document.write( "Question 651961: \"A cross section of a trough is a semi-ellipse with width at the top 18 in. and depth 12 in. The trough is filled with water to a depth of 8 in. Find the width at the surface of the water. \n" ); document.write( "
Algebra.Com's Answer #409792 by lwsshak3(11628)\"\" \"About 
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A cross section of a trough is a semi-ellipse with width at the top 18 in. and depth 12 in. The trough is filled with water to a depth of 8 in. Find the width at the surface of the water.
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\n" ); document.write( "Trough is a half of an ellipse with vertical major axis and center at (0,0)
\n" ); document.write( "Its standard form of equation: x^2/b^2+y^2/a^2=1
\n" ); document.write( "length of vertical major axis=24=2a
\n" ); document.write( "a=12
\n" ); document.write( "a^2=144
\n" ); document.write( "..
\n" ); document.write( "length of minor axis=18=2b
\n" ); document.write( "b=9
\n" ); document.write( "b^2=81
\n" ); document.write( "..
\n" ); document.write( "equation of trough ellipse: x^2/81+y^2/144=1
\n" ); document.write( "at a depth of 8, coordinates are (x,y)=(x,-4)
\n" ); document.write( "substitute y-value into equation and solve for x
\n" ); document.write( "..
\n" ); document.write( "x^2/81+16/144=1
\n" ); document.write( "x^2/81=1-16/144
\n" ); document.write( "x^2/81=128/144
\n" ); document.write( "x^2=81*128/144
\n" ); document.write( "x=±(3/4)*√128≈±8.48
\n" ); document.write( "width of surface water=2x=16.97 in
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