Question
A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The graph below shows the height, y
, of the ball from he ground after x
seconds.
(1 point)
Responses
x≥2
x is greater than or equal to 2
0≤x≤2.5
0≤x≤2.5
0<x<5.5
0<x<5.5
2.5<x<5.5
, of the ball from he ground after x
seconds.
(1 point)
Responses
x≥2
x is greater than or equal to 2
0≤x≤2.5
0≤x≤2.5
0<x<5.5
0<x<5.5
2.5<x<5.5
Answers
GPT-4o mini
The provided intervals suggest various aspects of the ball's height over time. Assuming the height graph represents the ball's trajectory:
1. **\(x \geq 2\)**: This interval indicates that the ball is above ground or at a specific height from 2 seconds onwards.
2. **\(0 \leq x \leq 2.5\)**: This suggests that the ball is being thrown from the cliff and may be at some height for this time period, potentially rising and then beginning to descend.
3. **\(0 < x < 5.5\)**: This indicates the ball is in the air but does not define its specific trajectory or height, simply that it's not on the ground within this time frame.
4. **\(2.5 < x < 5.5\)**: This could represent a time when the ball is on its downward path after reaching its peak.
To determine which of these is appropriate, we would typically look for where the height \(y\) equals zero to find when the ball hits the ground. Assuming the graph shows the behavior of the ball's height over time, we need the interval when the height is zero as a key indicator of when the ball lands. Depending on the context of the graph you posted, you would select the range that corresponds to the curve intersecting the x-axis (ground level).
If we assume the ball reaches the ground after a height decline, the most relevant interval when the ball comes back down would likely be **\(2.5 < x < 5.5\)**, as it indicates it is falling after reaching its peak.
If you have specifics of the graph's behavior, you could conclude more accurately.
1. **\(x \geq 2\)**: This interval indicates that the ball is above ground or at a specific height from 2 seconds onwards.
2. **\(0 \leq x \leq 2.5\)**: This suggests that the ball is being thrown from the cliff and may be at some height for this time period, potentially rising and then beginning to descend.
3. **\(0 < x < 5.5\)**: This indicates the ball is in the air but does not define its specific trajectory or height, simply that it's not on the ground within this time frame.
4. **\(2.5 < x < 5.5\)**: This could represent a time when the ball is on its downward path after reaching its peak.
To determine which of these is appropriate, we would typically look for where the height \(y\) equals zero to find when the ball hits the ground. Assuming the graph shows the behavior of the ball's height over time, we need the interval when the height is zero as a key indicator of when the ball lands. Depending on the context of the graph you posted, you would select the range that corresponds to the curve intersecting the x-axis (ground level).
If we assume the ball reaches the ground after a height decline, the most relevant interval when the ball comes back down would likely be **\(2.5 < x < 5.5\)**, as it indicates it is falling after reaching its peak.
If you have specifics of the graph's behavior, you could conclude more accurately.