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if x varies directly as the square of y and inversely as z and x = 14 when y = 2 and z = 4 find x when y = 3 and z = 9​

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[tex]\large{\mathcal{SOLUTION:}}[/tex]

Equation: x = ky²/z

[tex] \\ [/tex]

STEP 1: Solve for the constant k

Given: x = 14 , y = 2 , z = 4

  • x = ky²/z
  • 14 = k(2)²/4
  • 14 = 4k/4
  • 14 = k

[tex] \\ [/tex]

STEP 2: Solve for the unknown value

Given: x = ? , y = 3 , z = 9 , k = 14

  • x = ky²/z
  • x = (14)(3)²/9
  • x = 14(9)/9
  • x = 14

Therefore , the value of x is 14

[tex] \\ [/tex]

[tex]\large{\mathcal{ANSWER:}}[/tex]

  • x = 14

[tex] \\ [/tex]

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