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Question 398076: Hi! Im studying for an exam, im having a problem with this problem, i tried to input the values in the formula(x^2=4py) but cant get the answer.
The problem is:
the distance between two towers is 150m, the points of support of the cable on the towers are 22m above the roadway, and the lowest point on the cable is 7m above the roadway. Find the vertical distance to the cable from a point in the roadway 15m from the foot of a tower.
Can you show me how to get the ordinate of the focal parameter being asked? I tried for almost an hour but still cant get the correct answer. the answer stated in the book is 16.6m
THAN YOU VERY MUCH!!!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! the distance between two towers is 150m, the points of support of the cable on
the towers are 22m above the roadway, and the lowest point on the cable is 7m above the roadway.
Find the vertical distance to the cable from a point in the roadway 15m from the foot of a tower.
:
The cable is a parabola; calculate a quadratic equation from the given dimensions
Using the form: ax^2 + bx + c = y
x=0, y = 22, therefore c = 22
:
x=75, y=7; (the midpoint)
75^2a + 75b + 22 = 7
5625a + 75b = 7 - 22
5625a + 75b = -15
and
x=150, y=22 (far end)
150^2a + 150b + 22 = 22
22500a + 150b = 22 - 22
22500a + 150b = 0
:
Use elimination on these two equations, multiply the 1s equation by 2
subtract from the above equation
22500a + 150b = 0
11250a + 150b = -30
-----------------------subtraction eliminates b, find a
11250a = 30
a = 
a = .002667
:
Find b
22500(.002667) + 150b = 0
60 + 150b = 0
150b = -60
b = 
b = -.4
:
The quadratic equation: y = .00267x^2 -.4x + 22
:
Plotting this equation will help understand this:
You can see the cable is about 7 meters above 0, crossing the vert at 22
:
Find the vertical dist (y) at 15 m from the base of the tower (x)
Substitute 15 for x in the equation
y = .00267(15^2) -.4(15) + 22
y = .00267(225) - 6 + 22
y = .6 - 6 + 22
y = 16.6 is the vertical height, 15 m from the tower
:
How about this? Did it make sense to you? Carl
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