Answer:
Step-by-step explanation:
h(x)=ax^2
Given h=30 when x=150 we get
a(150)^2=30
a=30/22500=1/750 so
h(x)=x^2/750
The equation [tex]\rm h(x)= \frac{1}{750} x^2[/tex] represents the height of the cable at a distance x feet from the center.
It is given that the cable for a certain suspension bridge is modeled by a parabola with vertex (0,0).
It is required to derive the equation that represents the height of cable at a distance x feet from the center.
It is defined as the graph of a quadratic function that has something bowl-shaped.
We have the bridge is modeled by a parabola with vertex (0,0)
We know the general equation of parabola:
[tex]\rm y= a(x-h)^2+k[/tex] with vertex (h,k)
Here the value of h = 0 and k = 0
[tex]\rm h(x)= ax^2[/tex] ( ∵ y = h(x) represented the function in terms of height)
We have h = 30 at x = 150 (From the question)
Putting the value of h and x in the parabola equation, we get:
[tex]\rm 30 = a(150)^2[/tex]
[tex]\rm a = \frac{1}{750}[/tex]
Putting the value of 'a' in the parabola equation, we get:
[tex]\rm h(x)= \frac{1}{750} x^2[/tex]
Thus, the equation [tex]\rm h(x)= \frac{1}{750} x^2[/tex] represents the height of the cable at a distance x feet from the center.
Know more about the parabola here:
brainly.com/question/8708520
