During the interval (t1, t2), which statement is true about …

Mathematics Questions

During the interval (t1, t2), which statement is true about the function h modeling the distance from point B on the windmill to the ground? a. h is positive and increasing. b. h is positive and decreasing. c. h is negative and increasing. d. h is negative and decreasing. Additionally, how is the rate of change of h behaving during the interval (t1, t2)?

Short Answer

The steps outline the understanding of sinusoidal functions as models for periodic oscillations, highlighting their smooth cycles. Specifically, it focuses on a scenario where the height of a point decreases from a peak to a minimum between two time points, along with a decreasing rate of change in height during this interval.

Step-by-Step Solution

Step 1: Understand Sinusoidal Functions

Sinusoidal functions model smooth, periodic oscillations like the height of a rotating windmill blade. These functions are characterized by their harmony and repeating cycles, providing a great tool for understanding periodic phenomena.

Step 2: Analyze the Interval Between t1 and t2

During the interval from time t1 to t2, the height (h) of point B is both positive and decreasing. This typically occurs after the function reaches its peak height, at which point the height starts to drop before reaching a minimum. This illustrates the behavior of sinusoidal functions as they progress through their cycles.

Step 3: Rate of Change of Height

In the interval between t1 and t2, the rate of change of height (h) is also decreasing. This means that as the height decreases, the speed at which it decreases is slowing down until it reaches its minimum point, consistent with the properties of sinusoidal functions.

Related Concepts

Sinusoidal Functions

Mathematical functions that model smooth, periodic oscillations and are characterized by repeating cycles and harmonic behavior.

Interval

A specific duration of time during which a particular change or observation is made, often analyzed in relation to functions or phenomena.

Rate Of Change

A measure of how a quantity (such as height) changes over time, indicating the speed and direction of that change, which can vary throughout a function’s cycle.

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