# HW - le(chl528 – HW01 – Gilbert –(57195 1 This...

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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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## This note was uploaded on 02/28/2010 for the course M 52470 taught by Professor Radin during the Spring '10 term at University of Texas.

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HW - le(chl528 – HW01 – Gilbert –(57195 1 This...

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