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.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.