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it is varies directly as x and inversely as y and z = 9 when x = 2 and y = 2 find the value of constant of variation​

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Problem:

If z varies directly as x and inversely as y and z = 9 when x = 2 and y = 2 find the value of constant of variation.

Solution:

To translate into variation statement a relationship involving combined variation between two quantities.

The statement, "If z varies directly as x and inversely as y" translated into combined variation is z = kx/y where k is the constant of variation.

Solve if z is 9 when x is 2 and y is 2. So, find the constant using the equation of a combined variation.

  • z = kx/y
  • (9) = k(2)/(2)
  • 9 = 2k/2
  • 9 × 2 = 2k
  • 18 = 2k
  • 2k/2 = 18/2
  • k = 9

The constant of the variation is 9. In equation of variation.

  • z = 9x/y

Answer:

∴ Therefore, the value is 9 of constant variation.

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