Section 2.2: Inverse Variation Inverse Variation Function: y = k where k 0 and n>0 x n
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1 Section 2.2: Inverse Variation Inverse Variation Function: y = k where k 0 and n>0 x n We say: "y varies inversely as x n " where k = constant of variation OR "y is inversely proportional to x n " Life example: older your car the less it is worth (generally speaking) Sep 25 9:57 AM 1
2 1. What does it mean when we say a variable w varies inversely as a variable t? (what is the generic ordered pair) As t changes w changes in the opposite direction 2. Definition of inverse variations function. 3. What is another way to say that the time required to drive from Hartland to Madison varies inversely with the speed of the car you are in? AA22.pdf 4. Study example 1 The time required to drive from Hartland to Madison is inversely proportional to the speed of the car you are in. Nov 1 9:46 PM 2
3 5. In a given room, the floor space F per person varies inversely as the square of the number of people in the room. Write a GENERIC variation equation to express this relation. Sep 25 10:21 AM 3
4 6. Study example 2 Nov 1 9:53 PM 4
5 7. The time T required to do a job varies inversely as the number of workers W. It takes 5 hours for 8 cement finishers to do a certain job. a. Find k, the constant of variation. b. How long would it take 12 workers to do the same job? Sep 25 10:21 AM 5
6 8. Study example 3 Nov 1 9:55 PM 6
7 9. The intensity of light that reaches you from a light bulb varies inversely as the square of your distance d from the bulb. When you are standing 10 feet away from a certain light bulb, its intensity is 130 units. What is the intensity of the bulb when you are standing 4 feet away? Sep 25 10:52 AM 7
8 In direct variation a constant is multiplied by a positive power of the independent variable In inverse variation a constant is divided by a positive power of the independent variable Nov 3 8:08 PM 8
9 Nov 3 8:09 PM 9
10 1) Write a GENERIC equation that describes the generic variation relationship with the indicated variables, exponents and the constant of variation k 2) Solve for the constant of variation by substituting values for all variables leaving the constant of variation as the only unknown 3) Rewrite the generic variation function, from step one, as a SPECIFIC variation function using the actual constant of variation and the variables for the situation. 4) Use the specific function to answer any questions about this specific relationship. Nov 3 8:10 PM 10
11 1) Write a GENERIC equation that describes the generic variation relationship with the indicated variables, exponents and the constant of variation k 2) Solve for the constant of variation by substituting values for all variables leaving the constant of variation as the only unknown 3) Rewrite the generic variation function, from step one, as a SPECIFIC variation function using the actual constant of variation and the variables for the situation. 4) Use the specific function to answer any questions about this specific relationship. Nov 3 8:10 PM 11
12 Nov 3 8:10 PM 12
13 1) Write a GENERIC equation that describes the generic variation relationship with the indicated variables, exponents and the constant of variation k 2) Solve for the constant of variation by substituting values for all variables leaving the constant of variation as the only unknown 3) Rewrite the generic variation function, from step one, as a SPECIFIC variation function using the actual constant of variation and the variables for the situation. 4) Use the specific function to answer any questions about this specific relationship. Nov 3 8:11 PM 13
14 1) Write a GENERIC equation that describes the generic variation relationship with the indicated variables, exponents and the constant of variation k 2) Solve for the constant of variation by substituting values for all variables leaving the constant of variation as the only unknown 3) Rewrite the generic variation function, from step one, as a SPECIFIC variation function using the actual constant of variation and the variables for the situation. 4) Use the specific function to answer any questions about this specific relationship. Nov 3 8:11 PM 14
15 1) Write a GENERIC equation that describes the generic variation relationship with the indicated variables, exponents and the constant of variation k 2) Solve for the constant of variation by substituting values for all variables leaving the constant of variation as the only unknown 3) Rewrite the generic variation function, from step one, as a SPECIFIC variation function using the actual constant of variation and the variables for the situation. 4) Use the specific function to answer any questions about this specific relationship. Nov 3 8:11 PM 15
16 1) Write a GENERIC equation that describes the generic variation relationship with the indicated variables, exponents and the constant of variation k 2) Solve for the constant of variation by substituting values for all variables leaving the constant of variation as the only unknown 3) Rewrite the generic variation function, from step one, as a SPECIFIC variation function using the actual constant of variation and the variables for the situation. 4) Use the specific function to answer any questions about this specific relationship. Nov 3 8:11 PM 16
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32 Attachments Text Solutions 2.2.pdf AA22.pdf
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GENERATING EQUIVALENT EXPRESSIONS ENGAGE NY- LESSONS 1 & 2 FIND THE PRODUCT: -9.56 x 4.2 x -2 x CALCULATE: 3 6 7 + 5 1 2 CORE ENRICHMENT Interim Analysis Paper Pencil The cost (c) to hire a dog trainer
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Indirect Measurement Application of Similar Triangles. LEARNING GOALS In this lesson, you will: Identify similar triangles to calculate indirect measurements. Use proportions to solve for unknown measurements.
Portsmouth. July to Sept Online courses. Quarterly schedule July to Sept Customer Service Office
July to Sept. 2017 July to Sept. 2017 2017 Classroom Day(s) Aug. 30 Ergonomics: Basic Principles 1.0 Day Sept. 12 First Aid in the Workplace 1.0 Day Sept. 27 Lockout/Tagout and Safety-related Work Practices
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4.6. You would think that determining the tallest building in the world would be pretty. Indirect Measurement. Application of Similar Triangles
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GREENWOOD PUBLIC SCHOOL DISTRICT Grade Math Pacing Guide
Week Instructional Period/ Date Academic Focus 1 st Nine Weeks Common Core Standards I can statements 1 Aug. 7 th 11 th ( 5 days) 2 Aug. 14 th 18 th ( 5 days) 3 Aug. 7 th 11 th ( 5 days) 4 Aug. 21 st 25
about touching on a topic and then veering off to talk about something completely unrelated.
The Tangent Ratio Tangent Ratio, Cotangent Ratio, and Inverse Tangent 8.2 Learning Goals In this lesson, you will: Use the tangent ratio in a right triangle to solve for unknown side lengths. Use the cotangent