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The value of z is 7 when y = 7 and x = 14.
If x varies directly as y and inversely as z and when y = 16 and z = 14, x = 16. Enter the value of z when y = 7 and x = 14.
The variation involves a direct and inverse variation from x to y and z.
This is represented as:
[tex]x = \frac{ky}{z}[/tex]
Where k is the constant of variation
For the first set of values, we have:
[tex]16 = \frac{k * 16}{14}[/tex]
Solve for k
k = 14
For the second set of values, we have:
[tex]14 = \frac{k * 7}{z}[/tex]
Substitute 14 for k
[tex]14 = \frac{14 * 7}{z}[/tex]
Solve for z
z = 7
Hence, the value of z is 7
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