Question

A swing is located directly in front of a tree. As Danielle swings, she is 7.3 metres away from the treeat the furthest point of her swing and 3.5 metres away from the tree at the closest point. (Diagramis not drawn to scale.)3.5 metresIf a sinusoidal equation is used to represent Danielle's position with respect to the tree, determine:a) the medianb) the amplitude​.

Answer 1

The median of the swing's distance from the tree is 5.4 meters, and the amplitude of the sinusoidal function is 1.9 meters.

Step-by-step explanation:

To determine the median and the amplitude from a sinusoidal equation representing Danielle's position with respect to the tree while swinging, we will analyze the distance at the nearest and furthest points.

The median of the swing's distance from the tree is the average of the furthest and closest distances. Therefore, it would be the sum of the two divided by 2:

Median = (7.3 m + 3.5 m) / 2 = 5.4 m

The amplitude is half the distance between the maximum and minimum values. To find the amplitude:

Amplitude = (7.3 m - 3.5 m) / 2 = 1.9 m

The amplitude represents how far Danielle moves from the median position in both directions (towards and away from the tree).