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A rock is thrown from one side of a river to another. The function h(t) = −16t2 + 80t + 30 gives the height in inches of the ro...Asked by T-Swizzle
A rock is thrown from one side of a river to another. The function h(t) = -16t^2 + 80t + 30 gives the height in inches of the rock t seconds after it has been thrown. Does it make sense to find h (-10) in the context of this problem? Why or why not?
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GPT-4o mini
In the context of this problem, the function \( h(t) = -16t^2 + 80t + 30 \) describes the height of a rock over time after it has been thrown. The variable \( t \) represents time in seconds.
Evaluating \( h(-10) \) would involve substituting -10 for \( t \), which gives us the height of the rock 10 seconds before it was thrown. In real-world scenarios like throwing a rock, time cannot be negative; we cannot have a time before the action occurs.
Therefore, it does not make sense to find \( h(-10) \) in this context because negative time does not have a physical meaning in relation to the event of the rock being thrown. The domain of \( t \) should be restricted to \( t \geq 0 \), reflecting the time from the moment of the throw onward.
Evaluating \( h(-10) \) would involve substituting -10 for \( t \), which gives us the height of the rock 10 seconds before it was thrown. In real-world scenarios like throwing a rock, time cannot be negative; we cannot have a time before the action occurs.
Therefore, it does not make sense to find \( h(-10) \) in this context because negative time does not have a physical meaning in relation to the event of the rock being thrown. The domain of \( t \) should be restricted to \( t \geq 0 \), reflecting the time from the moment of the throw onward.
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