An arch is in the shape of a parabola with its vertex at the top. it has a span of 100 feet and a maximum height of 30 feet. find the equation of the parabola, and determine the height of the arch 35 feet from the center of the base of the arch.

The equation of parabola is , where origin is the center of base. The height of the arch 35 feet from the center of the base of the arch is 15.3 feet.

Step-by-step explanation:

The vertex form of a parabola is

         ... (1)

where, (h,k) is vertex and a is a constant.

Let origin be the center of base.

It is given that the arch is a parabola, it has a span of 100 feet and a maximum height of 30 feet. It means the vertex of the parabola is (0,30) and the parabola passes through the points (-50,0) and (50,0).

Substitute h=0 and k=30 in equation (1).

           ....(2)

The parabola passes through the point (0,50).

Substitute in equation (2).

Substitute x=35 to find the height of the arch 35 feet from the center of the base of the arch.

Therefore, the equation of parabola is , where origin is the center of base. The height of the arch 35 feet from the center of the base of the arch is 15.3 feet.

so, converting firstly the mixed fractions to improper fractions and then "adding".

6e14 is the answer.