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A fly is standing on a boulder, which is rolling down a hill. The forward torque the fly exerts on the boulder when it has rolled x meters, in newton meters, is given by tau(x)=(2)/(1000)sin((2pi(x+0.2))/(4)). What is the midline of this function? Give an exact answer. y=

A fly is standing on a boulder, which is rolling down a hill. The forward torque the fly exerts on the boulder when it has rolled x x meters, in newton meters, is given by\newlineτ(x)=21000sin⁡(2π(x+0.2)4). \tau(x)=\frac{2}{1000} \sin \left(\frac{2 \pi(x+0.2)}{4}\right) . \newlineWhat is the midline of this function? Give an exact answer.\newliney= y=

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Full solution

Q. A fly is standing on a boulder, which is rolling down a hill. The forward torque the fly exerts on the boulder when it has rolled x x meters, in newton meters, is given by\newlineτ(x)=21000sin⁡(2π(x+0.2)4). \tau(x)=\frac{2}{1000} \sin \left(\frac{2 \pi(x+0.2)}{4}\right) . \newlineWhat is the midline of this function? Give an exact answer.\newliney= y=
  1. Calculate Midline: The midline of a sinusoidal function is the average of its maximum and minimum values, which is also the vertical shift DD in the function τ(x)=A⋅sin⁡(Bx+C)+D\tau(x) = A \cdot \sin(Bx + C) + D.
  2. Identify Vertical Shift: In the given function τ(x)=21000⋅sin⁡(2π⋅(x+0.2)4)\tau(x) = \frac{2}{1000} \cdot \sin\left(\frac{2\pi \cdot (x + 0.2)}{4}\right), there is no vertical shift, so D=0D = 0.
  3. Final Midline: Therefore, the midline of the function is y=0y = 0.

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