Question

a construction crane lifts a steel beam 30 meters in the air. at a steady rate of 6 meters per minute, it takes the crane 5 minutes to raise the beam. the function a(t) represents the altitude, in meters, of the beam after t minutes. what is the range of a(t)?

Answer 1

The range of a(t) is the set of altitudes the steel beam achieves as it is lifted by the crane, which is from 0 to 30 meters. This range can be written as [0, 30] meters.

Step-by-step explanation:

The range of a(t) is the set of values that the function takes as the crane lifts the steel beam. Since the crane moves the beam at a steady rate of 6 meters per minute and it takes 5 minutes to lift the beam 30 meters, we can determine the range of a(t) by evaluating the function from t = 0 to t = 5.

Starting at t = 0, the beam is on the ground, so a(0) = 0 meters. At t = 5 minutes, the beam has been lifted to its maximum altitude, so a(5) = 30 meters. Since the crane is lifting the beam at a constant rate, the altitude increases linearly over time. Thus, the range of a(t) is all the values of altitude from 0 to 30 meters, inclusive.

Therefore, the range of a(t) is [0, 30] meters.

Answer 2

The range of the function a(t), representing the altitude of a steel beam after t minutes, is from 0 to 30 meters.

Step-by-step explanation:

The question asks us to determine the range of a(t), the function representing the altitude of a steel beam being lifted by a construction crane after t minutes.

Since the crane lifts the beam 30 meters in 5 minutes at a steady rate of 6 meters per minute, we can infer that the function is linear.

The beam starts at 0 meters (ground level) and ends at 30 meters (final altitude). Thus, the range of a(t) is from 0 to 30 meters.