copyright © 2011 pearson education, inc. slide 1.6-1 1.6 applications of linear functions solving...

Copyright © 2011 Pearson Education, Inc. Slide 1.6-1

1.6 Applications of Linear Functions

Solving Application Problems1. 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?


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

169

Length916 x

Widthx

inches 52.43)48.24(9

16Length and inches 24.48Width

48.24950

136

2932

136

29

162136

22Perimeter

x

x

xx

x

WLP


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.

136 and 29

162

21

yxxy

xxy 29

162

1

136

2y

0 50

200


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

)20(50. 00.1 )20(40. xx

added. bemust alcohol pure of liters 4 Therefore, 4

20050

501000100800

)20(50100)20(40

x

x

xx

xx


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?

10020)(cost fixed producednumber cost variableCost

xxC

xxR 24)(

( ) ( )24 20 100

4 10025

When 25 DVDs are sold, the company will break even.

R x C xx xxx


1.6 Break-Even Analysis

d) Graph in an appropriate window to support your answer.

e) Use a table to support your answer.

xyxy 24 and 1002021

00 95

120010020

1 xyxy 24

2


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

kxy


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?

15

8158 kk

8

158 56

(35) 18.6 or aproximately 19 inches15 3

y x

y


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.

3.5 ft.

r

h 11 ft.

3.5 ft.

11 ft.

feet cubic 4.36)7()227.2(3

1

3

1

227.2)7(11

5.3 have we,7 with ,

11

5.3

22

hrV

rhh

r


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.

)(212

1 bbhA 1

b

12

21

21

21

2

2

)(2

)(21

bbhA

bbhA

bbhA

bbhA

inches 71913

)169(21

b


1.6 Solving a Formula for a Specified Variable

• Solve each formula for the specified variable.

Solve 2 2 for .P W L L

2 22 22

2

2

P W LP W LP W

L

PL W

532

99

325

932

5

C F

C F

F C

5Solve C 32 for .

9F F

copyright © 2011 pearson education, inc. slide 1.6-1 1.6 applications of linear functions solving...

Documents