Applications of Quadratic Equations

Transcription

1 33 Chapter 6 Quadratic Equations and Inequalities Section 6. Applications of Quadratic Equations. Verbal model: Selling price per doz eggs.6 Number eggs sold Number eggs purchased Selling price Cost per doz eggs 8 dozen Profit per doz eggs $. per dozen 3. Verbal model: Selling price per video Number videos sold Number videos purchased 8 8 Cost per video videos Selling price 8 $3 6 Profit per video 5. Verbal model: Perimeter l.75 l l.75l l.5l 3.5l l inches w.75 l 9 inches Verbal model: 9 A 8 square inches A 7. Verbal model:.5w w 5.5w w 5.5w w w 5.5w Verbal model: 5 P 7 feet P Perimeter

2 Section 6. Applications of Quadratic Equations Verbal model: Verbal model:. Verbal model: l 3 l l 3l 9 3 l 9 l 576 l inches w 3 l 8 inches Perimeter Verbal model: w 3 w w 3 w 5 w 6 w 5 w km l w 3 5 km w 8 Perimeter 8 P 5 8 square kilometers A 8 6 P 6 inches P 3. Verbal model: l l l l, l l, l l, l, l ±, l meters w l meters 5. Verbal model: inches inches Verbal model: Perimeter meters P 7. Verbal model: Height 8 Base inches 8 6 inches Height Base reject 6 9. Verbal model: 35 35,5 35,5 35,5 75 6,5 75 ± 75 6, 5 75 ± 565 5, 5 35, 5 ft 5 ft. or 5 ft 5 ft. 75 ± 75

3 33 Chapter 6 Quadratic Equations and Inequalities. Verbal model: Side Side Side 3 55 b 55 b 55 b 55 Verbal model: Height Height Base Base 6 Base b 3, , , , , ( Base 55 87, This has no real solution, so it would be impossible to have an area of 3,56 square feet. ) 3. Verbal model: Height Height height inches width 8 8 inches 5. A P r 7. A P r 9. A P r r.66 r.8 r.8 r or 8% r 8.9 r r.6 r.6 r 6% r r.555 r.59 r.59 r or.59%

4 Section 6. Applications of Quadratic Equations Verbal model: Cost per member Number of members $ Number of members Number going to game Verbal model: Investment per person; current group Investment per person; new group 6 Number in current group Number in new group 3 3 8, 8, 3 8, 6 3 8,, 8, 6 8, 8 8 8, 8, 3 8, ,, investors 35. Common Formula: a b c ± ± , 5.86 miles 8 ± 88 reject.35

5 336 Chapter 6 Quadratic Equations and Inequalities 37. (a) d 3 Keystrokes: Y 3 X,T, X,T, Approimate value of 3.55 when d. (b) GRAPH 75 ± 75 ± 96 6 ± 796 ± 99 7 ± meters Verbal model: Work done by Person Work done by Person One complete job Time to do job by Person Time to do job by Person 8 ± ± 6 8 ± 9. hours,. hours reject.

6 Section 6. Applications of Quadratic Equations 337. Verbal model: Rate Company Rate Company Rate together Time Company A 3 Time Company B ± 5 5 ± days ± h h 6t 5. 6t 6t t 9 t 3 seconds h h 6t 5 6t 6t 5 t t seconds 9.5 seconds 7. h 3 75t 6t 3 75t 6t 6t 75t 3 t 75 ± t t t 75 ± ± ± t.776,.7 seconds reject (a) (b) 336 6t 6t 6t 6t 336 t t t 7t 3 at 3 seconds and at 7 seconds 6t 6t 6tt t, after seconds.

7 338 Chapter 6 Quadratic Equations and Inequalities 5. Verbal model: Integer First integer n Second integer n n n n n n n ± 96 n 5 n 6 n ± 96 n Integer 96 ± 3 Product n 6 n 5 reject 53. Verbal model: Even integer First even integer n Second even integer n n n n n n n 56 n 8n 7 n 8 n n 56 n 8 n 6 reject n Even integer Product n 7 n 7 n n Verbal model: Odd integer Odd integer Product 57. Verbal model: First odd integer n Second odd integer n 3 n n 3 83 n 8n 8 n n n n n n 8n 3 83 n Original time n n n n 3 3 Speed Increased speed , 36, ±, New time ± 6 576, ± 76 36, 5 miles per hour

8 Section 6. Applications of Quadratic Equations Verbal model: Total Cost Wage Cost Fuel Cost Label: Time ± ,.67 v 6 mihr.39 or.3 ± v 65 mihr (a) a b A ab b a A a a (b) a A A A 7 7 A A 3 3 A (c) 3 a a (d) A a a a a 3 Keystrokes: a a 3 Y X,T, X,T, GRAPH a ± 3 a ± a., 7.9

9 3 Chapter 6 Quadratic Equations and Inequalities 63. Guidelines for solving word problems: (a) Write a verbal model that will describe what you need to know. (b) Assign labels to each part of the verbal model numbers to the known quantities and letters to the variable quantities. (c) Use the labels to write an algebraic model based on the verbal model. (d) Solve the resulting algebraic equation and check your solution. 65. Unit Analysis 9 dollars hours 8 dollars hour 67. An eample of a quadratic equation that has only one repeated solution is. Any equation of the form c, where c is a constant will have only one repeated solution. Section 6.5 Quadratic and Rational Inequalities ± Critical numbers, 5 Critical numbers: 9, 9 Critical numbers: 5, Critical numbers 3, 5 Critical number: 5. Negative:, Positive:, + Choose a test value from each interval., <, 5 5 > 3. Negative: 6, Positive:, Choose a test value from each interval., > 6, < 5. Positive:, Negative:, Positive:, + + Choose a test value from each interval., >, 6 <, 5 55 >