Answer: The given function h(t)=6sin(3πt−π3)+4h(t)=6sin(3πt−3π)+4 models the movement of a spinning wheel relative to the ground, where h(t)h(t) represents the height of the wheel at time tt in meters.The equation itself appears to be mathematically correct and properly formatted. However, there may be some issues or considerations to address:Amplitude and Vertical Shift: The amplitude of the function is 6, which means the maximum height of the wheel is 6 meters above the ground. The vertical shift is 4, indicating that the wheel is initially positioned 4 meters above the ground. It's essential to ensure that these values accurately represent the physical characteristics of the spinning wheel.Angular Frequency: The angular frequency of the sine function is 3π3π, which means the wheel completes three full cycles per unit time (in this case, per second). It's crucial to verify whether this frequency corresponds to the actual rotational speed of the spinning wheel.Phase Shift: The phase shift of the function is −π3−3π, which indicates a horizontal shift of the sine wave to the right by π33π seconds. It's essential to determine whether this phase shift accurately reflects any delays or advances in the spinning motion of the wheel relative to time tt.Units and Consistency: The equation specifies that h(t)h(t) is in meters and tt is in seconds, which is appropriate for modeling the physical movement of the wheel. However, it's crucial to ensure consistency in units throughout any calculations or interpretations of the model.Real-world Validation: While the equation may accurately represent the mathematical relationship between the height of the wheel and time tt, it's essential to validate the model against real-world observations or measurements of the spinning wheel's movement. This validation can help confirm whether the equation effectively captures the dynamics of the spinning wheel relative to the ground.Overall, the equation appears mathematically sound, but it's essential to carefully consider the physical implications of its parameters and validate its accuracy against real-world observations.
Step-by-step explanation: