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Question 1013457: a parabolic arch has a width of 18 m across the bottom. at a vertical distance 3 m above the bottom, the width across the arch is 12 m. what is the height of the arch in meters?
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! a parabolic arch has a width of 18 m across the bottom. at a vertical distance 3 m above the bottom, the width across the arch is 12 m. what is the height of the arch in meters?
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Plot the points (-9,0) and (9,0) for the bottom.
2 other points are (-6,3) and (6,3)
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The form is y = -ax^2 + c
0 = -a*81 + c
3 = -a*36 + c
----------------- Subtract
-3 = -45a
a = 1/15
=================
0 = -81/15 + c
c = 5.4
===============
--> 
Height of the arch at the center = 5.4 meters
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! a parabolic arch has a width of 18 m across the bottom.
at a vertical distance 3 m above the bottom, the width across the arch is 12 m. what is the height of the arch in meters?
:
Using the form ax^2 + bx + c = y
arch will be going thru origin, 0,0 so c = 0
Using two pairs; x=3; y=3 and x=15, y=3, construct two equations
x=3; y=3
9a + 3b = 3
Simplify,divide by 3
3a + b = 1
b = (-3a+1)
:
x=15; y=3
225a + 15b = 3
simplify, divide b 3
75a + 5b = 1
Replace b with (-3a+1)
75a + 5(-3a+1) = 1
75a - 15a + 5 = 1
60a = 1 - 5
a = -4/60
a = -.0667
Find b using b = -3a+1
b = -3(-.0667) + 1
b = .2 + 1
b = 1.2
:
The equation for our arch: y = -.0667x^2 + 1.2x
:
Looks like this, green line is y = 3
Axis of symmetry x=9
Find max, the height of the arch
y = -.0667(9^2) + 1.2(9)
y = -5.4 + 10.8
y = 5.4 meters is the height of the arch
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