Combined Variation
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This document discusses combined variation and how to solve problems involving quantities that vary directly and inversely with other variables. It provides examples of translating statements of combined variation into mathematical equations. It also works through an example problem, showing how to solve for an unknown variable value when the quantities it varies with are given. The document concludes by instructing the reader to practice additional combined variation problems from their workbook.
Combined Variation
- 1. Prepared by: REYBETH D. RACELIS, LPT COMBINED VARIATION
- 2. OBJECTIVES Translates the given variation statement into mathematical equation. Solves problems involving combined variation.
- 3. COMBINED VARIATION The statement “t varies directly as x and inversely as y” In symbol: t = kx/y , k = ty/x where k is the constant of variation.
- 4. Translates the following statement into mathematical equation. T varies directly as a and inversely b. T =ka/b Y varies directly as x and inversely as the square of z. Y=kx/z² P varies directly as the square of x and inversely as s. P=kx²/s The time t required to travel is directly proportional to the temperature T and inversely proportional to the pressure P. t=kT/P The pressure P of a gas varies directly as its temperature t and inversely as its volume V. P=kt/V
- 5. Problem Solving If z varies directly as x and inversely as y, and z = 9 when x = 6, and y = 2, find z when x = 8 and y = 12.
- 6. Solution: z = kx/y z = 3x/y 9 = k(6)/2 z = 3(8)/12 9 = 6k/2 z = 24/12 2(9) = 6k z = 2 18 = 6k k = 3
- 7. GENERALIZATION: How do you solve problems involving combined variation?
- 8. EVALUATION Perform Activity 21 Letter A #1-5 and Letter B #1 a-c only, LM page 221
- 9. THANK YOU for your cooperation and participation!!!