Two vertical poles of lengths 11 ft and 14 ft stand 16 ft apart. a cable reaches from the top of one pole to some point on the ground between the poles and then to the top of the other pole. where should this point be located to use 30 ft of cable?

Two vertical poles of lengths 11 ft and 14 ft stand 16 ft apart. A cable reaches from the top of one pole to some point on the ground between the poles and then to the top of the other pole.

Let the distance of that point from smaller pole( 11 ft) be x ft. Hence the distance of that point from the larger pole would be (16-x)ft.

The cable forms a right angle triangle with each pole. In Right angle triangle Hypotenuse^2 = Base^2 + Perpendicular^2

The length of the cable connecting the point and the smaller pole is √(11² + x²)

The length of the cable connecting the point and the larger pole is √(14² + (16-x)² )

Total length of the cable is 30 ft

So, √(11² + x²) + √(14² + (16-x)² ) = 30

or, √(11² + x²) - 30 = √(14² + (16-x)² )

squaring both sides,

(11² + x²) + 900 - 60√(11² + x²) = (14² + (16-x)² )

or, 121 + x² + 900 - 60√(11² + x²) = 196 + 256 + x² - 32x

or, 32x + 569 = 60√(11² + x²)

Squaring both sides,

or, (32x + 569)² = 3600(11² + x²)

or, 1024x² + 323761 + 36416x = 3600( 121 + x²)

or, 1024x² + 323761 + 36416x = 435600 + 3600x²

or, 2576x² -36416x + 111839 = 0

Using the quadratic formula, x = 9.6267 ft or 4.5099 ft

Therefore, the point is located at a distance of 9.6267 ft or 4.5099 ft from the smaller pole of height 11 ft.

Hope this helps ..!!

Thank you :)

answer: 38.47 is your answer

step-by-step explanation: hope i you and who ever sees this answer have a great rest of your day : )

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.