SOLUTION: A bridge spans a river. Its two towers are 3500 feet apart and rise 323 feet above the road. The cable between the towers has the shape of a parabola and the cable just touches the

Question 1110582: A bridge spans a river. Its two towers are 3500 feet apart and rise 323 feet above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. The parabola is positioned in a rectangular coordinate system with its vertex at the origin. The point (1750,323) lies on the parabola, as shown. Complete parts a and b.
a. Write an equation in the form y=ax`2 the parabolic cable. Do this by substituting 1750 for x and 323 for y and determining the value of a.
y=_____x`2 (Round to seven decimal places as needed.)
Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Work that out to 7 decimal places.
Why 7? Why not 19?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A bridge spans a river. Its two towers are 3500 feet apart and rise 323 feet above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. The parabola is positioned in a rectangular coordinate system with its vertex at the origin. The point (1750,323) lies on the parabola, as shown. Complete parts a and b.
a. Write an equation in the form y=ax`2 the parabolic cable. Do this by substituting 1750 for x and 323 for y and determining the value of a.
----------
Three points are known: (-1750,323), (0,0) and (1750,323)
ax^2 + bx + c = 0 is the parabola.
c = 0 since the vertex is at the Origin.
---
y = ax^2 + bx
ax^2 + bx = y
a*(-1750)^2 - 1750b = 323
a*1750^2 + 1750b = 323
----------------------------------- Add
2a*1750^2 = 646
a =~ 0.00010546939
---
b = 0
------
y = 0.00010546939x^2

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