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Sagot :
To determine which table could represent Brady's distance from the fountain after jogging around a circular path for a number of minutes, we need to analyze the distances provided in each table. Brady's jogging around a circular park should exhibit a cyclic pattern since he returns to the same point periodically.
Table 1:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time} & \text{Distance (feet)} \\ \hline 0 & 50 \\ \hline 2 & 60 \\ \hline 4 & 70 \\ \hline 6 & 80 \\ \hline 8 & 100 \\ \hline \end{array} \][/tex]
This table indicates a linear increase in distance from the fountain. Since Brady is jogging on a circular path, his distance from the fountain should not be increasing linearly.
Table 2:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time} & \text{Distance (feet)} \\ \hline 0 & 50 \\ \hline 2 & 60 \\ \hline 4 & 70 \\ \hline 6 & 60 \\ \hline 8 & 50 \\ \hline \end{array} \][/tex]
This table starts and ends at the same distance (50 feet), showing a pattern that increases to a peak (70 feet) and then returns back to the starting distance. This cyclic or repeating pattern is a characteristic of circular motion and indicates that Brady jogs around and returns to points that are progressively closer and then further from the fountain.
Table 3:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time} & \text{Distance (feet)} \\ \hline 0 & 50 \\ \hline 2 & 50 \\ \hline 4 & 50 \\ \hline 6 & 50 \\ \hline 8 & 50 \\ \hline \end{array} \][/tex]
The distance remains constant over time irrespective of Brady jogging, which does not fit the scenario of jogging around a circular park. Therefore, this table is not correct.
Table 4:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time} & \text{Distance (feet)} \\ \hline 0 & 50 \\ \hline 2 & 40 \\ \hline 4 & 30 \\ \hline 6 & 20 \\ \hline 8 & 10 \\ \hline \end{array} \][/tex]
This table shows a consistently decreasing distance, which suggests Brady is continuously moving towards the center of the circle (towards the fountain) and does not depict a circular jogging path. Thus, this table is not correct either.
Given the observation, Table 2 is the one which shows distance measurements that correspond to the cyclic motion of jogging around a circular park. Therefore, the correct table that represents Brady's distance from the fountain is:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time} & \text{Distance (feet)} \\ \hline 0 & 50 \\ \hline 2 & 60 \\ \hline 4 & 70 \\ \hline 6 & 60 \\ \hline 8 & 50 \\ \hline \end{array} \][/tex]
Table 1:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time} & \text{Distance (feet)} \\ \hline 0 & 50 \\ \hline 2 & 60 \\ \hline 4 & 70 \\ \hline 6 & 80 \\ \hline 8 & 100 \\ \hline \end{array} \][/tex]
This table indicates a linear increase in distance from the fountain. Since Brady is jogging on a circular path, his distance from the fountain should not be increasing linearly.
Table 2:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time} & \text{Distance (feet)} \\ \hline 0 & 50 \\ \hline 2 & 60 \\ \hline 4 & 70 \\ \hline 6 & 60 \\ \hline 8 & 50 \\ \hline \end{array} \][/tex]
This table starts and ends at the same distance (50 feet), showing a pattern that increases to a peak (70 feet) and then returns back to the starting distance. This cyclic or repeating pattern is a characteristic of circular motion and indicates that Brady jogs around and returns to points that are progressively closer and then further from the fountain.
Table 3:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time} & \text{Distance (feet)} \\ \hline 0 & 50 \\ \hline 2 & 50 \\ \hline 4 & 50 \\ \hline 6 & 50 \\ \hline 8 & 50 \\ \hline \end{array} \][/tex]
The distance remains constant over time irrespective of Brady jogging, which does not fit the scenario of jogging around a circular park. Therefore, this table is not correct.
Table 4:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time} & \text{Distance (feet)} \\ \hline 0 & 50 \\ \hline 2 & 40 \\ \hline 4 & 30 \\ \hline 6 & 20 \\ \hline 8 & 10 \\ \hline \end{array} \][/tex]
This table shows a consistently decreasing distance, which suggests Brady is continuously moving towards the center of the circle (towards the fountain) and does not depict a circular jogging path. Thus, this table is not correct either.
Given the observation, Table 2 is the one which shows distance measurements that correspond to the cyclic motion of jogging around a circular park. Therefore, the correct table that represents Brady's distance from the fountain is:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time} & \text{Distance (feet)} \\ \hline 0 & 50 \\ \hline 2 & 60 \\ \hline 4 & 70 \\ \hline 6 & 60 \\ \hline 8 & 50 \\ \hline \end{array} \][/tex]
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