1. Copyright © 2011 Pearson Education, Inc. Slide 1.6-1 1.6 Applications of Linear Functions Solving Application Problems 1.Read the problem and make sure you understand it. Assign a variable to what you are being asked to find. If necessary, write other quantities in terms of this variable. 2.Write an equation that relates the quantities described in the problem. You may need to sketch a diagram and refer to known formulas. 3.Solve the equation and determine the solution. 4.Look back and check your solution. Does it seem reasonable?

2. Copyright © 2011 Pearson Education, Inc. Slide 1.6-2 1.6 Dimensions of a Television Screen The new generation of televisions has a 16:9 aspect ratio. The length of its rectangular screen is times its width. If the perimeter of the screen is 136 inches, find the length and width of the screen. Analytic Solution

3. Copyright © 2011 Pearson Education, Inc. Slide 1.6-3 1.6 Dimensions of a Television Screen Graphical Solution Notice that the point of intersection is the point (24.48,136). The x-coordinate supports our previous result from the analytic solution. 0 50 200

4. Copyright © 2011 Pearson Education, Inc. Slide 1.6-4 1.6 A Mixture-of-Concentrations Problem How much pure alcohol should be added to 20 liters of 40% alcohol to increase the concentration to 50% alcohol? –Let x represent the number of liters of pure alcohol to be added 20.40 x 1.0 20 + x.50 Liters of Liquid Alcohol Concentration

5. Copyright © 2011 Pearson Education, Inc. Slide 1.6-5 1.6 Break-Even Analysis Peripheral Visions, Inc., produces high-definition DVDs of live concerts. The company places an ad in a trade newsletter. The cost of the ad is $100. Each DVD costs $20 to produce, and the company charges $24 per DVD. a)Express the cost C as a function of x, the number of DVDs produced. b)Express the revenue R as a function of x, the number of DVDs sold. c)For what value of x does revenue equal cost?

6. Copyright © 2011 Pearson Education, Inc. Slide 1.6-6 1.6 Break-Even Analysis d)Graph in an appropriate window to support your answer. e)Use a table to support your answer. 0 095 1200

7. Copyright © 2011 Pearson Education, Inc. Slide 1.6-7 1.6 Direct Variation A number y varies directly with x if there is a nonzero number k such that The number k is called the constant of variation

8. Copyright © 2011 Pearson Education, Inc. Slide 1.6-8 1.6 Direct Variation Example –Hooke’s Law states that the distance (y) a spring stretches varies directly with the force (x) applied. If a force of 15 lbs stretches a spring 8 inches, how much will a force of 35 lbs stretch the spring?

9. Copyright © 2011 Pearson Education, Inc. Slide 1.6-9 1.6 Using Similar Triangles A grain bin in the shape of an inverted cone has height 11 feet and radius 3.5 feet. If the grain is 7 feet high in the bin, calculate the volume of the grain. 11 ft. 3.5 ft. 11 ft.

10. Copyright © 2011 Pearson Education, Inc. Slide 1.6-10 1.6 Solving a Formula for a Specified Variable A trapezoid has area 169 square inches, height 13 inches, and base 19 inches. Find the length of the other base by solving the formula for and substituting.

11. Copyright © 2011 Pearson Education, Inc. Slide 1.6-11 1.6 Solving a Formula for a Specified Variable Solve each formula for the specified variable.