3.8 Direct, Inverse and Joint Variation

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3.8 Direct, Inverse and Joint Variation
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Direct Variationy kxn, ngt0k is the constant
of variation

• The relationship between braking distance and car
  speed. As the speed of the car increases, the
  braking distance also increases at a constant rate

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Ex 1suppose y varies directly as x and y 45
when x 5/2

• Find the constant of variation and write an
  equation
• Use the equation to find the value of y when x 4

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Ex 2

• When an object such as a car is accelerating,
  twice the distance d it travels varies directly
  with the square of the time t elapsed. One car
  accelerating for 4 minutes travels 1440 ft.
  Write an equation.
• Find the distance traveled in 8 minutes.

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Ex 3

• If y varies directly as the square of x and y
  30 and x 4, find x when y 270.

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Inverse Variation(Inversely proportional)

• As one value increases the other decreases.
• When you travel to a higher elevation above
  Earths surface, the air temperature decreases.

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Can use proportions to solve inverse variation
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Ex 4If y varies inversely as x and y 14 when x
3, find x when y 30.
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Joint Variation when one quantity varies
directly as the product of two or more other
quantities.

• y kxnzn where x and z cannot 0 and n gt 0

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Ex 5

• In Physics, the work W done in charging a
  capacitor varies jointly as the charge q and the
  voltage V. Find the equation of joint variation
  if a capacitor with a charge of 0.004 coulomb and
  a voltage of 100 volts performs 0.20 joule of
  work.