1. Objectives Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Additional Application Problem Solving 1. Solve polynomial problems involving perimeter, area, and volume. 2. Solve surface area problems. 3. Solve problems involving a falling object. 4. Solve net-profit problems. 3.7

2. 3.7 - 2 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 1 Solve polynomial problems involving perimeter, area, and volume.

3. 3.7 - 3 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 1 Write an expression in simplest form for the perimeter of the triangle. Find the perimeter if x is 7 feet. 2x + 5 x

4. 3.7 - 4 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Connection Simplifying an expression makes it much easier to evaluate. If we didn’t simplify x + 2x + 5 + 2x + 5 and instead replaced all the x’s with 7, we’d still get 45, but it is much easier to use 5x + 10. Evaluating the un- simplified expression. Evaluating the simplified expression.

5. 3.7 - 5 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 2 Solve surface area problems.

6. 3.7 - 6 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definition Surface area: The total number of square units that completely cover the outer shell of an object. To develop a formula for the surface area of a box, we will cut and unfold a box to see all its surfaces.

7. 3.7 - 7 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley front back top bottom left side right side front right side bottom top left side h back l w w w w l l w l h Surface area = top + bottom + front + back + left side + right side of box area area area area area area SA = lw + lw + lh + lh + wh + wh

8. 3.7 - 8 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley front back top bottom left side right side front right side bottom top left side h back l w w w w l l w l h We can simplify the polynomial that describes the surface area of a box by combining like terms SA = lw + lw + lh + lh + wh + wh SA = 2lw + 2lh + 2wh

9. 3.7 - 9 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley front back top bottom left side right side front right side bottom top left side h back l w w w w l l w l h We could also factor out a common factor, 2. SA = 2lw + 2lh + 2wh SA = 2(lw + lh + wh)

10. 3.7 - 10 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 2 A company produces metal boxes that are 2 feet long by 3 feet wide by 1 foot high. How many square feet of metal are needed to produce one box?

11. 3.7 - 11 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 3 Solve problems involving a falling object.

12. 3.7 - 12 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley The polynomial – 16t 2 + h 0 describes the height in feet of a falling object at any time during the fall. The variable h 0 represents the initial height of the object on feet from the ground. The variable t represents the number of seconds after that object is dropped from that initial height. If we choose h to represent the height of the object after falling for t seconds, we can write the following formula.

13. 3.7 - 13 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 3 A skydiver jumps from a plane at an altitude of 10,000 feet and deploys her parachute after 20 seconds of free fall. What was her altitude upon deploying the parachute?

14. 3.7 - 14 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 4 Solve net profit problems.

15. 3.7 - 15 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley In Section 2.3 we developed the formula for net profit or loss given revenue and cost.

16. 3.7 - 16 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 4 The expression 7b + 9d + 1265 describes the revenue for a toy manufacturer, where b represents the number of toy bears sold and d represents the number of toy dogs sold. The expression 8b + 3d + 742 describes the cost of producing the toy bears and toy dogs. a. Write an expression in simplest form for the net.

17. 3.7 - 17 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 4 The expression 7b + 9d + 1265 describes the revenue for a toy manufacturer, where b represents the number of toy bears sold and d represents the number of toy dogs sold. The expression 8b + 3d + 742 describes the cost of producing the toy bears and toy dogs. b. In one month, the company sold 2345 bears and 3687 dogs. Find the net profit or loss