Homework 1-solutions - saliyev (is4663) Homework 1 knopf...

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Unformatted text preview: saliyev (is4663) Homework 1 knopf (55420) 1 This print-out should have 20 questions. Multiple-choice 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.

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Homework 1-solutions - saliyev (is4663) Homework 1 knopf...

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