To find the change in height of the parasail, we need to subtract the initial height from the final height.
The initial height is \( \frac{1}{20} \) of a kilometer and the final height is \( \frac{1}{50} \) of a kilometer.
First, we need to convert these fractions to have a common denominator in order to subtract them easily.
The least common multiple of 20 and 50 is 100.
Now we convert both heights:
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For \( \frac{1}{20} \): \[ \frac{1}{20} = \frac{5}{100} \]
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For \( \frac{1}{50} \): \[ \frac{1}{50} = \frac{2}{100} \]
Now, we can calculate the change in height:
\[ \text{Change in height} = \text{Final height} - \text{Initial height} = \frac{2}{100} - \frac{5}{100} = \frac{2 - 5}{100} = \frac{-3}{100} \]
Since the change in height is negative, it indicates a decrease in height.
However, we want the absolute value to represent the change in height:
\[ \text{Change in height} = \frac{3}{100} \text{ kilometers} \]
Thus, the change in height is \( \frac{3}{100} \) kilometers.
The answer is \( \frac{3}{100} \) kilometers, which is not among the options you provided. However, based on the options given, the closest representation of this change is:
3/100 kilometers.