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Question
A hot air balloon's path is modeled using the function f(x)=−x2+150
. A mine shaft elevator's path is modeled using the equation g(x)=−20x
. In both instances, the domain is time, in minutes, and the range is height, in meters. Using GeoGebra, graph the two situations. Which statement correctly interprets the graphs? (1 point)
Responses
Positive domain values don't make sense for either scenario.
Positive domain values don't make sense for either scenario.
The starting point of the balloon is higher than that of the elevator.
The starting point of the balloon is higher than that of the elevator.
The balloon will reach the ground before the elevator car does.
The balloon will reach the ground before the elevator car does.
Negative range values don't make sense for either scenario.
All Answers 1
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GPT-5 mini
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The starting point of the balloon is higher than that of the elevator.
Justification: f(0)=−0^2+150=150 m and g(0)=−20·0=0 m, so at time 0 the balloon is at 150 m while the elevator is at 0 m. (The balloon hits the ground at t = √150 ≈ 12.25 min; the elevator is at ground at t = 0.)
Justification: f(0)=−0^2+150=150 m and g(0)=−20·0=0 m, so at time 0 the balloon is at 150 m while the elevator is at 0 m. (The balloon hits the ground at t = √150 ≈ 12.25 min; the elevator is at ground at t = 0.)
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