document.write( "Question 590887: a one-way road passes under an overpass in the shape of half and ellipse, 15ft high at the center and 20ft wide. Assuming a truck is 16ft wide, what is the tallest truck that can pass under the overpass? \n" ); document.write( "
Algebra.Com's Answer #375460 by lwsshak3(11628)\"\" \"About 
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a one-way road passes under an overpass in the shape of half and ellipse, 15ft high at the center and 20ft wide. Assuming a truck is 16ft wide, what is the tallest truck that can pass under the overpass?
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\n" ); document.write( "This problem can be represented by an ellipse with a vertical major axis of the standard form:
\n" ); document.write( "(x-h)^2/b^2+(y-k)^2/a^2=1, a>b, (h,k)=(x,y) coordinates of center.
\n" ); document.write( "..
\n" ); document.write( "center: (0,0) (center line of road)
\n" ); document.write( "a=15 ft (height of overpass at center)
\n" ); document.write( "a^2=225
\n" ); document.write( "b=10 (1/2 the width of the road)
\n" ); document.write( "b^2=100
\n" ); document.write( "equation of ellipse:
\n" ); document.write( "x^2/100+y^2/225=1
\n" ); document.write( "The point at which a truck 16 ft wide would touch the overpass would have and x-coordinates ±8 ft from center. Its y-coordinate is the answer to given problem.
\n" ); document.write( "Plug in x=8 ft in equation to solve for y.
\n" ); document.write( "8^2/100+y^2/225=1
\n" ); document.write( "y^2/225=1-64/100
\n" ); document.write( "y^2=225-225*64/100=81
\n" ); document.write( "y=9 ft
\n" ); document.write( "ans:
\n" ); document.write( "The tallest truck that can pass under the overpass would be 9 feet in height\r
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