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Direct and Inverse Variation Problems

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  1. Chapter 7 Section 8

  2. Variation Solve direct variation problems. Solve inverse variation problems. 7.8 2

  3. Objective 1 Solve direct variation problems. Slide 7.8-3

  4. Two variables vary directly if one is a constant multiple of the other. Direct Variation y varies directly as x if there exists a constant k such that Solve direct variation problems. In these equations,y is said to be proportionaltox. The constant kin the equation for direct variation is a numerical value. This value is called the constant of variation. Some simple examples of variation include: Direct Variation: The harder one pushes on a car’s gas pedal, the faster the car goes. Inverse Variation: The harder one pushes on a car’s brake pedal, the slower the car goes. Slide 7.8-4

  5. Solving a Variation Problem Step 1:Write the variation equation. Step 2:Substitute the appropriate given values and solve for k. Step 3:Rewrite the variation equation with the value of k from Step 2. Step 4:Substitute the remaining values, solve for the unknown, and find the required answer. Solve direct variation problems. (cont’d) Slide 7.8-5

  6. If z varies directly as t, and z = 11 when t = 4, find z when t = 32. EXAMPLE 1 Using Direct Variation Solution: Slide 7.8-6

  7. Direct Variation as a Power y varies directly as the nth power of x if there exists a real number k such that Solve direct variation problems. (cont’d) The direct variation equation y = kx is a linear equation. Other kinds of variation involve other types of equations. Slide 7.8-7

  8. The circumference of a circle varies directly as the radius. A circle with a radius of 7 cm has a circumference of 43.96 cm. Find the circumference if the radius is 11 cm. EXAMPLE 2 Solving a Direct Variation Problem Solution: Thus, the circumference of the circle is 69.08 cm if the radius equals 11 cm. Slide 7.8-8

  9. Objective 2 Solve inverse variation problems. Slide 7.8-9

  10. Inverse Variation y varies inversely as x if there exists a real number k such that Also,y varies inversely as the nth power of x if there exists a real number k such that Solve inverse variation problems Unlike direct variation, where k > 0 and k increases as y increases. Inverse variation is the opposite. As one variable increases, the other variable decreases. Slide 7.8-10

  11. Suppose y varies inversely as the square of x. If y = 5 when x = 2, find y when x = 10. EXAMPLE 3 Using Inverse Variation Solution: Slide 7.8-11

  12. If the cost of producing pairs of rubber gloves varies inversely as the number of pairs produced, and 5000 pairs can be produced for $0.50 per pair, how much will it cost per pair to produce 10,000 pairs? EXAMPLE 4 Using Inverse Variation Solution: Slide 7.8-12

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