By Soo T. Tan

Renowned for accuracy, Soo Tan's utilized CALCULUS FOR THE MANAGERIAL, lifestyles, AND SOCIAL SCIENCES, 8th variation balances purposes, pedagogy, and know-how to supply scholars the context they should remain encouraged within the path and attracted to the cloth. available for majors and non-majors alike, the textual content makes use of an intuitive strategy that introduces summary strategies via examples drawn from universal, real-life reports to which scholars can relate. It additionally attracts purposes from readers' fields of curiosity. additionally, insightful Portfolios spotlight the careers of genuine humans and speak about how they contain math into their day-by-day operations. a variety of exercises--including new Diagnostic Tests--ensure scholars have a great figuring out of recommendations prior to advancing to the subsequent subject. Algebra evaluate notes, keyed to the overview bankruptcy Preliminaries, look the place scholars want them, after they desire them. Bringing robust assets to students' fingertips, the text's intriguing array of supplementations, together with more advantageous net Assign, equips scholars with huge studying help to assist them maximize their examine time.

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**Extra resources for Applied Calculus for the Managerial, Life, and Social Sciences (8th Edition)**

**Sample text**

Find an expression in terms of the time t (in hours) giving the distance between the two ships. b. Using the expression obtained in part (a), find the distance between the two ships 2 hr after leaving port. 2 1 B (400, 300) x (miles) A (0, 0) Q(x, 0) 1000 38. MINIMIZING SHIPPING COSTS Refer to the figure for Exer- cise 37. Suppose a fleet of 100 automobiles are to be shipped from an assembly plant in town A to town D. They may be shipped either by freight train along Route 1 at a cost of 22¢/mile per automobile or by truck along Route 2 at a cost of 21¢/mile per automobile.

2. a. What is the distance between P1(x1, y1) and P2(x2, y2)? b. When you use the distance formula, does it matter which point is labeled P1 and which point is labeled P2? Explain. 3 Exercises In Exercises 1–6, refer to the following figure and determine the coordinates of each point and the quadrant in which it is located. y 18. aϪ , b 5 3 2 2 19. 5) 20. 4) In Exercises 21–24, find the distance between the given points. D 3 A 21. (1, 3) and (4, 7) B 1 22. (1, 0) and (4, 4) x –5 –3 1 –1 3 5 7 25.

A y4 x6 Law 4 y 3/2 Ϫ2 y 13/22 1Ϫ22 yϪ3 x1/2 b ϭ ϭ ϭ x1/4 xϪ1/2 y3 x 11/42 1Ϫ22 Law 5 We can also use the laws of exponents to simplify expressions involving radicals, as illustrated in the next example. EXAMPLE 2 Simplify the expressions. ) 4 a. 216x y 4 8 b. 212m n # 23m5n 3 c. 3 2 Ϫ27x6 3 2 8y3 Solution 4 a. 216x4y8 ϭ 116x4y8 2 1/4 ϭ 161/4 # x4/4y8/4 ϭ 2xy2 b. 212m3n # 23m5n ϭ 236m8n2 ϭ 136m8n2 2 1/2 ϭ 361/2 # m8/2n2/2 ϭ 6m4n 3 1Ϫ27x6 2 1/3 Ϫ271/3x6/3 3x2 2 Ϫ27x6 c. ᎏ ϭ ϭ ϭ Ϫ 3 2y 18y3 2 1/3 81/3y3/3 28y3 If a radical appears in the numerator or denominator of an algebraic expression, we often try to simplify the expression by eliminating the radical from the numerator or denominator.