Question
To determine the height of the ball when it reaches its fourth peak, we can analyze the sequence of the heights that the ball reaches after each bounce. The heights at the peaks are as follows:
1. First peak: 27 feet
2. Second peak: 18 feet
3. Third peak: 12 feet
To find a pattern, we can observe the changes in height between each peak:
- From the first peak to the second peak: 27 feet to 18 feet
- Change: 27 - 18 = 9 feet
- From the second peak to the third peak: 18 feet to 12 feet
- Change: 18 - 12 = 6 feet
Next, we can examine the pattern of the changes:
- The first change (from 27 to 18) is a decrease of 9 feet.
- The second change (from 18 to 12) is a decrease of 6 feet.
Now let's determine if there is a consistent pattern in these changes. The decrease from the first to the second peak is by 9 feet, and from the second to the third peak is by 6 feet. The decrease itself seems to be decreasing by 3 feet each time (9 - 6 = 3).
If we assume the pattern continues, we can expect the change from the third peak to the fourth peak to also decrease by 3 feet from the previous change (6 feet). Thus, the expected decrease from the third peak to the fourth peak would be:
6 - 3 = 3 feet decrease.
Now we can apply this change to the height of the third peak (12 feet):
Height at the fourth peak = Height at the third peak - Decrease from third to fourth peak
Height at the fourth peak = 12 - 3 = 9 feet.
Therefore, the height of the ball when it reaches its fourth peak is expected to be **9 feet**.
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1. First peak: 27 feet
2. Second peak: 18 feet
3. Third peak: 12 feet
To find a pattern, we can observe the changes in height between each peak:
- From the first peak to the second peak: 27 feet to 18 feet
- Change: 27 - 18 = 9 feet
- From the second peak to the third peak: 18 feet to 12 feet
- Change: 18 - 12 = 6 feet
Next, we can examine the pattern of the changes:
- The first change (from 27 to 18) is a decrease of 9 feet.
- The second change (from 18 to 12) is a decrease of 6 feet.
Now let's determine if there is a consistent pattern in these changes. The decrease from the first to the second peak is by 9 feet, and from the second to the third peak is by 6 feet. The decrease itself seems to be decreasing by 3 feet each time (9 - 6 = 3).
If we assume the pattern continues, we can expect the change from the third peak to the fourth peak to also decrease by 3 feet from the previous change (6 feet). Thus, the expected decrease from the third peak to the fourth peak would be:
6 - 3 = 3 feet decrease.
Now we can apply this change to the height of the third peak (12 feet):
Height at the fourth peak = Height at the third peak - Decrease from third to fourth peak
Height at the fourth peak = 12 - 3 = 9 feet.
Therefore, the height of the ball when it reaches its fourth peak is expected to be **9 feet**.
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Answers
GPT-4o mini
To find the height of the ball at its fourth peak, we observe the following sequence of heights:
1. First peak: 27 feet
2. Second peak: 18 feet (decrease of 9 feet)
3. Third peak: 12 feet (decrease of 6 feet)
The decreases are 9 feet and 6 feet, indicating a pattern where the decrease diminishes by 3 feet each time.
Following this pattern, the decrease from the third to the fourth peak would be:
6 - 3 = 3 feet decrease.
Thus, the height at the fourth peak is:
12 - 3 = 9 feet.
So, the height of the ball at its fourth peak is **9 feet**.
1. First peak: 27 feet
2. Second peak: 18 feet (decrease of 9 feet)
3. Third peak: 12 feet (decrease of 6 feet)
The decreases are 9 feet and 6 feet, indicating a pattern where the decrease diminishes by 3 feet each time.
Following this pattern, the decrease from the third to the fourth peak would be:
6 - 3 = 3 feet decrease.
Thus, the height at the fourth peak is:
12 - 3 = 9 feet.
So, the height of the ball at its fourth peak is **9 feet**.