Answer:
A. The lowest point of the hammock is at the point 1 meters above the ground and 3 meters from one end of the hammock
B. The two trees are 6 meters away from one another
Step-by-step explanation:
The given equation of the parabola representing the hammock is as follows;
y = 0.4·(x - 3)² + 1
The general equation of a parabola is a·(x - h)² + k;
Where the coordinates of the vertex point of the parabola, which is the lowest (or highest, furthest) point on the vertex is (h, k) = (3, 1)
Therefore, we have;
A, The coordinates of the lowest point on the hammock is (3, 1)
Therefore, the lowest point of the hammock is at 1 meters above the ground and 3 meters from one end of the hammock
B. Given that the distance from one end is "x", we have;
The height at which the hammock is attached is given as the point where x = 0 as follows;
Given that the vertex of the parabola represents the axis of symmetry of the parabola, we have that the horizontal distance from one end of the hammock to the vertex point of the parabola that the hammock forms is (3 - 0) meters = 3 meters
Therefore, by the definition of symmetry, the distance from the vertex point to the other end of the parabola that the hammock forms is also 3 meters
From which we have, the distance the two trees are from one another is 3 meters + 3 meters = 6 meters.
