In Gabriel's village there is an electrical wire suspended between two poles across a gully.the poles are on the edges of the gully and the wire is at the same height on both sides of the gully. The curve of the wire can be modeled by the equation: h = (d - 6) + 3.
When h is the height, in meters, of the wire above the floor of the gully and d is the distance, in meters, from the left-hand post.
Use the information to answer these two questions:
1. How far apart are the two poles?
2. How is this shown on the graph?
To answer both questions, we need to understand the relationship between the height of the wire above the floor and the distance from the left-hand post.
The equation given is h = (d - 6) + 3, where h represents the height of the wire above the floor and d represents the distance from the left-hand post.
1. How far apart are the two poles?
The distance between the two poles can be determined by finding the value of d when h is zero. In other words, we need to solve the equation h = 0.
0 = (d - 6) + 3
Simplifying the equation:
0 = d - 3
Rearranging the equation to solve for d:
d = 3
Therefore, the two poles are 3 meters apart.
2. How is this shown on the graph?
To show this information on a graph, we can plot the height of the wire (h) on the y-axis and the distance from the left-hand post (d) on the x-axis.
The x-axis will represent the distance in meters from the left-hand post, and the y-axis will represent the height in meters above the floor.
The point (d, h) with d = 3 and h = 0 represents the location of the left-hand pole.
The point (d+3, h) with d = 3 and h = 0 represents the location of the right-hand pole.
By plotting these two points on the graph and connecting them with a line, we can visualize the wire suspended between the two poles.
To answer these questions, we need to analyze the information given.
1. How far apart are the two poles?
To find the distance between the two poles, we can examine the equation given: h = (d - 6) + 3.
Here, "d" represents the distance from the left-hand post. The equation represents the height (h) of the wire above the floor of the gully at any given point on the wire.
In this equation, the constant term "-6" represents the distance of the left pole from the reference point (presumably the starting point), and the constant term "+3" represents the height of the wire above the floor.
Since the wire is at the same height on both sides of the gully, we can assume that the right pole is also 6 meters away from the reference point. Hence, the distance between the two poles is the sum of the distances on both sides of the reference point: 6 meters on the left and 6 meters on the right, making it a total of 12 meters.
Therefore, the two poles are 12 meters apart.
2. How is this shown on the graph?
To represent this information on a graph, we can plot the equation h = (d - 6) + 3, where "d" is the x-axis representing the distance from the left-hand post, and "h" is the y-axis representing the height above the floor of the gully.
On the graph, we would mark the points (6, 3) and (12, 3). These points represent the heights above the floor at a distance of 6 meters and 12 meters from the left-hand post, respectively.
By connecting these two points with a curve, which represents the wire suspended between the two poles, we can visualize how the wire is modeled across the gully. The curve will be at a height of 3 meters above the floor throughout, as both sides of the wire have the same height.
1. To find the distance between the two poles, we need to find the value of d when h is equal to zero. Let's set the equation h = 0 and solve for d:
0 = (d - 6) + 3
-3 = d - 6
d = 3
Therefore, the distance between the two poles is 3 meters.
2. On the graph, the distance between the two poles would be represented by the horizontal axis. The height of the wire (h) would be represented by the vertical axis. The curve of the wire would be shown increasing in height as d increases from 0 to 3, and then remaining at a constant height of 3 meters for any values of d greater than 3.