Oliver is observing a windmill. The vertical distance between the ground and the tip of one of the mill's blades, in meters, is modeled by $H(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted.

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
2) What is the meaning of the highlighted segment?

Choose 1 answer:
(A) The mill has 10 blades.
(B) The length of the blade is $\mathbf{1 0}$ meters.
(c) The mill completes a single cycle in 10 seconds.
(D) The mill completes 10 cycles in a second.

Question

Oliver is observing a windmill. The vertical distance between the ground and the tip of one of the mill's blades, in meters, is modeled by $H(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted.

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
2) What is the meaning of the highlighted segment?

Choose 1 answer:
(A) The mill has 10 blades.
(B) The length of the blade is $\mathbf{1 0}$ meters.
(c) The mill completes a single cycle in 10 seconds.
(D) The mill completes 10 cycles in a second.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Review the graph and the highlighted segment from t=10 to t=15. ‖ ‖ step 2 ⋮ Determine the feature of the graph that the highlighted segment represents. ‖ ‖ step 3 ⋮ The segment does not represent the midline or amplitude. It spans a complete cycle of the wave, indicating it represents the period. ‖ ∻[question 1] Answer∻ ***C*** ∻Key Concept∻ ⚹Period of a Trigonometric Function⚹ ∻Explanation∻ ⚹The period of a trigonometric function is the length of one complete cycle of the wave.⚹ ‖ step 4 ⋮ Analyze the meaning of the highlighted segment in the context of the windmill's blade movement. ‖ ‖ step 5 ⋮ The segment represents the time it takes for the windmill to complete one full rotation. ‖ ‖ step 6 ⋮ Since the segment spans from t=10 to t=15, it indicates that the mill completes a single cycle in 5 seconds. ‖ ∻[question 2] Answer∻ ***C*** ∻Key Concept∻ ⚹Meaning of the Highlighted Segment⚹ ∻Explanation∻ ⚹The highlighted segment on the graph represents the duration of one complete cycle of the windmill's blade rotation.⚹◊What is the formula to calculate the amplitude of a trigonometric function based on its graph?⍭ Generate me a similar question◊

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