Solutions HW 1

Solutions HW 1 - mao(tm23477 HW01 gualdani(57180 This...

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mao (tm23477) – HW01 – gualdani – (57180) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. Welcome to Quest 001 10.0 points ±ind the solution set oF the inequality x 2 < 3 x + 10 , expressing your answer in interval notation. 1. ( −∞ , 5] 2. ( −∞ , 5) (2 , ) 3. ( 5 , 2) correct 4. (2 , ) 5. [ 5 , 2] Explanation: AFter Factoring we can rewrite the inequal- ity in the Form ( x + 5)( x 2) < 0 . Now the leFt hand side changes sign at its zeros, i.e. , at x = 5 , 2, and the sign chart −∞ 5 2 + + determines which sign it takes on a given interval. Consequently, the given inequality has solution set = ( 5 , 2) . 002 10.0 points A company manuFacturing computers has fxed costs $21000 per month and variable costs oF $800 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 = 40 2. break-even point = 50 3. break-even point = 60 4. break-even point = 20 5. break-even point = 30 correct Explanation: Let x be the number oF computers produced each month. Then the production costs are given by C ( x ) = 21000 + 800 x, while the revenue From selling these comput- ers is given by R ( x ) = 1500 x. ±or 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 21000 + 800 x = 1500 x. Solving For x we see that the break-even point = 30. 003 10.0 points A car purchased For $17000 has a resale value oF $3000 aFter 10 years. Assuming its resale value decreased linearly over these years, what was the resale value oF the car aFter 7 years? 1. $7400 2. $7000 3. $7100 4. $7300 5. $7200 correct
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mao (tm23477) – HW01 – gualdani – (57180) 2 Explanation: 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 $17000, so b = 17000. On the other hand, over 10 years the value decreases to $3000, so m = 3000 17000 10 = 1400 . Thus the resale value is given by y = 1400 x + 17000 . After 7 years, therefore, the resale value is 1400 · 7 + 17000 = $7200. 004 10.0 points Find the function g that is ±nally graphed after the following transformations are ap- plied in the order given to the graph of a function f : (1) re²ect about the x -axis; (2) shift down 3 units; (3) stretch vertically by a factor 8; (4) re²ect about the y -axis. 1. g ( x ) = 8 f ( x ) 24 2. g ( x ) = 24 8 f ( x ) 3. g ( x ) = 24 3 f ( x ) 4. g ( x ) = 24 8 f ( x ) correct 5. g ( x ) = 24 + 8 f ( x ) 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
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Solutions HW 1 - mao(tm23477 HW01 gualdani(57180 This...

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