Question 547162: A concrete bridge over a river has an underside in the shape of a parabolic arch. At the water level, the arch os 20m wide. It jas a maximum height of 10m about the water. The minimum vertical thickness of the concrete is 1.5m.
a) find an algebraic relation that represents the shape of the arch.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A concrete bridge over a river has an underside in the shape of a parabolic arch. At the water level, the arch is 20m wide. It has a maximum height of 10m above the water. The minimum vertical thickness of the concrete is 1.5m.
:
I am not sure what the thickness of the concrete means to this problem, anyway, this is an equation for the underside of the arch
:
a) find an algebraic relation that represents the shape of the arch.
three ordered pairs
x=0, y=0; the left side of the arch at the waterline
x=10,y=10; the max height of the arch (the vertex)
x=20,y=0; the right side of the arc at the waterline
:
Using the form ax^2 + bx + c = y
c = 0, so we just need two equations to find a and b
:
x=10, y=10
a*10^2 + 10b = 10
100a + 10b = 10
:
x=20, y=0
a*20^2 + 20b = 0
400a + 20b = 0
Multiply the 1st equation by 2, subtract from the above equation
400a + 20b = 0
200a + 20b = 20
----------------subtraction eliminates b, find a
200a = -20
a = -20/200
a = -.1
;
Use the 1st equation to find b
100(-.1) + 10b = 10
-10 + 10b = 10
10b = 10 + 10
10b = 20
b = 20/10
b = 2
:
The equation for this arch: y = -.1x^2 + 2x
:
Graphically
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