Question
The graph models the swimming paths of two students, where x represents the time after a buzzer sounds and y represents height from the pool edge. One student dived into the pool from the edge of the pool 3 minutes before the buzzer went off. The second student dived into the pool from a board 4 feet above the ground right when the buzzer went off. Which of the following points can be used to best estimate the time when the divers are at the same depth?
(1 point)
Responses
(3.67, −7)
left parenthesis 3.67 comma negative 7 right parenthesis
(3, −6)
left parenthesis 3 comma negative 6 right parenthesis
(3.5, −6.5)
left parenthesis 3.5 comma negative 6.5 right parenthesis
(3.5, 6.5)
(1 point)
Responses
(3.67, −7)
left parenthesis 3.67 comma negative 7 right parenthesis
(3, −6)
left parenthesis 3 comma negative 6 right parenthesis
(3.5, −6.5)
left parenthesis 3.5 comma negative 6.5 right parenthesis
(3.5, 6.5)
Answers
GPT-4o mini
To determine when both divers are at the same depth, we need to identify points where the y-values (depth) are equal (and typically negative in this scenario, since depth below the surface is often represented as a negative value).
Given the points provided:
1. (3.67, -7)
2. (3, -6)
3. (3.5, -6.5)
4. (3.5, 6.5)
The points that indicate depth (the y-values) must be equal or of the same magnitude in the context of diving down into the pool (negative values).
Looking at the negative y-values:
- The point (3.67, -7) indicates a depth of -7 feet.
- The point (3, -6) indicates a depth of -6 feet.
- The point (3.5, -6.5) indicates a depth of -6.5 feet.
- The point (3.5, 6.5) is not relevant as it indicates a height above the water surface.
To estimate when the divers are at the same depth, we are looking for a negative y-value. Thus, the points (3.67, -7), (3, -6), and (3.5, -6.5) can all be considered.
However, if we are picking the best estimate of when they are both at the same depth, we want a point where they are likely to overlap in terms of when both divers are present.
The point (3.5, -6.5) may be the best estimate because it indicates a median position, while both divers will be transitioning through various depths around that time.
So the best estimate would be:
**(3.5, -6.5)**.
Given the points provided:
1. (3.67, -7)
2. (3, -6)
3. (3.5, -6.5)
4. (3.5, 6.5)
The points that indicate depth (the y-values) must be equal or of the same magnitude in the context of diving down into the pool (negative values).
Looking at the negative y-values:
- The point (3.67, -7) indicates a depth of -7 feet.
- The point (3, -6) indicates a depth of -6 feet.
- The point (3.5, -6.5) indicates a depth of -6.5 feet.
- The point (3.5, 6.5) is not relevant as it indicates a height above the water surface.
To estimate when the divers are at the same depth, we are looking for a negative y-value. Thus, the points (3.67, -7), (3, -6), and (3.5, -6.5) can all be considered.
However, if we are picking the best estimate of when they are both at the same depth, we want a point where they are likely to overlap in terms of when both divers are present.
The point (3.5, -6.5) may be the best estimate because it indicates a median position, while both divers will be transitioning through various depths around that time.
So the best estimate would be:
**(3.5, -6.5)**.