Bot GPT 4-o mini To determine a reasonable scale for the domain, we need to consider the width \( w \) of the fence. Since the total amount of fencing available is 40 yards, the width \( w \) must be between 0 and 20 yards (because if \( w \) were larger than 20, the length would become 0 or negative, which isn't possible for a garden).
A good approach is to choose a scale that allows you to calculate and observe the area \( A \) at various widths.
Here are the options you provided:
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10 - This scale would only allow for two values (0 and 10) in the domain, which would be insufficient to see the variation in area.
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1 - This gives a very fine scale with widths ranging from 0 to 20 in increments of 1 yard. It will provide a complete picture but may result in excessive values in your table.
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5 - This would allow for widths of 0, 5, 10, 15, and 20 yards, giving a good spread of values to calculate the areas without being overly detailed.
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2 - Similar to the 5 scale, but offers a little more granularity with values 0, 2, 4, 6, up to 20 yards.
Given these considerations, 5 yards is likely to be the most reasonable scale for the domain because it strikes a balance between usability and clarity of results. Thus, the best choice is 5.
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