Question

a circular crop field has an irrigation system in which a pipe, with one end attached to a tower at the center of the field, turns continuously to deliver water. the horizontal distance, in meters, from the tip of the pipe to the farmhouse is represented by y = 400 sin(π/8 x + π)+500, where x represents time in hours. what does the amplitude of this function represent? the length of the pipe the distance between the tower and the farmhouse the time it takes for the pipe to complete one full circle the difference between the maximum and minimum distances from the tip of the pipe to the farmhouse

Explanation:

The general form of a sinusoidal function is $y = A\sin(Bx - C)+D$. In this case, the function is $y = 400\sin(\frac{\pi}{8}x+\pi)+500$, and the amplitude is $|A|$. The amplitude of a sinusoidal - type function represents half of the difference between the maximum and minimum values of the function. Here, the maximum value of $y$ is $400 + 500$ and the minimum value is $- 400+500$. The difference between the maximum and minimum values is $(400 + 500)-(-400 + 500)=800$, and half of this difference is the amplitude, which is 400. So the amplitude represents the difference between the maximum and minimum distances from the tip of the pipe to the farmhouse divided by 2.

Answer:

the difference between the maximum and minimum distances from the tip of the pipe to the farmhouse