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Joint and Combined Variation

Joint and Combined Variation. Review of Variations. Joint Variation. The variable y is said to vary jointly as x and z if y=kxz. In the equation y=kxz, k is the constant of variation . Example: y varies jointly as x and z, and y = 54 when x = 2 and z=9. Example.

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Joint and Combined Variation

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  1. Joint and Combined Variation

  2. Review of Variations

  3. Joint Variation • The variable y is said to vary jointly as x and z if y=kxz. • In the equation y=kxz, k is the constant of variation. • Example: y varies jointly as x and z, and y = 54 when x = 2 and z=9.

  4. Example • If y varies jointly as x and z, and y = 54 when x = 2 and z=9. • Find the constant of variation

  5. Example continued… • If y varies jointly as x and z, and y = 54 when x = 2 and z=9, find y when x = 7 and z = 10. • Since k = 3, then

  6. Combined Variation • In combined variation the relation involves both direct and inverse variation. • In the equation , k is the constant of variation. • Example: y varies directly as x and inversely as z, and y = 30 when x = 20 and z = 50.

  7. Example • If y varies directly as x and inversely as z, and y = 30 when x = 20 and z = 50, find the constant of variation.

  8. Example continued… • If y varies directly as x and inversely as z, and y = 30 when x = 20 and z = 50, find y when x = 40 and z = 25. • Since k = 75, then

  9. Examples • If y varies jointly as x and z, and y = 48 when x = 3 and z = 4, find the constant of variation. • If z varies inversely as t2, and t = 10 when z = 4, then find z when t = 8. K=4 Z = 6.25

  10. Examples • If x varies jointly as y and z, and x = 36 when y = 36 and z = 4, find x when y = 12 and z = 8. • If r varies directly as t2 and inversely as s, and r = 192 when t = 8 and s = 3, find s when t = 9 and r = 486. X =24 S =1.5

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