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9.1 Inverse & Joint Variation. What you should learn:. Goal. 1. Write and use inverse variation models, as applied in Example 4. p.534. Goal. 2. Write and use Joint variation models, as applied in Example 6. 9.1 Inverse $ Joint Variation. Just a reminder from chapter 2. Direct Variation

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## 9.1 Inverse & Joint Variation

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**9.1 Inverse & Joint Variation**Whatyou should learn: Goal 1 Write and use inverse variation models, as applied in Example 4. p.534 Goal 2 Write and use Joint variation models, as applied in Example 6. 9.1 Inverse $ Joint Variation**Just a reminder from chapter 2**Direct Variation Use y = kx Means “yvaries directly with x.” k is called the constant of variation. 9.1 Inverse $ Joint Variation**New stuff!**Inverse Variation “y varies inversely with x.” k is the constant of variation. 9.1 Inverse $ Joint Variation**Ex: tell whether x & y show Direct Variation, Inverse**Variation, or neither. • xy=4.8 • y=x+4 Inverse Variation Hint: Solve the equation for y and take notice of the relationship. Neither Direct Variation 9.1 Inverse $ Joint Variation**Ex: The variables x & y vary inversely, and y = 8 when x =**3. • Write an equation that relates x & y. k=24 • Find y when x= -4. y= -6 9.1 Inverse $ Joint Variation**Joint Variation**• When a quantity varies directly as the product of 2 or more other quantities. • For example: if z varies jointly with x & y, then z=kxy. • Ex: if y varies inversely with the square of x, then y=k/x2. • Ex: if z varies directly with y and inversely with x, then z=ky/x. 9.1 Inverse $ Joint Variation**Part 1:The variable z varies Jointly withx & y. Use the**given values to write an equation relation x, y, and z. Part 2: Then find z wheny = 7andx = -4. for Part 2: Find z. for Part 1:Find k. Given values: x = -12, y = 4, z = 2 9.1 Inverse $ Joint Variation**Examples: Write an equation.**• y varies directly with x and inversely with z2. • y varies inversely with x3. • y varies directly with x2 and inversely with z. • z varies jointly with x2 and y. • y varies inversely with x and z. 9.1 Inverse $ Joint Variation**Assignment**Page 537 # 1 – 47 odd 9.1 Inverse $ Joint Variation

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