The suspension bridge cables are in the shape of a parabola. The distance between two towers supporting the cable are 800 feet apart and the height is 200 feet. If the vertical support cables are at 100 feet intervals along
To determine the height of each vertical support cable, we can use the equation of a parabola in vertex form: y = a(x - h)^2 + k, where (h, k) represents the vertex.
In this case, the vertex of the parabola represents the highest point, and we know it is located at the midpoint between the two towers. The x-coordinate of the vertex is the halfway point between the two towers, which is (800/2), or 400. The y-coordinate of the vertex is the height of the bridge, which is 200.
Now, let's substitute the known values into the equation: y = a(x - 400)^2 + 200.
To determine the value of 'a,' we'll use one of the vertical support cables. We know that the vertical support cables are located at 100-foot intervals, so we can take the coordinates of one of these points and substitute them into the equation.
Selecting the coordinates (x, y) = (400, 300), we can substitute them into the equation: 300 = a(400 - 400)^2 + 200.
Simplifying the equation: 300 = a(0) + 200
300 = 200
Since 300 ≠ 200, this means that there was an error in selecting the coordinates. The correct coordinates for the vertical support cables should satisfy the equation. Let's try a different set of coordinates, (x, y) = (400, 100).
Substituting these coordinates into the equation: 100 = a(400 - 400)^2 + 200.
100 = a(0) + 200
100 = 200
Again, 100 ≠ 200, so there was an error in selecting the coordinates. It seems that I made a mistake in understanding the problem, as the equation does not seem to have a valid solution. I apologize for any confusion caused.