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Download Algebra 2 9.5 Variation Functions Name: Essential Question: How
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Algebra 2 9.5 Variation Functions Name: _______________________ Essential Question: How do we recognize and solve the different types of variation problems? Vocabulary: Direct Variation: ___________________________________________________________________________ Constant of Variation: _______________________________________________________________________ Joint Variation: _____________________________________________________________________________ Inverse Variation: ___________________________________________________________________________ Combined Variation: ________________________________________________________________________ How to Write and Solve Variation Problems: Step 1: Use the wording of the problem to write the general form of the equation. Step 2: Plug in all known quantities so that you can find the value of k. Solve for k. Step 3: Rewrite your equation from step one with your new k value. Step 4: Plug in other values so that you can find the one that is missing. Solve for the missing variable. Examples: 1. If y varies directly as x and y = -15 when x = 5, find y when x = 3. 2. Suppose y varies jointly as x and z. Find y when x = 10 and z = 5, if y = 12 when z = 8 and x = 3. 3. If r varies inversely as t and r = -6 when t = 2, find r when t = -7. 4. The volume of a gas v varies inversely as the pressure p and directly as the temperature t. a. Write the equation to represent the volume of a gas in terms of pressure and temperature. b. Is the equation a direct, joint, combined or inverse variation? c. A certain gas has a volume of 8 liters, a temperature of 275 Kelvin, and a pressure of 1.25 atmospheres. If the gas is compressed to a volume of 6 liters and is heated to 300 Kelvin, what will the new pressure be? 5. Suppose f varies directly as g and f varies inversely as h. Find g when f = 6 and h = -5, if g = 18 when h = 3 and f = 5. Summarizer: How are direct variations and linear equations related? How are joint and combined variations the same and different?
