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9.1 Inverse & Joint Variation

9.1 Inverse & Joint Variation. Just a reminder from chapter 2. Direct Variation Use y=kx. Means “y varies directly with x.” k is called the constant of variation. If y varies directly as x, and y=24 and x=3 find: (a) the constant of variation (b) Find y when x=2.

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9.1 Inverse & Joint Variation

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  1. 9.1 Inverse & Joint Variation

  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. If y varies directly as x, and y=24 and x=3 find: (a) the constant of variation (b) Find y when x=2 (a) Find the constant of variation Write the general equation Substitute

  4. (b) Find y when x=2 First we find the constant of variation, which was k=8 Now we substitute into y=kx.

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

  6. 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

  7. Determine whether x and y show direct variation, inverse variation, or neither.

  8. Determine whether x and y show direct variation, inverse variation, or neither.

  9. Determine whether x and y show direct variation, inverse variation, or neither. NEITHER

  10. Find y when x=15, if y varies inversely as x and x=10 when y=12 Solve by equation:

  11. 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

  12. Inverse Variation If y varies inversely with x and y = 12 when x = 2, find y when x = 8. x1y1 = x2y2 2(12) = 8y 24 = 8y y = 3

  13. 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.

  14. Joint Variation The variable z varies jointly with x & y. Write an equation that relates x, y, and z if x = 3, y = 7 and z = 8. Then find z when x = 9 and y = 4.

  15. 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.

  16. Assignment Section 9.1: page 537 – 538 # 21 – 42 (every 3rd), 45 - 47

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