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
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Work with an ellipse with a horizontal major axis with center at the origin.
Its form of equation: {{{x^2/a^2+y^2/b^2=1}}}
a=60
a^2=3600
b=25
b^2=625
equation:
{{{x^2/3600+y^2/625=1}}}
{{{y^2/625=1-x^2/3600}}}
take sqrt of both sides:
{{{y/25=sqrt(1-x^2/3600)}}}
{{{y=25sqrt(1-x^2/3600)}}}
{{{y=25(sqrt(3600-x^2)/60)}}}
{{{y=5(sqrt(3600-x^2)/12)}}}
f(10)={{{5(sqrt(3600-100)/12)=5(sqrt(3500)/12)}}}≈24.65
f(30)={{{5(sqrt(3600-900)/12)=5(sqrt(2700)/12)}}}≈21.65
f(50)={{{5(sqrt(3600-2500)/12)=5(sqrt(1100)/12)}}}≈13.82