Question 711274
A bridge is built in the shape of a semielliptical arch. The bridge has a span of 60 feet and a maximum height of 20 feet. Find the height of the arch at distances 5, 10, and 20 feet from the center. 
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Equation of an ellipse with horizontal major axis with center at (0,0):
{{{x^2/a^2+y^2/b^2=1}}}
For given problem:
b=20
b^2=400
a=30
a^2=900
equation: {{{x^2/900+y^2/400=1}}}
{{{y^2/400=1-x^2/900}}}
{{{y^2=(1-x^2/900)(400)}}}
y=√[(1-x^2/900)(400)]
plug in x-values of 5, 10, and 20 ft
f(5)=√[(1-25/900)(400)]≈19.72 ft (arch height 5 ft from center)
f(10)=√[(1-100/900)(400)]≈18.86 ft (arch height 10 ft from center)
f(20)=√[(1-400/900)(400)]≈14.91 ft (arch height 20 ft from center)