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PreCalculus

PreCalculus. Section 1.6 Mathematical Modeling. Direct Variation. y = kx y varies directly as x y is directly proportional to x k is the constant of variation or constant of proportionality As one variable increases so does the other. Example 1.

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PreCalculus

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  1. PreCalculus Section 1.6 Mathematical Modeling

  2. Direct Variation • y = kx • y varies directly as x • y is directly proportional to x • k is the constant of variation or constant of proportionality • As one variable increases so does the other

  3. Example 1 • FICA taxes are directly proportional to gross income. If your annual gross income is $33,000 and $2524.50 was deducted in FICA taxes, write a model that gives taxes in terms of gross income.

  4. Direct Variation as an nth Power • y = kxn Example 2: The distance a ball rolls down a hill is directly proportional to the square of the time it rolls. During the first two seconds the ball rolls 20 feet. • Write an equation relating distance to time. • How far will the ball roll after 10 seconds

  5. Inverse Variation • y = k/x • y varies inversely as x • y is inversely proportional to x • As one variable increases, the other decreases.

  6. Combined Variation • A model that involves both direct and indirect variation.

  7. Example 3 • The volume of an enclosed gas varies directly as the temperature and moles and inversely as the pressure. The pressure of 0.582 mol of a gas is 81.8kPa when the temperature is 288K and the volume is 17.03 L. A. Find a model that relates pressure, temp, and volume. B. Find pressure when temp is 27 ° C and volume is 10L.

  8. Joint Variation • z varies jointly as x and y • z is jointly proportional to x and y • z = kxy

  9. Example 4 • The simple interest on an account is jointly proportional to the time (in years) and the principal. After 6 months the interest on a principal of $4000 is $38.00. • A. Write a model. • B. Find the interest after 9 months.

  10. assignment • Page 124: 3- 61 odds

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