Answer:
(b) y = 18/x; y = 9/4
Step-by-step explanation:
Different kinds of variation are generally described by the equation ...
y = k·( ) . . . . . . . where k is the constant of proportionality
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kinds of variation
What goes in parentheses depends on the kind of variation. Here is a partial list of kinds that may be seen in algebra problems.
- direct: x
- inverse: 1/x
- as the square: x²
- as the square root: √x
- as the inverse of the square: 1/x²
- jointly as: xz
The value of k can be found by solving the variation equation with given values of the variables.
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inverse variation
The variables x and y are said to vary inversely, so the appropriate equation is ...
y = k(1/x) = k/x
Using the given values, we can find k:
9 = k/2
9·2 = k = 18
So, the equation is ...
y = k/18
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for x=8
Using the above equation, the value of y for x=8 is ...
y = 18/8 = 9/4
Note: you can also get there by realizing that x=8 is 4 times x=2, so the new value of y will be the old value of y multiplied by the inverse of this factor. 1/4 times the old value of y: (1/4)9 = 9/4.
