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Direct, Inverse and Joint Variation

Direct, Inverse and Joint Variation. Direct Variation. y varies directly as x if there is some nonzero constant k such that y = kx. k is called the constant of variation. Example. If y varies directly as x and y = 9 when x is -15, find y when x = 21. Inverse Variation.

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Direct, Inverse and Joint Variation

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  1. Direct, Inverse and Joint Variation

  2. Direct Variation • y varies directly as x if there is some nonzero constant k such that y = kx. k is called the constant of variation

  3. Example • If y varies directly as x and y = 9 when x is -15, find y when x = 21.

  4. Inverse Variation • y varies inversely as x if there is some nonzero constant k such that xy = k or y = k/x

  5. Example • If y varies inversely as x and y = 4, when x = 12, find y when x = 5.

  6. Joint Variation • y varies jointly as x and z if there is some number k such that y = kxz, where and

  7. Example • The area A of a trapezoid varies jointly as the height h and the sum of its bases b1 and b2. Find the equation of joint variation if A = 48 in^3, h = 8 in., b1 = 5 in. and b2 = 7 in.

  8. Practice • If y varies jointly as x and z and y = 45 when x = 9 and z = 15, find y when x = 25 and z = 12

  9. Practice • If y varies inversely as x and y = ¼ when x = 24, find y when x = ¾ y = 8

  10. YU TRY! • If m varies directly as w and m = -15 when w = 2.5, find m when w = 12.5 y = ? A: 75 B:-25 C: -75 D: 25

  11. Example • The power P in watts of an electrical circuit varies jointly as the resistance R and the square of the current I. For a 600-watt microwave oven that draws a current of 5.0 amperes, the resistance is 24 ohms. • What is the resistance of a 200-watt refrigerator that draws a current of 1.7 amperes?

  12. YU Practice • The LEM (Lunar Exploration Module) used by astronauts to explore the moon’s surface during the Apollo space missions weighs about 30,000 pounds on Earth. On the moon there is less gravity so it weighs less, meaning that less fuel is needed to lift off from the moon’s surface. The force of gravity on Earth is about 6 times as much as that on the moon. How much does the LEM weigh on the moon? Enter the number pounds in your clicker!

  13. Answer • y =kx • 30,000 = 6x • x = 5,000 lbs

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