Respuesta :
Answer:
y = (x - 10)^2 / 100 + 1
Step-by-step explanation:
given:
A suspension footbridge has two 2-meter vertical supports 20 meters apart so the cable connecting 'em will be a convex parabola
The lowest point of the cable, which is the vertex, 1 meter above the path.
y-axis represents the left support and the other vertical support is at x=20
by symmetry, the vertex is mid-pt between the two supports, @ x=20/2=10
so vertex is at (10,1)
vertex form of parabola is y = a(x - h)^2 + k, where (h, k) is the vertex
so y = a(x-10)^2 + 1
at y-axis, x=0, y=2
2 = a(0-10)^2 + 1
2 - 1 = 100a
a = 1/100
so the eqn is y = (x - 10)^2 / 100 + 1
Answer:
The final equation is y = 0.01(x - 10)^2 + 1
Step-by-step explanation:
The vertex form of a parabola is given by f(x) = a(x - b)^2 + c, where (b, c) is the vertex of the parabola.
To find the vertex, it is given that " two 2-meter vertical supports 20 meters apart" and "The lowest point of the cable connecting them is 1 meter above."
The vertex will be at the mid-point between the two supports: b = 20/2 = 10m
It is 1m above so c = 1m
Substituting into f(x), y = f(x) = a(x - 10)^2 + 1
On the support 20m away from y-axis, x=20, y=2
2 = a(20 - 10)^2 + 1
1 = 100a
a = 0.01
The final equation is y = 0.01(x - 10)^2 + 1
