Abridge is built in the shape of a semielliptical arch. the bridge has a span of 100 feet and a maximum height of 20 feet. choose a suitable rectangular coordinate system and find the height of the arch at a distance of 30 feet from the center

16 feet height of the arch at a distance of 30 feet from the center

Step-by-step explanation:

Given data

span = 100 feet

height = 20 feet

to find out

the height of the arch at a distance of 30 feet from the center

solution

we know the equation of elliptical i.e.

x²/a² + y²/b² = 1     ......................1

from question we can say that length of major axis i.e

2a = 100

so a = 50

and height is

b = 20

so put a and b in equation 1

x²/a² + y²/b² = 1

x²/50² + y²/20² = 1

x²/2500 + y²/400 = 1

y²/400  = 1 -  x²/2500

y / 20 =  

y = 20

so now take value 30 for function f(30)

f(30) = 20

f(30) = 20

f(30) = 16 feet

so 16 feet height of the arch at a distance of 30 feet from the center