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Variation

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Steps to Find a Variation Model. Write a general variation model that relates the variables given in the problem. Let k represent the constant of variation. ... – PowerPoint PPT presentation

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Title: Variation


1
Variation
  • 4.4
  • SSC 105

2
Direct and Inverse Variation
  • Let k be a nonzero constant real number.
  • y varies directly as x.
  • y is directly proportional to x.
  • y varies inversely as x.
  • y is inversely proportional to x.
  • k is called the constant of variation.

3
  • For positive values of k,
  • When two variables are directly related, as one
    variable increases the other variable will also
    increase.
  • When two variables are inversely related, as one
    variable increases the other will decrease.

4
Joint Variation
  • Let k be a nonzero constant real number.
  • y varies jointly as w and z.
  • y is jointly proportional to w and z.

5
Steps to Find a Variation Model
  • Write a general variation model that relates the
    variables given in the problem. Let k represent
    the constant of variation.
  • Solve for k by substituting known values of the
    variables into the model from step 1.
  • Substitute the value of k into the original
    variation model from step 1.

6
Example
  • C varies directly as the square root of d and
    inversely as t. If C 12 when d is 9 and t is 6,
    find C if d is 16 and t is 12.
  • Step 1 Write a general model.
  • Step 2 Solve for k using known values.

7
Example (continued)
  • Step 3 Substitute the value of k and the other
    known variables to find C.

8
Exercise 10
  • In the equation y 9x, x and y vary
  • A) Directly
  • B) Inversely
  • C) Jointly

9
Exercise 11
  • Translate the statement into symbols
  • The number of hours it takes to paint a house
    is inversely proportional to the number of people
    painting. Let t number of hours, n number of
    workers.
  • A)   B) t kn 
  • C) tnk 1  D)

10
Exercise 12
  • The cost, in dollars, of filling your gas tank is
    directly proportional to the price per gallon of
    gas. If 15 gallons of gas costs 19.50, how much
    would 18 gallons cost?
  • A) 22.50
  • B) 23.40
  • C) 24.50
  • D) 11.54
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