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Unformatted text preview: le (chl528) HW01 Gilbert (57195) 1 This printout should have 22 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the solution set of the inequality x 2 < 2 x + 8 , expressing your answer in interval notation. 1. (2 , ) 2. ( , 4) (2 , ) 3. ( , 4] 4. ( 4 , 2) correct 5. [ 4 , 2] Explanation: After factoring we can rewrite the inequal ity in the form ( x + 4)( x 2) < . Now the left hand side changes sign at its zeros, i.e. , at x = 4 , 2, and the sign chart 4 2 + + determines which sign it takes on a given interval. Consequently, the given inequality has solution set = ( 4 , 2) . 002 10.0 points A company manufacturing computers has fixed costs $48000 per month and variable costs of $900 per computer. How many computers must be manufac tured and sold each month for the company to break even if the selling price of a computer is $1500? 1. breakeven point = 110 2. breakeven point = 80 correct 3. breakeven point = 70 4. breakeven point = 90 5. breakeven point = 100 Explanation: Let x be the number of computers produced each month. Then the production costs are given by C ( x ) = 48000 + 900 x, while the revenue from selling these comput ers is given by R ( x ) = 1500 x. For the company to break even the cost of production should be equal to the revenue; i.e. , C ( x ) = R ( x ), in other words when 48000 + 900 x = 1500 x. Solving for x we see that the breakeven point = 80. 003 10.0 points A car purchased for $10800 has a resale value of $2000 after 10 years. Assuming its resale value decreased linearly over these years, what was the resale value of the car after 5 years? 1. $6400 correct 2. $6600 3. $6300 4. $6200 5. $6500 Explanation: le (chl528) HW01 Gilbert (57195) 2 If the resale value y decreases linearly over time, its value x years after purchase is given by y = mx + b . Initially, i.e. , at x = 0, the value of the car is $10800, so b = 10800. On the other hand, over 10 years the value decreases to $2000, so m = 2000 10800 10 = 880 . Thus the resale value is given by y = 880 x + 10800 . After 5 years, therefore, the resale value is 880 5 + 10800 = $6400. 004 10.0 points Find the function g that is finally graphed after the following transformations are ap plied in the order given to the graph of a function f : (1) reflect about the xaxis; (2) shift down 3 units; (3) stretch vertically by a factor 8; (4) reflect about the yaxis. 1. g ( x ) = 24 3 f ( x ) 2. g ( x ) = 8 f ( x ) 24 3. g ( x ) = 24 + 8 f ( x ) 4. g ( x ) = 24 8 f ( x ) 5. g ( x ) = 24 8 f ( x ) correct Explanation: Beginning with a function y = f ( x ), the four transformations change f ( x ) as follows: f ( x ) (1) f ( x ) (2) 3 f ( x ) (3) 8( 3 f ( x )) (4) 24 8 f ( x ) ....
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 Spring '10
 RAdin

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