Question
A football is thrown into the air it reaches a maximum height of 18 yards and lands 78 yards from where it was thrown. Which answer option represents the domain,in terms of the context
Answers
GPT-4o mini
To determine the domain in the context of the football's motion, we need to consider the time interval during which the football is in the air.
When the football is thrown, it reaches a maximum height, and then it comes back down to the ground. The journey of the football from being thrown to reaching its maximum height, and then falling back down to where it landed can be represented as a function of time.
In this context:
1. The starting point (when the football is thrown) can be considered as \( t = 0 \).
2. The football is thrown into the air and returns to the ground after some time.
If the football lands 78 yards from where it was thrown, we can infer the entire motion occurs over a time span until it comes back down to the ground.
Thus, the domain, in terms of time and context, would typically be:
- From \( t = 0 \) (the moment it's thrown) to \( t = T \), where \( T \) is the total time the ball is in the air until it lands.
Because the problem does not specify the exact duration in seconds or any other time unit, the domain is more abstractly represented as:
\[ [0, T] \]
where \( T \) is a positive value denoting the total time the ball remains in the air until landing.
If you have specific answer options, please provide them so we can narrow it down further!
When the football is thrown, it reaches a maximum height, and then it comes back down to the ground. The journey of the football from being thrown to reaching its maximum height, and then falling back down to where it landed can be represented as a function of time.
In this context:
1. The starting point (when the football is thrown) can be considered as \( t = 0 \).
2. The football is thrown into the air and returns to the ground after some time.
If the football lands 78 yards from where it was thrown, we can infer the entire motion occurs over a time span until it comes back down to the ground.
Thus, the domain, in terms of time and context, would typically be:
- From \( t = 0 \) (the moment it's thrown) to \( t = T \), where \( T \) is the total time the ball is in the air until it lands.
Because the problem does not specify the exact duration in seconds or any other time unit, the domain is more abstractly represented as:
\[ [0, T] \]
where \( T \) is a positive value denoting the total time the ball remains in the air until landing.
If you have specific answer options, please provide them so we can narrow it down further!