Question

A science class designed a container to protect an egg. Each prototype is launched from a machine at 9.4 meters per second from a roof 40 meters tall. The function f(t) = –4.9t2 + 9.4t + 40 represents the path from the building to the ground on the t-axis, where t is the amount of time since the launch.
How do the mathematical range and reasonable range compare?

mathematical: y ≤ 52
reasonable: y ≥ 0
mathematical: y ≤ 52
reasonable: y ≥ 40
mathematical: y ≤ 52
reasonable: 0 ≤ y ≤ 52
mathematical: y ≤ 52
reasonable: 40 ≤ y ≤ 52

Answer 1

Answer:

• mathematical: y ≤ 52

• reasonable: 0 ≤ y ≤ 52

Step-by-step explanation:

The reasonable range is the set of heights between the maximum height and the ground (y=0).

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The maximum height is about 44.51 meters, so values between that and 52 meters are not in the reasonable range. A maximum height of 52 meters requires an initial velocity of about 15.4 m/s.