SOLUTION: A bridge underpass in the shape of an elliptical arch, that is, half of an ellipse, is 20 feet wide and 12 feet high. An eight foot wide rectangular truck is to drive (safely) unde

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A bridge underpass in the shape of an elliptical arch, that is, half of an ellipse, is 20 feet wide and 12 feet high. An eight foot wide rectangular truck is to drive (safely) unde      Log On


   

Question 969478: A bridge underpass in the shape of an elliptical arch, that is, half of an ellipse, is 20 feet wide and 12 feet high. An eight foot wide rectangular truck is to drive (safely) underneath. How high can it be?
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Answer by lwsshak3(11628) About Me  (Show Source):
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A bridge underpass in the shape of an elliptical arch, that is, half of an ellipse, is 20 feet wide and 12 feet high. An eight foot wide rectangular truck is to drive (safely) underneath. How high can it be?
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Draw an ellipse with vertical major axis with center center at the origin:
Form of equation:x%5E2%2Fb%5E2%2By%5E2%2Fa%5E2=1
For given problem:
a=12
a^2=144
b=10
b^2=100
equation: x%5E2%2F100%2By%5E2%2F144=1
x-coordinate where 8 ft rectangular truck can drive (safely) underneath=4
4%5E2%2F100%2By%5E2%2F144=1
y^2/144=1-16/100
y^2/144=84/100
y=√(144*84/100)
y≈11
How high can the truck be? 11 ft