SOLUTION: A bridge is built in the shape of a semielliptical arch. The bridge has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and fi

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Question 855099: A bridge is built in the shape of a semielliptical arch. The bridge has a span of 120 feet and a maximum
height of 25 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of
10, 30, and 50 feet from the center.

Answer by lwsshak3(11628) About Me  (Show Source):
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A bridge is built in the shape of a semielliptical arch. The bridge has a span of 120 feet and a maximum
height of 25 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of
10, 30, and 50 feet from the center
***
Work with an ellipse with a horizontal major axis with center at the origin.
Its form of equation: x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1
a=60
a^2=3600
b=25
b^2=625
equation:
x%5E2%2F3600%2By%5E2%2F625=1
y%5E2%2F625=1-x%5E2%2F3600
take sqrt of both sides:
y%2F25=sqrt%281-x%5E2%2F3600%29
y=25sqrt%281-x%5E2%2F3600%29
y=25%28sqrt%283600-x%5E2%29%2F60%29
y=5%28sqrt%283600-x%5E2%29%2F12%29
f(10)=5%28sqrt%283600-100%29%2F12%29=5%28sqrt%283500%29%2F12%29≈24.65
f(30)=5%28sqrt%283600-900%29%2F12%29=5%28sqrt%282700%29%2F12%29≈21.65
f(50)=5%28sqrt%283600-2500%29%2F12%29=5%28sqrt%281100%29%2F12%29≈13.82