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Unformatted text preview: saliyev (is4663) Homework 1 knopf (55420) 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. This assignment covers some review mate rial, as well as new material from Sections 2.1, 2.2, and 2.3. 001 (part 1 of 2) 10.0 points An open box is made from an 8 inch 12 inch rectangular piece of cardboard by cutting equal squares from the corners and turning up the sides as shown in the figure x x x x x x x x Determine the volume V of the box as a function of x . 1. V ( x ) = 96 x 40 x 2 + 4 x 3 correct 2. V ( x ) = 96 x 40 x 2 4 x 3 3. V ( x ) = 96 x + 40 x 2 + 4 x 3 4. V ( x ) = 192 x 40 x 2 + 4 x 3 5. V ( x ) = 96 x 40 x 2 + 2 x 3 Explanation: The length of one side of the base of the box is 8 2 x , while the length of the other side of the base is 12 2 x . Since the height of the box is x the volume will be V ( x ) = (length) (width) (height) = x (8 2 x )(12 2 x ) . Thus V ( x ) = 96 x 40 x 2 + 4 x 3 cu ins 002 (part 2 of 2) 10.0 points What is the domain of V for a box that makes physical sense? 1. domain = (0 , 4] 2. domain = (0 , 8) 3. domain = [0 , 4) 4. domain = (0 , 4) correct 5. domain = (0 , 5) Explanation: Since all the dimensions in the expression V ( x ) = 2 x (4 x )(12 2 x ) for the volume have to be positive for the box to make good physical sense, the domain of V is the solution set of the inequalities x > , 4 x > , 12 2 x > . Consequently, domain = (0 , 4) . 003 10.0 points United Express, an expensive nationwide package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each addi tional pound (or fraction thereof). If a customer would be billed $24 for ship ping a 4 pound package and $122 for shipping a 18 pound package, find the delivery cost of a 25 pound package. 1. delivery cost = $171 correct 2. delivery cost = $169 3. delivery cost = $165 4. delivery cost = $167 saliyev (is4663) Homework 1 knopf (55420) 2 5. delivery cost = $173 Explanation: Let w be the weight of a package. Then the price $ p for shipping this package is given by p = a ( w 1) + b where $ b is the base price for shipping a pack age weighing 1 pound or less and $ a is the shipping cost of each additional pound. Thus in the two cases described 24 = (4 1) a + b, 122 = (18 1) a + b. Solving this system of linear equations we see that a = $7 , b = $3 . Consequently, for a 25 pound package the delivery cost = $171 . 004 10.0 points If 1 2 3 1 2 3 1 2 3 is the graph of y = a  cos mx + c  , ( m > 0) , on [ 3 , 3], find the values of m and c ....
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This note was uploaded on 02/28/2011 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas at Austin.
 Spring '06
 McAdam
 Calculus

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