11 Pull It All Together

BIG idea Equivalence

Rational expressions can be represented in many ways. When a rational expression is simplified, the numerator and denominator have no common factors except 1.

Task 1

A cylinder with radius r and height 2r + 4 contains a cube with edge length r 2 , r square root of 2 , comma  as shown. What fraction of the cylinder's volume is taken up by the cube? Write your answer in simplified form.

BIG idea Functions

Rational functions have equations of the form f ( x ) = polynomial polynomial . f , open x close , equals . fraction polynomial , over polynomial end fraction . .  The graph of a rational function may have vertical and horizontal asymptotes.

Task 2

In a bike race, a rider covers a 5-mi flat stretch of road at a speed of s mi/h. She then doubles her speed down a hill 1 mi long. Finally, she reduces her downhill speed by 12 mi/h as she rides the last 3 mi of the race. What function gives the time t it takes the rider to finish the race in terms of s?

BIG idea Solving Equations and Inequalities

To isolate the variable in a rational equation, multiply each side by the LCD and then solve the resulting equation. Check for extraneous solutions.

Task 3

A restaurant has 45 tables. Each table seats 4 people. The manager has 4 employees to prepare the tables. The chart shows how fast each employee works. Use this information to answer the following questions.

1. In order to get the tables ready in the least amount of time, which two employees should the manager ask to fold napkins? Which two employees should the manager ask to set the tables?
2. If everyone starts working at the same time, how quickly can the employees get the tables ready for dinner? The first pair of employees to finish their job should help the other pair to finish the tables. Explain your answer.

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