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You can put this solution on YOUR website! let ABCD be your parallelogram A is bottom left B is top left C is top right D is bottom right. ----- let ABCD lean to the right so that point B is slightly to the right of point A. all you need is a little tilt to show that it's not a rectangle. ----- draw diagonals AC and BD...
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What does an octahedron have to do with BATSE? The octahedron represents the Large Area Detector (LAD) geometry when BATSE is installed on the Compton Gamma-Ray Observatory. The LADs on each of the eight BATSE modules are oriented so that when the module is in a horizontal position, the face of each LAD is at an angle ...
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constructing a line perpendicular to a line from a given point on the line Answers I don't really understand what you're asking, but if you're asking how to do it, then you take your compass, set it to some random length, and take that random length on both sides of the line. Then, at the intersections of the circle th...
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Inside this large rectangular border, draw a blob — yes, blob — with an area that's approximately 1/5 of the rectangle's area. No one will die if it's not quite 1/5. Next, draw a dot anywhere inside the rectangle but outside the blob. Label this dot H. Now, draw another dot — but listen carefully! — so that there's no ...
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It mentions subtracting the pivot point, but should I subtract the distance to the pivot point? Since my pivot point is $(0,0)$ it sounds too easy, to just subtract 0 (and also doesn't give me the results I expect). As an example, I have a point in $ (2328.30755138590, 1653.74059364716) $ (very accurate, I know). I nee...
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Going Down - Angles Of Depression Sorry, you need to install Flash and/or enable javascript in your browser to see this content. The latest version of Flash can be found at Adobe's website. Angles of depression are angles that are measured from the horizontal downwards. Learners should be able to recognise situations w...
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tan = sine/cosine cotan = cosine/sine arcfunctions are easy, they're 1/function (or is that inverse, or are arc and inverse the same?) or it might be arcfunction = function ^ -1? hell i barely remember trig, but thats what reference tables are for. all that really matters is that you can form all of the trigonometric f...
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Question 68027: CATS is a square. CT = 6 times the square root of 2. if CT is the diagnal of the square. what is the distance of CA (any one side of the square). My son has this problem and we've checked his Geometry book and see no samples that can assist us. Thank you. Click here to see answer by Nate(3500) Question ...
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(edit added more explanation) I'm trying for the best possible fit. at each angle a different part of the coasts fit, pretty well, but then the other corresponding shorelines, further away, went out of position. All the shoreline shapes, of both continents, would fit together perfectly on a smaller globe. Remember, the...
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where $A$, $B$, $C$ are the areas of the "leg-faces" and $D$ is the area of the "hypotenuse-face". For right-corner simplices in higher Euclidean dimensions, we have that the sum of the squares of the content of leg-simplices equals the square of the content of the hypotenuse-simplex. (I don't happen to know the non-Eu...
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It is not certain precisely what statements Euclid assumed for his postulates and axioms, nor, for that matter, exactly how many he had, for changes and additions were made by subsequent editors. There is fair evidence, however, that he adhered to the second distinction and that he probably assumed the equivalents of t...
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Proposition 78 If from a straight line there is subtracted a straight line which is incommensurable in square with the whole and which with the whole makes the sum of the squares on them medial, twice the rectangle contained by them medial, and further the sum of the squares on them incommensurable with twice the recta...
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Angular mil This article describes "mil" as a unit of angle. For alternative meanings, see Mil (disambiguation). The mil (in full, angular mil) is a unit of angular measure common in the military of many countries. There are three different specifications for the unit, each roughly 1000th of a radian. The name of the m...
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Triangles - Concurrent Lines - Altitudes and Medians This geometry worksheet contains problems on concurrent lines in triangles. Concepts and vocabulary include points of concurrency, perpendicular bisectors, angle bisectors, altitudes, medians, and centroids. There are also problems on finding the center of a circle t...
