Structured program list. First unit: Sets. In this unit the fundamental concepts of the theory of sets is addressed to provide the tools and the language of operation for subsequent units. Second unit: numbering systems. In this unit‚ we address numbering systems of different cultures until the one’s used current day‚ highlighting the importance of ten based numbering system (decimal)‚ which will be developed in depth by tackling its properties through the next unit. Unit Three: The field
Premium Analytic geometry Polynomial Number
CET11 Mathematics Question Bank – Straight Lines‚ Pair of Lines & Circles A straight line through the point A 3‚ 4 is such that its intercept between the axes is bisected at A . It’s equation is 1. (a) 4 x 3 y 24 Ans: a (b) 3x 4 y 25 (c) x y 7 (d) 3x 4 y 7 0 Sol: By formula required equation is given by x y 2 4 x 3 y 24 3 4 2. The equation of the line which is the perpendicular bisector of the line joining the points 3‚ 5 and 9‚3 is (a)
Premium Circle Euclidean geometry Analytic geometry
Analytic geometry‚ or analytical geometry‚ has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties. This article focuses on the classical and elementary meaning. In classical mathematics‚ analytic geometry‚ also known as coordinate geometry‚ or Cartesian geometry‚ is the study of geometry using a coordinate system and the principles of algebra and analysis. This contrasts with the synthetic approach of Euclidean geometry‚ which treats
Premium Analytic geometry Geometry Euclidean geometry
C OORDINATE GEOMETRY COORDINATE GEOMETRY 155 7 7.1 Introduction In Class IX‚ you have studied that to locate the position of a point on a plane‚ we require a pair of coordinate axes. The distance of a point from the y-axis is called its x-coordinate‚ or abscissa. The distance of a point from the x-axis is called its y-coordinate‚ or ordinate. The coordinates of a point on the x-axis are of the form (x‚ 0)‚ and of a point on the y-axis are of the form (0‚ y). Here is a play for you. Draw a set
Premium Analytic geometry Line
Coordinate geometry The Basics: Find the distance between two points using Pythagoras’ theorem. The midpoint is the average (mean) of the coordinates. The gradient = Parallel lines have the same gradient. The gradients of perpendicular lines have a product of -1. Straight Lines: Equation of a straight line is y = mx + c‚ where m = gradient‚ c = y-intercept. The equation of a line‚ if we know one point and the gradient is found using: (y - y1) = m(x - x1) (If given two points‚ find the
Premium Analytic geometry Euclidean geometry Cartesian coordinate system
Question:An architect designs two houses that are shaped and positioned like a part of the branches of the hyperbola whose equation is 625y^2 - 400x^2=250‚000‚ where x and y are in yards. How far apart are the houses at their closeset point? Answers:625y^2 - 400x^2=250‚000 y^2 / 20^2 - x^2 / 25^2 = 1 The closest two points on separate branches are the vertices‚ and their separation is 2 * 20 = 40yd. I find the question a little confusing‚ though. Question:LORAN (long distance radio navigation)
Premium Analytic geometry
robot kinematics‚ require a unified methodology to identify the variables of a robot’s or manipulator’s joints and links. Co-ordinate Frames Robotic kinematics depends on the use of right handed cartesian frames of reference. Manipulator Geometry A manipulator consists of two types of joints‚ connected by a link. Link A link is a solid mechanical structure which connects two joints. The main purpose of a link is to maintain a fixed relationship between the joints at its ends. The
Premium Robotics Euclidean geometry Analytic geometry
TIMELINE OF GEOMETRY It is believed that geometry first came to being when and Egyptian Pharaoh wanted to tax farmers who raised crops near the Nile River. To do that the pharaoh’s agents had to measure the amount of land that was being used. 1. 2900 BC – The first pyramid was constructed. The knowledge of geometry was important due to the fact it consisted a square base and triangular faces. 2. 2000 BC- It was the earliest record of calculating the area of a triangle‚ however there is
Premium Geometry Mathematics Pythagorean theorem
Geometry Rationale Geometry is Greek for geos‚ which means Earth‚ and metron meaning measure. It can conceivably lay claim to being the oldest branch of mathematics outside arithmetic‚ and humanity has probably used geometrical techniques since before the dawn of recorded history. Initially‚ as with the Egyptians‚ geometry originated from practical necessity and the need to measure land. Geometry today is the science of observing and measuring shapes‚ surfaces‚ angles‚ lines and the relationships
Premium Mathematics Shape Geometry
Geometry was throughly organized in about 300 B.C‚ when the Greek mathematician‚ Euclid gathered what was known at the time; added original book of his ownand arranged 465 propositions into 13 books called Elements. Geometry is the mathematics of space and shape‚ which is the basis of all things that exist. Understanding geometry is necessary step by understanding how the things in our world exist. The applications of geometry in real life are not always evident to teenagers‚ but the reality is
Premium Geometry Mathematics Dimension