procedure introduces summary ideas via examples drawn from universal reviews to that you would be able to relate. it is usually perception from execs approximately how they combine math into their daily operations. a number of workouts, together with Diagnostic checks, make sure you have a superb figuring out of textual content techniques ahead of advancing to the subsequent topic—or examination. an exhilarating array of supplements—Enhanced WebAssign, resolution movies, own Tutor—equips you with vast studying help that is helping maximize your learn efforts and increase your grade. putting off the apprehension many scholars suppose after they start this direction, Applied Calculus for the Managerial, lifestyles, and Social Sciences: a quick Approach, 8th variation, makes use of an obtainable presentation of strategies and techniques that makes it a great source for majors and non-majors alike.
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Additional info for Applied calculus for the managerial, life, and social sciences : a brief approach
3 Solutions to Self-Check Exercises 1. a. The points are plotted in the following figure: The distance between A and C is d1A, C2 ϭ 21Ϫ3 Ϫ 4 2 2 ϩ 3 1 Ϫ 1Ϫ22 4 2 y ϭ 21Ϫ72 2 ϩ 32 ϭ 249 ϩ 9 ϭ 258 5 B(2, 3) c. We will show that [d(A, C)]2 ϭ [d(A, B)]2 ϩ [d(B, C)]2 C(– 3, 1) x –5 5 A(4, –2) –5 From part (b), we see that [d(A, B)]2 ϭ 29, [d(B, C)]2 ϭ 29, and [d(A, C)]2 ϭ 58, and the desired result follows. 2. The distance between city A and city B is d1A, B2 ϭ 22002 ϩ 502 Ϸ 206 or 206 mi. The distance between city B and city C is b.
75. 3 THE CARTESIAN COORDINATE SYSTEM Explore & Discuss In the Cartesian coordinate system, the two axes are perpendicular to each other. Consider a coordinate system in which the x- and y-axes are not collinear and are not perpendicular to each other (see the accompanying figure). y x O 1. Describe how a point is represented in this coordinate system by an ordered pair (x, y) of real numbers. Conversely, show how an ordered pair (x, y) of real numbers uniquely determines a point in the plane. 2.
97. 4x Ϫ 12x Ϫ 6x 5 4 3 131. 1 2 x Ϫxϩ1ϭ0 4 132. 2 PRECALCULUS REVIEW II In Exercises 133–138, solve the equation by using the quadratic formula. 133. 4x2 ϩ 5x Ϫ 6 ϭ 0 134. 3x2 Ϫ 4x ϩ 1 ϭ 0 135. 8x2 Ϫ 8x Ϫ 3 ϭ 0 136. x2 Ϫ 6x ϩ 6 ϭ 0 137. 2x2 ϩ 4x Ϫ 3 ϭ 0 138. 2x2 ϩ 7x Ϫ 15 ϭ 0 15 In Exercises 140–142, determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. 139. 5, where y is the number of families with an income of x or more dollars.