A cable hangs in a parabolic arc between two poles 100 feet apart. The poles are 30 feet high and the lowest point on a suspended cable is 5 feet above the ground
a) find the equation of the arc if the vertex is the lowest points of the cable
b) find the height of the cable at a point 10 feet from one of the poles
a) Let point "(0, 5)" be the vertex of the parabola. Then the equation of the parabola will be
Given "y(-50)=y(50)=30." Substitute
"a=0.01"
The equation of the arc is
"y=0.01x^2+5"b)
If "x_1=50-10=40"
"y=0.01(40)^2+5""y=21"
The height of the cable at a point 10 feet from one of the poles is "21" feet.
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