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Preet kumar

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Football as most enthusiasts call it, takes the crown as the most played and watched sport across the globe. But is football just a sport of running and kicking? Is there any strategy to it at all? fo

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QUESTION ON APPLICATION OF ARITHMETIC PROGRESSION  

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QUESTION ON APPLICATION OF ARITHMETIC PROGRESSION  

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A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: 200 for the first day, 250 for the second day, 300 for the third day, etc., the penalty for each succeeding day being 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days ?

The amount paid in the form of penalty is in the form of following AP:

Here, a = 200, d = 250 - 200 = 50 and n = 30. The sum of n terms of an AP is given by

Sn = n/2 [2a + (n - 1)d]

→ S30= 30/2[2(200) + (30 – 1)(50)]

= 15[400 + 1450]

15(1850) = 27750

Hence, the contractor has to pay 27750 as penalty for the delay of 30 days.

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The uses of geometry in our daily conversation. 

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The uses of geometry in our daily conversation. 

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There are many uses of coordinate geometry but some of them are :

1.Point your finger towards that student.
2.Walk towards his or her seat.
3.Say something like "the person sitting in the 4th row and 5th column", or "the person sitting in the left corner", or "the first student in the second last bench".

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Applications of Coordinate geometry.

Digital World of Mobiles, Computers: The Coordinate Geometry is used in each and every process of Digitronics. Whenever you open a PDF file or Text file, where the images and texts are modified with the use of coordinate geometry. Consider a PDF file with images, words, different shapes, they’re placed in a 2D coordinate plane of X and Y axes. Distances, Slopes, Trigonometry are also applicable here.

Describing position of an object: The Coordinate Geometry is used to find and describe the position of an object from it’s initial position, called Origin, where, all the coordinate axes intersect. Say, a book is placed above 10 m from the ground, 20 m from the place the observer is sitting. The width of room is 30 m. So, using this information, it’s easy to find the coordinates and distance from observer and the object, i.e., book.

Location of Aeroplanes or other Areal transports: We have all seen the planes and it’s all depended on Coordinate Geometry that the plane reaches it’s destination correctly. The RADAR technology is combined with Coordinate Geometry to get the correct position and make it reach exact destination.

Map Projections: All of us use Google Maps every day to navigate and commute. We see the graph like lines before loading the maps. So, easily we can tell Coordinate Geometry is used. We also have 2D and 3D maps, all accurate. Thanks to Coordinate Geometry.

Latitude and Longitudes: Latitudes and Longitudes are completely based on Coordinate Geometry.

Global Positioning System(GPS)

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In Islamic culture , geometric design is everywhere : you can find it in mosques , palaces and private homes . And despite the remarkable complexity of these designs , they can be created with just a compass to draw circles and a ruler to make lines within them .

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The complex geometry of Islamic design - Eric Broug

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The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (x; y) coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −).

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The invention of calculus was an extremely important development in mathematics that enabled mathematicians and physicists to model the real world in ways that was previously impossible. It brought together nearly all of algebra and geometry using the coordinate plane. The invention of calculus depended on the development of coordinate geometry

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Choose a point in the plane, called the origin, and draw two perpendicular axes through it, one horizontal and one vertical. Any point in the plane can be reached from the origin by travelling a certain distance x along the horizontal axis and a certain distance y along the vertical axis. The numbers (x,y) are the coordinates of the point. The origin itself has coordinates (0,0). The part of the horizontal axis (also called the x-axis) that lies to the left of the origin and the part of the vertical axis (the y-axis) below the origin are described by negative numbers.