Question

lincoln is observing a wind turbine. the sensor that spins (blades) is graphed and the top of one of the blade’s height, in meters, is modeled by ( h(t) ) where ( t ) is time in seconds. the graph that is graphed (below) has a base (midline) highlighted. graph of a sinusoidal wave with ( t )-axis (time in seconds) and ( h )-axis (height in meters)
answer two questions about the highlighted segment.

1. which feature of the graph corresponds to the highlighted segment?

choose 1 answer:
a midline
b amplitude
c period

1. what is the meaning of the highlighted segment?

choose 1 answer:
a the turbine completes a single cycle in 35 seconds.
b the turbine’s center is 35 meters above the ground.
c the length of the blade is 35 meters.
d the turbine has 35 blades.

Explanation:

Question 1

• Midline: The midline of a sinusoidal graph is the horizontal line that the graph oscillates around. It's the average of the maximum and minimum values.
• Amplitude: Amplitude is the distance from the midline to the maximum (or minimum) value, representing the height of the oscillation.
• Period: The period is the length of one complete cycle of the sinusoidal graph (the horizontal distance between two consecutive peaks or troughs).

The highlighted segment is a horizontal line, which is the midline as it's the center around which the turbine blade's height (the sinusoidal graph) oscillates. So the correct option is A.

• Option A: The period (time for one cycle) would be the horizontal length of one full wave, not related to the midline's value.
• Option B: The midline in a sinusoidal graph for a turbine blade's height ($H(t)$) represents the center (average) height of the blade's motion. So if the midline is at 35 meters, it means the turbine’s center (the axis around which the blade rotates) is 35 meters above the ground.
• Option C: Amplitude (not midline) relates to the blade’s length (distance from center to tip), so this is incorrect.
• Option D: The midline doesn’t represent the number of blades.

So the correct option is B.

Answer:

A. Midline

Question 2