Chapter 7 Section 8

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Chapter 7 Section 8

• Variation

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Direct Variation

• When a situation gives rise to a linear function
  of the form f(x) kx where k is a nonzero
  constant, we say that there is direct variation.
  That is y varies directly as x or y is
  proportional to x. The number k is called the
  variation constant or the constant of
  proportionality.

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• Find the variation constant and an equation of
  variation if y varies directly as x with the
  following conditions(1) y 5 when x 12(2)
  y 20 when x 3

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Applications

• Hookes Law states that the distance D that a
  spring is stretched by a hanging object varies
  directly as the mass M of the object. If the
  distance is 20 cm when a mass in 3 kg, what is
  the distance when the mass is 5 kg?

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Weight on Mars

• The weight M of an object on Mars varies directly
  as its weight E on Earth. A person who weighs 95
  lb on Earth weighs 38 lb on Mars. Find the
  equation of variation and use it to find out how
  much a 210 lb person would weigh on Mars.

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Spring Activity

• Form groups of 3.
• Everyone turns in a graph.
• For question 1, select two of the points and use
  them to find the equation of the line that you
  feel best fits the data.
• Use your equation to predict the length of the
  spring for a suspended mass of 250 kg.

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Collaborative Corner

• Page 279 Draw the Graph and Match the Math.