11 a special window in the shape of a rectangle with

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Unformatted text preview: 11. A special window in the shape of a rectangle with semicircles at each end is to be constructed so that the outside dimensions are 100 feet in length. Find the dimensions of the rectangle that maximizes its area. Math 10 – Precalculus RCC – Norco Fall 2009 Jason Rey 12. Beth has 3,000 feet of fencing available to enclose a rectangular field. a. Express the area A of the rectangle as a function of x, where x is the length of the rectangle. b. What is the domain of A? c. For what value of x is the area largest? d. What is the maximum area? 13. The price p (in dollars) and the quantity x sold for a certain product obey the demand equation g G ¡ ¢ £ ¤ ¥ uUU ¦U § ¤ § ¨UU© . a. Express the revenue R as a function of x. b. What is the revenue if 100 units are sold? c. What quantity x maximizes the revenue? What is the maximum revenue? d. What price should the company charge to maximize revenue? 14. Determine the end behavior of the polynomial function a. ( ) 7 6 2 3 +- = x x x g b. ( ) ( ) ( ) 7 4 2 3 2-- = x x x x p c. ( ) ( )( ) 7 2 5 3--- = x x x q 15. Find all zeros of the polynomial function, then create a sign chart and use it to sketch the graph of: a. ( ) 4 4 5 3 2 3-- + = x x x x p b. ( ) x x x x x g 30 40 25 5 2 3 4 +- +- = 16. Sketch the graph of the rational function: a. ( ) 12 4 2 2 2- + + = x x x x x R b. ( ) 16 6 4 2 2 3- + +- = x x x x x R c. ( ) 16 4 3 2-- = x x x f d. ( ) 2 3 6 2 2 + +-- = x x x x x g 17. Solve the inequality: a. 1 3 > +- x x b. 2 4 x x ≥ c. 1 3 2 1 + ≤ + x x...
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