Rational Expressions and Functions Chapter 8 Rational Expressions and Functions

Applications of Rational Expressions 8.5 Applications of Rational Expressions

8.5 Applications of Rational Expressions Objectives Find the value of an unknown variable in a formula. Solve a formula for a specified variable. Solve applications using proportions. Solve applications about distance, rate, and time. Solve applications about work rates. Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Find the Value of an Unknown Variable in a Formula Current Total resistance In electronics, the formula for calculating the total resistance r of parallel resistors r1 and r2 is given by the formula Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Find the Value of an Unknown Variable in a Formula Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Solve a Formula for a Specified Variable To solve for a variable means to isolate that variable on one side of the equal sign. Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Solve a Formula for a Specified Variable Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Solve Applications Using Proportions Ratios enable us to compare numerical quantities. A certain chainsaw requires that the gasoline be mixed with oil in the ratio of 32 to 1. In the stock market, winning stocks might outnumber losing stocks in the ratio of 7 to 3. The ratio of a to b may be written in any of the following ways: Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Solve Applications Using Proportions A proportion is a statement that two ratios are equal. Examples of proportions: Proportions are a useful and important type of rational equation. Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Solve Applications Using Proportions A toy model indicates on the box that 1 inch on the model is equivalent to 18 inches on the actual automobile. How long will the model be if the actual automobile is 15.75 feet long? 1 inch : 18 inches x Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Solve Applications Using Proportions Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Solve a Proportion Problem Involving Rates Alicia spent 5 hours studying for her last accounting exam and got 60% on the exam. She has already studied 2 hours for her upcoming second exam and would like to get 90% on that exam. If we assume that Alicia continues to increase her score at the same rate as before, how much more should she study to get 90%? Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Solve a Proportion Problem Involving Rates Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Applications Involving Distance, Rate, and Time The current of a river is 3 miles/hour. It takes a motorboat a total of 3 hours to travel 12 miles upstream and return 12 miles downstream. What is the speed of the boat in still water? Solution Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Applications Involving Distance, Rate, and Time Total time is 3 hours. Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Applications Involving Distance, Rate, and Time Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Applications Involving Distance, Rate, and Time Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Applications About Work Rates Work problems are closely related to time, rate, and distance problems. Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Applications About Work Rates An inlet pipe can fill a backyard pool in 10 hours, while the drain can empty it in 12 hours. If both the inlet pipe and the drain are open, how long will it take to fill the pool? 10 hours to fill pool 12 hours to empty pool Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Applications About Work Rates Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Applications About Work Rates Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.5 Applications of Rational Expressions Applications About Work Rates Copyright © 2010 Pearson Education, Inc. All rights reserved.