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
(3.5, 6.5)
left parenthesis 3.5 comma 6.5 right parenthesis
(3.5, −6.5)
left parenthesis 3.5 comma negative 6.5 right parenthesis
(3, −6)
left parenthesis 3 comma negative 6 right parenthesis
(3.67, −7)
left parenthesis 3.67 comma negative 7 right parenthesis
(1 point)
Responses
(3.5, 6.5)
left parenthesis 3.5 comma 6.5 right parenthesis
(3.5, −6.5)
left parenthesis 3.5 comma negative 6.5 right parenthesis
(3, −6)
left parenthesis 3 comma negative 6 right parenthesis
(3.67, −7)
left parenthesis 3.67 comma negative 7 right parenthesis
Answers
Answered by
GPT-4o mini
To find the point that best estimates when the two divers are at the same depth, we need to consider the swimming paths represented by the height (y) of each diver over time (x).
1. The first student dived into the pool 3 minutes before the buzzer, so their dive starts at \(x = -3\) minutes.
2. The second student dived from a board 4 feet above the ground when the buzzer went off, meaning their dive starts at \(x = 0\) minutes.
To find when they are at the same depth, we are looking for a coordinate where the y-values are the same for both students at a certain x-value.
Without more context about how the divers' heights change over time, we'll focus on the y-values. For both students to be at the same depth, the y-values must be negative (since they are below the surface of the water) and equal.
If we analyze the provided responses:
- (3.5, 6.5): This positive y-value indicates the diver is above the surface, which is not suitable.
- (3.5, −6.5): This y-value is negative and suggests one diver could be at a depth of 6.5 feet below.
- (3, −6): This also indicates one diver is at a depth of 6 feet below the surface.
- (3.67, −7): This suggests one diver is at a depth of 7 feet below the surface.
Any of the negative y-values could indicate possible depths. However, we want to estimate when they could be at the same depth. Comparing possible depths, let's assume they could reach equal depths around 6.5 feet or 7 feet.
The best options for likely equal depth are:
- \( (3.5, -6.5) \)
- \( (3.67, -7) \)
Thus, if we have to choose, the point that seems to best estimate when the divers are at the same depth is \( (3.5, -6.5) \).
Therefore, the correct answer is:
**(3.5, -6.5)**.
1. The first student dived into the pool 3 minutes before the buzzer, so their dive starts at \(x = -3\) minutes.
2. The second student dived from a board 4 feet above the ground when the buzzer went off, meaning their dive starts at \(x = 0\) minutes.
To find when they are at the same depth, we are looking for a coordinate where the y-values are the same for both students at a certain x-value.
Without more context about how the divers' heights change over time, we'll focus on the y-values. For both students to be at the same depth, the y-values must be negative (since they are below the surface of the water) and equal.
If we analyze the provided responses:
- (3.5, 6.5): This positive y-value indicates the diver is above the surface, which is not suitable.
- (3.5, −6.5): This y-value is negative and suggests one diver could be at a depth of 6.5 feet below.
- (3, −6): This also indicates one diver is at a depth of 6 feet below the surface.
- (3.67, −7): This suggests one diver is at a depth of 7 feet below the surface.
Any of the negative y-values could indicate possible depths. However, we want to estimate when they could be at the same depth. Comparing possible depths, let's assume they could reach equal depths around 6.5 feet or 7 feet.
The best options for likely equal depth are:
- \( (3.5, -6.5) \)
- \( (3.67, -7) \)
Thus, if we have to choose, the point that seems to best estimate when the divers are at the same depth is \( (3.5, -6.5) \).
Therefore, the correct answer is:
**(3.5, -6.5)**.
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