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2.8

2.8. Solving Equations in One Variable. Quick Review. Quick Review Solutions. What you’ll learn about. Solving Rational Equations Extraneous Solutions Applications … and why Applications involving rational functions as models often require that an equation involving

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2.8

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  1. 2.8 Solving Equations in One Variable

  2. Quick Review

  3. Quick Review Solutions

  4. What you’ll learn about • Solving Rational Equations • Extraneous Solutions • Applications … and why Applications involving rational functions as models often require that an equation involving fractions be solved.

  5. Example Solving by Clearing Fractions

  6. Example Solving by Clearing Fractions

  7. Solving a Rational Equation

  8. Solving a Rational Equation Solve Graphically The graph in Figure 2.56 suggests that the function has two zeros. We can use the graph to find that the zeros are about 0.268 and 3.732, agreeing with the values found algebraically.

  9. Extraneous Solutions When we multiply or divide an equation by an expression containing variables, the resulting equation may have solutions that are not solutions of the original equation. These are extraneous solutions. For this reason we must check each solution of the resulting equation in the original equation.

  10. Example Eliminating Extraneous Solutions

  11. Example Eliminating Extraneous Solutions

  12. Example Eliminating Extraneous Solutions

  13. Calculating Acid Mixtures How much pure acid must be added to 50 mL of a 35% acid solution to produce a mixture that is 75% acid?

  14. Calculating Acid Mixtures How much pure acid must be added to 50 mL of a 35% acid solution to produce a mixture that is 75% acid?

  15. Example Finding a Minimum Perimeter

  16. Example Finding a Minimum Perimeter

  17. Designing a Juice Can Stewart Cannery will package tomato juice in 2-liter cylindrical cans. Find the radius and height of the cans if the cans have a surface area of 1000 cm2. (1 liter = 1000 cm3) Model S =surface area of can in cm2 r = radius of can in centimeters h = height of can in centimeters

  18. Designing a Juice Can

  19. Designing a Juice Can

  20. pg 254: ,#1-35 odd

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