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9.1 Inverse & Joint Variation

9.1 Inverse & Joint Variation. By: L. Keali’i Alicea. Just a reminder from chapter 2. Direct Variation Use y=kx. Means “y varies directly with x.” k is called the constant of variation. New stuff!. Inverse Variation “y varies inversely with x.” k is the constant of variation.

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9.1 Inverse & Joint Variation

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  1. 9.1 Inverse & Joint Variation By: L. Keali’i Alicea

  2. Just a reminder from chapter 2 Direct Variation Use y=kx. Means “y varies directly with x.” k is called the constant of variation.

  3. New stuff! Inverse Variation “y varies inversely with x.” k is the constant of variation.

  4. Ex: tell whether x & y show direct variation, inverse variation, or neither. • xy=5 • x+y = 7 Inverse Variation Hint: Solve the equation for y and take notice of the relationship. Neither Direct Variation

  5. Ex: The variables x & y vary inversely. Use the given values to write an equation relating x and y. Then find y when x =4. • x=2, y=4 k=8 • Find y when x= 4. y= 2

  6. Ex: The variables x & y vary inversely. Use the given values to write an equation relating x and y. Then find y when x =4. • x=16, y= 1/4 k=(1/4)16= 4 • Find y when x= 4. y= 1

  7. 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.

  8. 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. The variable z varies jointly with x and y. Use the given values to write an equation relating x, y, and z. Then find z when x= -3 and y= 4. • x= 1, y=2, z=6 We use: z = kxy We put in the values for z, x, and y to solve for k. 6= k(1)(2) Then solve for k. k= 6/2 = 3 z = 3xy We then put in the values for x and y and solve for z. z= 3(-3)(4)= -36

  10. Assignment 9.1 B (2-12 even, 13-18)

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