DISTANCE CALCULATION
Because of the near-spherical shape of the Earth (technically an oblate spheroid) , calculating an accurate distance between two points requires the use of spherical geometry and trigonometric math functions. However, you can calculate an approximate distance using much simpler math functions. For many applications the approximate distance calculation provides sufficient accuracy with much less complexity.

The following approximate distance calculations are relatively simple, but can produce distance errors of 10 percent of more. These approximate calculations are performed using latitude and longitude values in degrees. The first approximation requires only simple math functions:

Approximate distance in miles:
sqrt(x * x + y * y)
where x = 69.1 * (lat2 - lat1)
and y = 53.0 * (lon2 - lon1)

You can improve the accuracy of this approximate distance calculation by adding the cosine math function Improved approximate distance in miles:
sqrt(x * x + y * y)
where x = 69.1 * (lat2 - lat1)
and y = 69.1 * (lon2 - lon1) * cos(lat1/57.3)

If you need greater accuracy, you can use the Great Circle Distance Formula. This formula requires use of spherical geometry and a high level of floating point mathematical accuracy - about 15 digits of accuracy (sometimes called "double-precision"). In order to use this formula properly make sure your software application or programming language is capable of double-precision floating point calculations. In addition, the trig math functions used in this formula require conversion of the latitude and longitude values from decimal degrees to radians. To convert latitude or longitude from decimal degrees to radians, divide the latitude and longitude values in this database by 180/pi, or approximately 57.29577951. The radius of the Earth is assumed to be 6,378.8 kilometers, or 3,963.0 miles.

If you convert all latitude and longitude values in the database to radians before the calculation, use...

...DistanceBetween 2 points in a Coordinate Plane
Short Description of Lesson: This is a lesson that introduces or reinforces how to find the distancebetween 2 points on a coordinate plane by using the absolute value between 2 points or using the distance formula.
Lesson Objectives: Students will learn how to find the distancebetween two points on a coordinate plane and apply their leaning to find the distancebetween 2 perpendicular lines on a coordinate plane (Glencoe-Geometry 3.6 Perpendiculars and Distance), transformations in the coordinate plane (Glencoe-Geometry 4.3 Congruent Triangles), SSS on the coordinate plane (Glencoe-Geometry 4.4 Proving Congruence –SSS, SAS) and The Distance Formula (Glencoe-Algebra 1 11.5 The Distance Formula).
Materials / Equipments: Computers, LCD projectors for demonstration, virtual manipulative from http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=64 , http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=183 .
Distance Formula Activities I: Students will measure the distancebetween 2...

...Vincenty formula for distancebetween two Latitude/Longitude points
For the benefit of the terminally obsessive (as well as the genuinely needy), Thaddeus Vincenty (‘TV’) devised formulae for calculating geodesic distancesbetween a pair of latitude/longitude points on the earth’s surface, using an accurate ellipsoidal model of the earth.
When I looked up the references (‘Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of nested equations’), I discovered to my surprise that while the mathematics is utterly beyond me, it is actually quite simple to program.
Vincenty’s formula is accurate to within 0.5mm, or 0.000015″ (!), on the ellipsoid being used. Calculations based on a spherical model, such as the (much simpler) Haversine, are accurate to around 0.3% (which is still good enough for most purposes, of course).
Note: the accuracy quoted by Vincenty applies to the theoretical ellipsoid being used, which will differ (to varying degree) from the real earth geoid. If you happen to be located in Colorado, 2km above msl, distances will be 0.03% greater. In the UK, if you measure the distance from Land’s End to John O’ Groats using WGS-84, it will be 28m – 0.003% – less than using the Airy ellipsoid, which provides a better fit for the...

...Calculating the break-even point
To avoid making a loss every business must at least break-even by achieving a level of sales that covers its total costs. But what level of sales is necessary to break-even?
To explore the concept of break-even, we need to define some basic terms:
Fixed costs: Costs that do not vary with output or sales e.g. managers salaries, rent and rates on business premises.
Variable costs: Costs that vary with the quantity produced or sold e.g. costs of materials and wages
Total cost: Fixed costs plus variable costs for any possible level of output.
Sales revenue: The price of the product multiplied by total sales
Profit: The difference between total revenue and total cost (where revenues are higher than costs
Loss: The difference between total revenue and total cost (where costs are higher than revenues)
Selling very small quantities of a product usually results in a loss as any profit fails to cover the overheads or fixed costs of the business.
For example, suppose that the fixed costs (eg management salaries, rent, business rates) for a firm making bookshelves are £1 000 per month. Assume that the varaible cost (materials and labour) for each set of shelves is £30. This means that £20 is generated by each sale (called the 'contribution') towards paying the fixed costs. It follows, therefore, that no profit can be made until 50 bookcases have been sold...

