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. A variable z varies jointly as x and y and inversely as u. if z = 14 when x = 4, y = 7 and u = 6, find the value of y when x = 10, u = 5, and z = 6​

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Hanimeyago

✒ COMBINED VARIATION

[tex] \large{••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\large\sf\underline{Problem:}[/tex]

  • A variable z varies jointly as x and y and inversely as u. if z = 14 when x = 4, y = 7 and u = 6, find the value of y when x = 10, u = 5, and z = 6

[tex] \large{••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\large\sf\underline{Answer:}[/tex]

[tex] \huge\tt\purple{\:\:\:\:\:\:\:\:\:y = 1}[/tex]

[tex] \large{••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\large\sf\underline{Solution:}[/tex]

  • [tex] \large\tt{ z = \frac{kxy}{u}}[/tex]

  • [tex] \large\tt{ 14 = \frac{4(7) k}{6} }[/tex]

  • [tex] \large\tt{ 14 = \frac{28k}{6}}[/tex]

  • [tex]\large\tt{ k = 3 }[/tex]

______

  • [tex] \large\tt{ z = \frac{3xy}{u}}[/tex]

  • [tex] \large\tt{ 6 = \frac{3(10)y}{5}}[/tex]

  • [tex] \large\tt{ 6 = \frac{30y}{5}}[/tex]

  • [tex] \large\tt\purple{ y = 1 }[/tex]

[tex] \because[/tex] The value of y is 1 when x = 10, u = 5, and z = 6

[tex] \large{••••••••••••••••••••••••••••••••••••••}[/tex]

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