9.1 Inverse

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9.1 Inverse Joint Variation

• By L. Kealii Alicea

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Just a reminder from chapter 2

• Direct Variation
• Use ykx.
• Means y varies directly with x.
• k is called the constant of variation.

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New stuff!

• Inverse Variation
• y varies inversely with x.
• k is the constant of variation.

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Ex tell whether x y show direct variation,
inverse variation, or neither.

1. xy5
2. xy 7

Inverse Variation
Hint Solve the equation for y and take notice
of the relationship.
Neither
Direct Variation
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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.

• x2, y4
• k8
• Find y when x 4.
• y 2

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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.

• x16, y 1/4
• k(1/4)16 4
• Find y when x 4.
• y 1

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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 zkxy.
• Ex if y varies inversely with the square of x,
  then yk/x2.
• Ex if z varies directly with y and inversely
  with x, then zky/x.

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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.

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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, y2, z6
• 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

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