An arch for a bridge over a highway is in the form of a semiellipse. the top of the arch is 35 feet above ground (the major axis). what should the span of the bridge be (the length of its minor axis) if the height 25 feet from the center is to be 10 feet above ground?

For given problem:

Put midpoint of ellipse, (0,0) at epicenter of bridge at ground level.

Specified length of vertical major axis = 70=2a

a=35

a^2=1225

 

Equation of ellipse:

 

x^2/b^2+y^2=1

 

plug in coordinates of given point on ellipse(25, 10)

 

25^2/b^2 + 10^2/a^2 = 1

 

625/b^2 + 100/1225=1

 

625/b^2 = 1 - 100/ 1225 = .918

 

b^2 = 625/.918 ≈ 681

 

b ≈ 26.09

 

length of minor axis = 2b = 2(26.09) ≈ 52.16 ft

 

Span of bridge ≈ 52.16 ft

Socrat use det app ok

At a constant it will take one hour to travel 32 mi.at that speed it will take 1/2 hr to travel the remaining 16 mi.it will take 1+1/2 hr to travel the 48mi @ 32mph.so 1 hr = 60 min& 1/2 hr = 30 min1+1/2 hr = 90 min.there are 60s in each 90 × 60 = 3600 seconds.the real question seriously is he why are they driving so slow? ! lol.