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)
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Studying artifacts is like looking through a keyhole into the past. Although artifacts themselves cannot speak‚ a lot can be learned from studying primary documents and artifacts. For thousands of years‚ historians have been using primary documents and artifacts to make inferences about the people‚ places‚ and events that surrounded the time period. In our study of the Rixford Cemetry‚ we were able to use primary documents and artifacts to make analyses about the surrounding area. There are many
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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
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The first trigonometric table was apparently compiled by Hipparchus‚ who is now consequently known as "the father of trigonometry."[3] Sumerian astronomers introduced angle measure‚ using a division of circles into 360 degrees.[4]They and their successors the Babylonians studied the ratios of the sides of similar triangles and discovered some properties of these ratios‚ but did not turn that into a systematic method for finding sides and angles of triangles. The ancient Nubians used a similar methodology
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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
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Performance Task in GEOMETRY * Computation of the surface area‚ amount and type of needed material and the volume of the package. Volume V= L x H x W = (23 cm) (4 cm) (12cm) = (276) (4) = 1 104 cm Area A= L x W = (23cm) (12cm) = 276cm Surface Area A= 2(Lh) + 2(Lw) + 2(Wh) / 2( lh + lw + wh) = 2(23*4) + 2(23*12) + 2(12*4) = 2(92) + 2(276) + 2(48)
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THE DEFINITION ESSAY EXPLANATION PART I One of the main goals of our definition assignment unit is to practice and learn how to make an argument. Yes! A definition of an abstract concept can be thought of as an argument that you make. “Why? How?” you ask. Think about it this way: when you define an abstract concept you are arguing YOUR DEFINITION is the best definition of that term and you have to convince the reader of that by showing and developing your points. Take the abstract term “courage:”
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Geometry Definitions‚ Postulates and Theorems Definitions Name Complementary Angles Supplementary Angles Theorem Vertical Angles Transversal Corresponding angles Same-side interior angles Alternate interior angles Congruent triangles Similar triangles Angle bisector Segment bisector Legs of an isosceles triangle Base of an isosceles triangle Equiangular Perpendicular bisector Altitude Definition Two angles whose measures have a sum of 90o Two angles whose measures have a sum of 180o A statement
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The Bronx Science Geometry Teachers Proudly Present… THE (ULTIMATE) GEOMETRY REVIEW SHEET (2012 Edition) Some General Information The Regents Exam Basics: Time: 3 hours Problems: 38 ● Part I: 28 multiple choice problems (2 pts each) = 56 pts ● Part II: 6 short answer problems (2 pts each) = 12 pts ● Part III: 3 short answer problems (4 pts each) = 12 pts ● Part IV: 1 long answer problem (6 pts each) = 6 pts ● Total: 86 pts
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Geometry Final Exam Review #1 Semester 2 Name:________________________ Hour:_______ GEOMETRY SEMESTER 2 FINAL REVIEW #1 1. The ratio of the side lengths of ΔOMN to ΔHGI is 4:3. Find x and y. 2. Find f. 3. The triangles are similar. Which choice below is NOT a correct statement? (A) B F (B) ΔBAC~ΔFDE BA FE (C) BC FD AC BC (D) DE FE (E) A D 4. Which of the following statements is not true? (A) ΔABC ~ ΔEDC by SAS~ (B) ΔABC ~ ΔEDC by AA~ (C) ΔABC ~ ΔEDC by SSS~ (D) ΔCDE ~ ΔCBA by SAS~
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