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SOLVING:, 1. y varies directly as z and inversely as x and y = 8 when z = 4 and x = 2158, 2. y varies directly as x and inversely as z and y = 6 when x = 3 and z = 2

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SOLVING:


1. y varies directly as z and inversely as x and y = 8 when z = 4 and x = ⅘

2. y varies directly as x and inversely as z and y = 6 when x = 3 and z = 2​

✏️COMBINED VARIATIONS

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nderline{\mathbb{PROBLEMS:}}

  • #1. y varies directly as z and inversely as x and y = 8 when z = 4 and x = ⅘.
  • #2. y varies directly as x and inversely as z and y = 6 when x = 3 and z = 2.

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nderline{\mathbb{ANSWERS:}}

\qquad\LARGE\rm»\:\: 1. \:\green{k=\frac58}

\qquad\LARGE\rm»\:\: 2. \:\green{k=4}

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nderline{\mathbb{SOLUTIONS:}}

– Write the equation for combined variations and then find the constant k.

#1.

  • y =  \frac{kz}{x}  \\
  • 8 =  \frac{k(4)}{ \frac{4}{5} }  \\
  • 8 =  \frac{4k}{ \frac{4}{5} }  \\
  • 8 = 4k \div  \frac{4}{5}   \\
  • 8 = 4k \cdot  \frac{5}{4}   \\
  • 8 = \frac{20k}{4}   \\
  • 8 = 5k
  •  \frac{8}{5} =  \frac{ \cancel5k}{ \cancel5}  \\
  •  \frac{8}{5} = k  \\

\therefore The constant of the variation is 8/5.

\rm

#2.

  • y =  \frac{kx}{z}  \\
  • 6 =  \frac{k(3)}{2}  \\
  • 6 =  \frac{3k}{2}  \\
  • 6 \cdot2 =  \frac{3k}{ \cancel2} \cdot \cancel2  \\
  • 12 = 3k
  •  \frac{12}{3} =  \frac{ \cancel3k}{ \cancel3}  \\
  • 4 = k

\therefore The constant of the variation is 4.

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