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$ABCD$ is a square with a side of length 4. P is on AB, S is on CD and Q is on PS such that: $AP = CS$ The triangles $PBR$ and $SDQ$ are both equilateral triangles. See the image below. Calculate the combined area of the 2 triangles. What would be the easiest way the solve this? I first tried to name SC x, and then mak...
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About the CSEM Club The purpose of the CSEM Club at CCBC-Catonsville is to develop and nurture interest in mathematics and Computer Science among the students at the Catonsville campus of the Community College of Baltimore County (CCBC) through meetings, informal mutual discussions, field trips, etc. The CSEM Club also...
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some ideas By cptjway You could have the students work in pairs to do a "scavenger hunt" in your room, to find examples of each type of angles. Example: the squares on the floor are right angles, the letter A on the bulletin board shows an acute angle. They could write each example on a sticky, then stick them on the b...
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Let t and s (t > s) be the sides of the two inscribed squares in a right triangle with hypotenuse c. Then s2 equals half the harmonic mean of c2 and t2. Let a trapezoid have vertices A, B, C, and D in sequence and have parallel sides AB and CD. Let E be the intersection of the diagonals, and let F be on side DA and G b...
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repeated with the fixed point outside the circle. The result is an envelope of tangent lines of the hyperbola with foci at the fixed point and the center of the circle. The lemniscate An interesting extension for the hyperbola is to consider an envelope of circles generated by taking a variable point on the hyperbola a...
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I don't even know where to begin with this. Someone please help me step by step? Thanks! 1 solutions Answer 209906 by richwmiller(9135) on 2010-04-08 12:25:22 (Show Source): Triangles/289968: C. If the triangle has one angle that measures 35 degrees and another angle that measures 105 degrees, what is the measure of it...
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These names follow from the fact that they are customarily written in terms of the haversine function, given by haversin(θ) = sin2(θ/2). The formulas could equally be written in terms of any multiple of the haversine, such as the older versine function (twice the haversine). Historically, the haversine had, perhaps, a ...
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There is something wrong with the third problem, if 2 of the three angels of the triangles formed are the same it means the third angles are the same meaning so why are the arcs different lengths? Answers Nothing is wrong with this problem because no central angles are present. If the vertex of the third angle in each ...
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The same construction can also be applied to the hyperbola. If P0 is taken to be the point (1,1), P1 the point (x1,1/x1), and P2 the point (x2,1/x2), then the parallel condition requires that Q be the point (x1x2,1/x11/x2). It thus makes sense to define the hyperbolic angle from P0 to an arbitrary point on the curve as...
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In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight. This entails that a line is a special case of curve, namely a curve with null curvature. Often curves in two-dimensional (plane curves) or three-dimensional (s...
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In mathematics, domain is an important concept in a function. Domain is defined as a set of input value or arguments. The set of all the output values is called as a range. The range is an interval ... In geometry, a Cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are two competing (bu...
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measure, side length, perimeter, and area learn this concept to design a 45*, 90* or 180* of all types of triangles. haircut. G1.2.5 Solve multi-step problems and construct Salon design project. proofs about the properties of medians, altitudes, and perpendicular bisectors to the sides of a triangle, and the angle bise...
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A sketch of the proof can be found below. Hence, we know that if a weeble of uniform density exists then it cannot be effectively two-dimensional. What we can observe is that the 2D oval has two stable equilibria and for any number greater or equal to three the regular polygon with "n" sides will have "n" stable equili...
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Given a line and a point not on it, at most one parallel to the given line can be drawn through the point. It is equivalent to Euclid's parallel postulate and was named after the Scottish mathematicianJohn Playfair. It is only required to state "at most" because the rest of the postulates will imply that there is exact...
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It is numerically less efficient than Newton's method but it much less prone to odd behavior. In geometry, bisection refers to dividing an object exactly in half, usually by a line, which is then called a bisector. The most often considered types of bisectors are segment bisectors and angle bisectors. A segment bisecto...
