Chapter Review 131 (c) What is the volume if a 10-inch square is cut out? (d) Graph V V x . ( ) = For what value of x is V largest? (e) What is the largest volume? 26. Challenge Problem Filling a Conical Tank Water is poured into a container in the shape of a right circular cone with radius 4 feet and height 16 feet. See the figure. Express the volume V of the water in the cone as a function of the height h of the water. 2 7. Challenge Problem Inventory Management A retailer buys 600 USB Flash Drives per year from a distributor. The retailer wants to determine how many drives to order, x, per shipment so that her inventory is exhausted just as the next shipment arrives. The processing fee is $15 per shipment, the yearly storage cost is x $1.60 , and each drive costs the retailer $4.85. (a) Express the total yearly cost C as a function of the number x of drives in each shipment. (b) Use a graphing utility to determine the minimum yearly cost and the number of drives per order that yields the minimum cost. (c) How much material is required for such a box with a base 2 feet by 2 feet? (d) Use a graphing utility to graph A A x . ( ) = For what value of x is A smallest? (e) What is the least amount of material needed? 25. Constructing an Open Box An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides. See the figure. 24 in. 24 in. x x x x x x x x (a) Express the volume V of the box as a function of the length x of the side of the square cut from each corner. (b) What is the volume if a 3-inch square is cut out? h 16 4 r Retain Your Knowledge Problems 28–37 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for subsequent sections, a final exam, or later courses such as calculus. 28. Solve: x2 3 5 2 − − = − 29. A 16-foot-long Ford Fusion wants to pass a 50-foot truck traveling at 55 mi/h. How fast must the car travel to completely pass the truck in 5 seconds? 30. Find the slope of the line containing the points 3, 2 ( ) − and 1, 6 . ( ) 31. Find the missing length x for the given pair of similar triangles. 10 14 4 x 32. Given y x x 1 = + and u x 1, = + express y in terms of u. 33. Write x x x 5 3 2/3 1/3 + + as a single quotient with only positive exponents. 34. Solve x3 2 4. − − ≥ 35. If the point 3, 2 ( ) − is on the graph of an equation that is symmetric about the origin, what other point must be on the graph? 36. Solve v t d E P 2.6 2 = for P. 37. Find the discriminant of the quadratic equation x x x 3 7 4 2. 2 − = − Chapter Review Library of Functions Constant function (p. 102) f x b ( ) = The graph is a horizontal line with y-intercept b. x y f(x) = b (0, b) Identity function (p. 102) f x x ( ) = The graph is a line with slope 1 and y-intercept 0. x y 3 3 –3 (1, 1) (–1, –1) (0, 0) Square function (p. 103) f x x2 ( ) = The graph is a parabola with intercept at 0, 0 ( ) x y 4 4 –4 (2, 4) (0, 0) (–2, 4) (1, 1) (–1, 1)
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