...
The DistanceBetween Us Essay
In the memoir, “The DistanceBetween Us,” by Reyna Grande, Reyna explains how her and her three siblings managed to grow up without any parents. Mago, Carlos, Reyna and their new sister, Betty, all live a rough life without any real type of love from their parents so they have to rely on each other for guidance and support. The four Grande children formed a special bond over the years that they will not leave anyone behind. Each character in the memoir contributes significant personality traits that help the others cope with their current situation.
First, one of the oldest Grande child, Mago, who is caring, courageous, develops leadership amongst everyone and is capable of being a good mother at such a young age. Mago’s mother left her with a huge responsibility to be “their little mother” (12). Mago was stripped of her childhood and forced to mature up. Mago molded Carlos and Reyna into who they are today because of the absence of their mother when they were younger. When she found out the news about the new baby coming, she quickly said, “they’re replacing us”(33). Mago wasn’t please with her mom new baby because she told her mom. Carlos and Reyna believes Mago portrays a much more better mom than their real mom.
Following by Carlos, the second oldest who has a great sense of humor and has ambition to support his sisters. Carlos may not have been the bravest, but he did...

...The distancebetween psychological and social
The distancebetween psychological and social
Emily was often set apart from the town's people because they viewed her as a social icon. She was well respected in the town, because of her father’s wealth and the neighborhood she lives in. This was obvious in the text when it was stated, “Miss Emily had been a tradition, a duty and a care a sort of hereditary obligation upon the town.” (Faulkener, 1)
The town’s people also felt a sense of obligation to Emily, because the town’s previous mayor suspended Emily’s tax responsibilities to the town after her father’s death. Emily seems to be a privileged woman, which may be due to the fact that her father once lent the town money. However, when Emily’s father passed and the man whom she taught would marry her left, she becomes very secluded. This statement from the text gave us an idea of the time frame Emily remained in seclusion, “Two years after her father passed and a short time after her sweetheart went away, people hardly saw her.” (Faulkener, 3) The town’s people tried to visit with her, but she did not receive them. It was not just Emily’s isolation and her suspended taxes that keep the towns people talking about Emily, it was also the horrible, disturbing and offensive smell that came from her house. Just how offensive of a smell it was, was stated in the text when one of the town’s residents stated, “We...

...Jennifer Voisin
Mrs. Johnston
English Composition (sec2)
26 March 2014
The DistanceBetween Us: A Memoir by Reyna Grande
The term “The American Dream” is very broad with many meanings and certainly broader than any single statistic can measure; however we all our own definition of that. Some would say it is building their dream house, going to college, being wealthy, or just having a family. While Reyna Grande’s memoir, The DistanceBetween Us it became clear that term defines most people no matter where you were legally born, how much money you have, or the family you were blessed with. We all go through many struggles throughout our lifetime and Reyna was no different, even after her family’s incomprehensible trials and tribulations; although weighed heavy on her mind, she never let that stop her from letting go of her aspirations and dreams. She had three people in her life that influenced and motivated her, her father, Mago, and Diana. Alike Reyna, I also had three people that inspired me to never give up my dream. My Father, my Aunt Mirta and my husband Scott.
Reyna’s father was a very hard working man, and wanted the best for his children. He might have showed his love for his them in very strange ways; however he always made it very clear that education was the key to their success. “I brought you to this country to get an education and to take advantage of all the opportunities this country has to...

..."Between Heaven and Earth"
Written by Alana Aston
"Between Heaven and Earth" features the dynamic physical theatre performer Stace Callaghan as she attends a "Boot Camp for the Soul". Recently performed at the Powerhouse, the show is a pilgrimage through time, space and soul as it traverses the crevasse between psychological breakdowns and spiritual breakthroughs. Callaghan has said that the show is an "offering of healing" and she has successfully achieved this through the manipulation of dramatic styles, elements and conventions. This intention can be likened to the aim of Greek tragedies, in which the audience would experience a form of emotional cleansing called "catharsis". Throughout the play the tragedy would lead the audience to the realisation that other people suffer much more than them, and consequently the audience felt "ekstasis" or a state of relief. Through a discussion of human context, mood and symbol, it will be discussed how the show was constructed to facilitate "catharsis" and "ekstasis" and consequently become an "offering of healing".
Human context has been skilfully used as all eight characters are mediums through which inspiration and healing was offered to the audience. For Example, Guru Frank's role was to utilise the very powerful tool of laughter. Through doing so, the audience becomes more open to his philosophical ideas and participating in some of his...

...Chapter 42 – Epilogue
Rennie
Rennie sat in the lobby with his coat waiting for his cousins to come pick him up. As he waited, he fiddled with the zipper of his coat looking back at his adventure in Iceland. He wondered to himself how he lived through such a cold environment. After waiting a while, I turn around to see my cousing D.J. looking at me.
“Rennie!” he cried scaring me out of my pants. “Yipes! You scared me!” I replied. I’ve never seen D.J. before, but he has a pretty similar resemblance to me. I find my luggage, pick it up and look inside of it. Nothing was missing. Good. As we walk to our car, I see the old man and shoot him a thanks. He winks back.
D.J.
D.J was smiling the whole way back. “All cousins accounted for” he thought to himself. He couldn’t wait to share his adventures on Mount Kilimanjaro with the rest of his cousins. He pondered on the thought of his grandfather, and how he would be proud that everyone has completed their tasks successfully. He even wondered if spirits from the dead visit them on Halloween.
After an hour long drive, they reached the old and wrecked house their grandfather used to live in. Everyone was at the door welcoming Rennie; the lost cousin. As D.J. entered his grandfather’s old home he saw streamers and junk food as if this were a birthday party. But this was a celebration party. We partied for a while, then rested on the couch playing video games. 10 minutes into our game, My mother stood up real high on a stool and...

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