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In this context (a,b) changes meaning; it means a is party to the same information as b which implies that b is party to the same information as a. Again, in this context (a,b) is the same as (b,a). An arc (a,b) or a → b in digraph G has changed because of the perspective or interpretation into an edge (a,b) or a ↔ b. ...
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A new era in determining the size of Earth began through the introduction of triangulation. The idea of triangulation was apparently conceived by the Danish astronomer Tycho Brahe before the end of the 16th century, but it was developed as a science by a contemporary Dutch mathematician, Willebrord van Roijen Snell. Sn...
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where $A$, $B$, $C$ are the areas of the "leg-faces" and $D$ is the area of the "hypotenuse-face". For right-corner simplices in higher Euclidean dimensions, we have that the sum of the squares of the content of leg-simplices equals the square of the content of the hypotenuse-simplex. (I don't happen to know the non-Eu...
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In this lesson, students develop the area formula for a triangle. Students find the area of rectangles and squares, and compare them to the areas of triangles derived from the original shape. Student handouts are included here. Congruence of Triangles (Grades 6-8) With this virtual manipulative, students arrange sides ...
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Question 146950: THIS IS THE MOST IMPORTANT QUESTION ON MY HOMEWORK AND I JUST CAN'T FIGURE IT OUT!!! please help ! A 25 foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top of the ladder slips down by 4 feet, by how many feet will the bottom slide out? Click here t...
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Question 147271: If it is know that one pair of alternate interior angles is equal, what can be said about... -the other pair of alternate interior angles -either pair of alternate EXTERIOR angles -any pair of corresponding angles -either pair of non-alternate interior angles. Question 147488: Let A = (1,1), B = (3,5),...
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From the Delaunay triangulation one can compute a list of adjacent triangles and the three angles of each triangle. Table 1 displays a list of the angles and the adjacent tringles for each triangle in FIG. 3. TABLE 1 Adjacent Triangles angles Triangle 1 0 0 2 30 31 119 Triangle 2 3 1 4 89 61 30 Triangle 3 0 2 5 45 88 4...
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Arc BE measures 118 because it is twice the measure of the inscribed angle D which is 59 degrees. Therefore, angle y is 1/2 the measure of arc BE because it is also an inscribed angle. Angle y is the same measure as angle D because they both intercept the same arc BE. To find the measure of arc DF we have to subtract t...
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OK, we all know average people tend to use either degrees or turns to measure angles, whereas mathematicians use radians, some other people use gradians, mils, or both, and there are other standards besides (points for boxing the compass, quadrants for studying your geometry, etc.). My question is, are any of these mor...
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Points, Lines and Curves The most practical branch of mathematics is geometry. The term 'geometry' is derived from the Greek word 'geometron'. Lesson Demo The most practical branch of mathematics is geometry. The term 'geometry' is derived from the Greek word 'geometron'. It means Earth's measurement. The fundamental e...
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Question 150882: Hello, can you please help me solve this problems: 1.) The sum of the measures of two angles is 180 degrees. Three times the measure of one angle is 24 less than the measure of the other angle. What is the measure of each angle? 2.) The length of a rectangle is 17cm larger than its width. When its widt...
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The coordinate geometry is not difficult. The best way to do well on the coordinate geometry is to know the formulas very well. Here we list the most commonly used formulas on coordinate geometry. By knowing these formulas, we guarantee you will do well on the coordinate geometry. The Distance Formula: The distance d b...
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Facebook Daily Deal - Parts of a Circle Charts $9.00 Add to Cart: Help your students remember the different parts of a circle and brighten up your classroom with these 9 colourful posters. Each card contains a diagram and description of the following: Semi-circle, arc, radius, diameter, circumference, centre, chord, qu...
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Polar Coordinates Remember that when r is negative, you go to the opposite side of the graph. Remember that each point has many different possible sets of polar coordinates. (This is different from rectangular coordinates, where each point has a unique (x, y) pair.) To find the limits, you often have to draw the graph ...
