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Answer :
Final answer:
The table is filled by substituting the values of x into the given function. The resistance when x = 45.5 is approximately 5.3 and when x = 75.5 is approximately 1.8. The relationship between the diameter of the copper wire and the resistance is that as the diameter decreases, the resistance increases.
Explanation:
To fill in the table, we substitute the values of x into the given function y = 10370 / x^2. For example, when x = 10, y = 10370 / 10^2 = 103.7. Continuing this process for all the given values of x, we get the table:
x y
10 103.7
20 25.9
30 11.5
40 6.5
50 4.2
60 2.9
70 2.1
80 1.6
90 1.3
100 1.0
To estimate the resistance when x = 45.5 and x = 75.5, we can interpolate between the values in the table. When x = 45.5, y is approximately 5.3. When x = 75.5, y is approximately 1.8.
Comparing these estimates with the values calculated using the function, we can see that they are close. This suggests that the function is a good approximation for the relationship between the diameter of the copper wire and the resistance.
We can conclude that as the diameter of the copper wire decreases, the resistance increases. This is because a smaller diameter means a smaller cross-sectional area, which leads to a higher resistance based on the given function.
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