A hot air balloon rising vertically is tracked by an observer located 3 km from the lift‑off point. At a certain moment, the angle between the observer's line of sight and the horizontal is pi/5, and it is changing at a rate of 0.4 rad/min. How fast is the balloon rising at this moment? Let y be the height of the balloon (in km), t be time (in minutes), and theta the angle between the line‑of‑sight and the horizontal (in radians). (Use decimal notation. Give your answer to two decimal places.)

Trigonometry (MindTap Course List)
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ISBN:9781337278461
Author:Ron Larson
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Chapter1: Trigonometry
Section1.1: Radian And Degree Measure
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A hot air balloon rising vertically is tracked by an observer located 3 km from the lift‑off point. At a certain moment, the angle between the observer's line of sight and the horizontal is pi/5, and it is changing at a rate of 0.4 rad/min. How fast is the balloon rising at this moment?

Let y be the height of the balloon (in km), t
be time (in minutes), and theta the angle between the line‑of‑sight and the horizontal (in radians).

(Use decimal notation. Give your answer to two decimal places.)

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