HW - le (chl528) HW01 Gilbert (57195) 1 This print-out...

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Unformatted text preview: le (chl528) HW01 Gilbert (57195) 1 This print-out should have 22 questions. Multiple-choice 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. break-even point = 110 2. break-even point = 80 correct 3. break-even point = 70 4. break-even point = 90 5. break-even 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 break-even 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 x-axis; (2) shift down 3 units; (3) stretch vertically by a factor 8; (4) reflect about the y-axis. 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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HW - le (chl528) HW01 Gilbert (57195) 1 This print-out...

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