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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.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 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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Trough is a half of an ellipse with vertical major axis and center at (0,0)
Its standard form of equation: x^2/b^2+y^2/a^2=1
length of vertical major axis=24=2a
a=12
a^2=144
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length of minor axis=18=2b
b=9
b^2=81
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equation of trough ellipse: x^2/81+y^2/144=1
at a depth of 8, coordinates are (x,y)=(x,-4)
substitute y-value into equation and solve for x
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x^2/81+16/144=1
x^2/81=1-16/144
x^2/81=128/144
x^2=81*128/144
x=±(3/4)*√128≈±8.48
width of surface water=2x=16.97 in
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