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Lesson 12-1

Lesson 12-1. Inverse Variation. Objectives. Graph inverse variations Solve problems involving inverse variations. Vocabulary. xxxxx –. Four Step Problem Solving Plan. Step 1: Explore the Problem Identify what information is given (the facts)

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Lesson 12-1

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  1. Lesson 12-1 Inverse Variation

  2. Objectives • Graph inverse variations • Solve problems involving inverse variations

  3. Vocabulary • xxxxx –

  4. Four Step Problem Solving Plan • Step 1: Explore the Problem • Identify what information is given (the facts) • Identify what you are asked to find (the question) • Step 2: Plan the Solution • Find an equation the represents the problem • Let a variable represent what you are looking for • Step 3: Solve the Problem • Plug into your equation and solve for the variable • Step 4: Examine the Solution • Does your answer make sense? • Does it fit the facts in the problem?

  5. Solve for Manufacturing The owner of Superfast Computer Company has calculated that the time t in hours that it takes to build a particular model of computer varies inversely with the number of people p working on the computer. The equation can be used to represent the people building a computer. Complete the table and draw a graph of the relation. Original equation Replace p with 2. Divide each side by 2. Simplify. Example 1

  6. Example 1 cont Solve the equation for the other values of p. Answer: 6 3 2 1.5 1.2 1 Answer: Graph the ordered pairs: (2, 6), (4, 3), (6, 2), (8, 1.5), (10, 1.2), and (12, 1). As the number of people p increases, the time t it takes to build a computer decreases.

  7. Graph an inverse variation in which y varies inversely as x and Inverse variation equation The constant of variation is 4. Example 2 Solve for k. Choose values for x and y whose product is 4.

  8. If y varies inversely as x andfind x when Product rule for inverse variations Divide each side by 15. Simplify. Example 3 Method 1 Use the product rule.

  9. Proportion rule for inverse variations Cross multiply. Divide each side by 15. Answer: Both methods show that Example 3 cont Method 2 Use a proportion.

  10. If y varies inversely as x and find y when Product rule for inverse variations Divide each side by 4. Simplify. Answer: Example 4 Use the product rule.

  11. Example 5 Physical Science When two objects are balanced on a lever, their distances from the fulcrum are inversely proportional to their weights. How far should a 2-kilogram weight be from the fulcrum if a 6-kilogram weight is 3.2 meters from the fulcrum?

  12. Original equation Divide each side by 2. Simplify. Example 5 cont Answer: The 2-kilogram weight should be 9.6 meters from the fulcrum.

  13. Summary & Homework • Summary: • The product rule for inverse variations states that if (x1, y1) and (x2, y2) are solutions of an inverse variation, then x1y1 = k and x2y2 = k • You can use proportions to solve problems involving inverse variations • Homework: • pg x1 y2 ---- = ----- x2 y1

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