Question 826452: Okay, I am stuck with Paul's trucking company which hauls oversized loads. The truck travels through a tunnel with a wide opening in the shape of a parabola that is 12 meters wide and and 6 meters high.
How do I find a function, T(x), for the shape of the tunnel. I am also supposed to draw it but it would be a huge favor if I get a walk-in through this and that won't be much of a work if I get that far.
I appreciate the help in advance, and I look forward to get a reply soon. Thanks :)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The truck travels through a tunnel with a wide opening in the shape of a parabola that is 12 meters wide and and 6 meters high.
:
using the form ax^2 + bx + c = y
Let's have the parabola have the axis of symmetry at 0, then c = 6
and the x intercepts will be -6 and +6 (12 m apart)
write an equation for x = 6, y = 0 and for x = -6, y = 0
36a + 6b + 6 = 0
36a - 6b + 6 = 0
-----------------adding eliminates b, find a
72a + 12 = 0
72a = -12
a = -12/72
a = -.167
The middle term cancels so we can write the equation
T(x) = -.167x^2 + 6
y = -.167x^2 + 6, graphically
note that it is 12m wide and 6 m high
:
You can create a table using x and finding y to determine what the height the
truck can be if you know the width of the truck
For example if the truck were 8 ft wide, (x = +4, -4), then
-.167(4^2) + 6 = 3.3 meter, load height has to be less than 3.3 meters (green line)
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