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3.7 Variation and Applications Mon Oct 14

3.7 Variation and Applications Mon Oct 14. Do Now Solve the inequality. HW Review: p.327 #41-57. Direct Variation. If a situation gives rise to a linear function f(x) = kx , or y = kx , where k is a positive constant, we say that y varies directly as x

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3.7 Variation and Applications Mon Oct 14

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  1. 3.7 Variation and ApplicationsMon Oct 14 Do Now Solve the inequality

  2. HW Review: p.327 #41-57

  3. Direct Variation • If a situation gives rise to a linear function f(x) = kx, or y = kx, where k is a positive constant, we say that y varies directly as x • This is direct variation, and the number k is called the variation constant

  4. Ex1 • Find the variation constant and an equation of variation in which y varies directly as x, and y = 32 when x = 2

  5. Ex2 • The number of centimeters W of water produced from melting snow varies directly as S, the number of centimeters of snow. Meteorologists have found that 150 cm of snow will melt to 16.8 cm of water. To how many centimeters of water will 200 cm of snow melt?

  6. Inverse Variation • If a situation gives rise to a function f(x) = k/x, where k is a positive constant, we say that y varies inversely with x. • This is called inverse variation, and the number k is called the variation constant

  7. Ex3 • Find the variation constant and an equation of variation in which y varies inversely as x, and y = 16 when x = 0.3

  8. Ex4 • The time T required to do a job varies inversely as the number of people P who work on the job (assuming all work at the same rate). If it takes 72 hr for 9 people to frame a house, how long will it take 12 people to complete the same job?

  9. Combined Variation • More variation examples: • Y varies directly as the nth power of x • Y varies inversely as the nth power of x • Y varies jointly as x and z

  10. Ex5 • Find an equation of variation in which y varies directly as the square of x, and y = 12 when x = 2

  11. Ex7 • Find an equation in which y varies jointly as x and z and inversely as the square of w, and y = 105 when x = 3, z = 20, and w = 2

  12. Closure • What are the different types of variations? What do the key words (direct, inverse, joint) stand for? • HW: p.336-337 #9-37 odds

  13. 3.5-3.7 ReviewTues Oct 15 • Do Now • Find an equation of variation in which y varies directly as x and inversely as z, and y = 4 when x = 12 and z = 15

  14. HW Review: p.337 #9-37 odds

  15. Quiz Review • 3.5 Rational Functions • Finding vertical, horizontal, and oblique asymptotes • Graphing rational functions • 3.6 Polynomial and Rational Inequalities • Solving for 0, then using sign tests • 3.7 Variation and Applications • Writing the equation, then solving for a variable given values

  16. Closure • What do rational functions and variation have in common? • 3.5-3.7 Quiz Wed Oct 16

  17. 3.5-3.7 QuizWed Oct 16

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