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Math: Trigonometric Identities These sites are about trigonometric identities. The topics cover trigonometric identities, functions, and properties. Learn how to apply trigonometric identities to solve trigonometric problems. There are also interactive illustrations on Proof of the Pythagorean Theorem and Triangles and...
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Chapter Fifteen With the Canon of Sines for Hundredths or Thousandths of Degrees, the Canons of Tangents, Secants, and of Logarithms are being provided with the same parts. Prop.1. Tangents and Secants are most conveniently being found by the Rule of Proportion. For any Sine is to the Sine of the Complement : as The Ra...
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Circle Graphs A circle graph is a way to organize data using the sectors of a circle. Example: Suppose you take a poll of the students in your class to find out their favorite foods, and get the following results: Pizza – 41% Ice Cream – 24% Raw Mushrooms – 9% Dog Food – 11% Chicken Livers – 15% Organize this data in a...
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Graph Angles in a Standard Position In trigonometry and most other math topics, you draw angles in a standard, universal position, so that mathematicians around the world are drawing and talking about the same thing. An angle in standard position. An angle in standard position has its vertex at the origin of the coordi...
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Below you have been given figure A. Draw figure B by reflecting figure A in the given line. Draw figure C by translating figure B 8 units right and 2 units down. Then rotate figure C 180 ° around the point marked X in figure A to give figure D. We can say that figure D is a complex transformation of figure A, as we nee...
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Imagine you had a robot, consisting of series of arms. They would be of same length, and each one would be attached to the end of the previous one, so it could rotate in the same 2d plane. If each joint were given some angular speed, what would the curve traced by the end-most point look like? Well, here are several ex...
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VBForums - Maths Forum By popular request, a place for you to discuss Maths of all forms. Somewhere to think about algorithms and the applications of maths to programming too.enWed, 22 May 2013 00:28:12 GMTvBulletin60 - Maths Forum Mon, 06 May 2013 03:35:55 GMT I just saw the above on FaceBook.. Using the order of oper...
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This page consists of Animations showing how the conic sections are generated and lecture notes on the derivation of their algebraic equations. The conic sections are the curves of intersection of a double cone and a plane. In the following Animation We start with a horizontal plane intersecting the double cone in a ci...
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Question 638291: In my question there is a diagram which shows a circle with a circumference of 1cm being rolled around an equilateral triangle with sides of length 1cm. The circle is positioned haalfway between the top and bottom of one side of the triangle How many COMPLETE TURNS does the circle make as it rolls arou...
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Example 2 What is the height of the triangle in Figure 3.10? Even though the height is labeled h, it is not the hypotenuse. The longest side has length 10 feet, and thus must be alone on one side of the equation. h2 + 32 = 102 h2 = 100 – 9 h = √91 ≈ 9.54 With the help of a calculator, we can see that the height of this...
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Loci: Convergence Approximate Construction of Regular Polygons: Two Renaissance Artists by Raul A. Simon Albrecht Durer Albrecht Dürer (1471-1528), considered the father of modern German painting, was also a great mathematical amateur. He wrote a book titled Unterweysung der Messung..., which deals with all sorts of ge...
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We now use the law of sines fortriangle FBH; this gives sin(angleBHF) =√3 sin15° (observe that since angle BHF < 90°, there is no ambiguity). From hereangle BHF can be found and then angle HBF; then, subtractingangle ABF = 30° from angle HBF, we find that angle ABH is approximately 108°22', a value close to that of Ped...
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The angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle. Lengths If the side lengths of a triangle are , the se...
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Examples identities's examples An identity that shows that the cosine of the difference of two angles is related to the cosines and sines of the angles themselves. This identity is given below (A and B are used in place of alpha and beta, respectively since HTML does not support Greek characters). — "Algebra II: Trigon...
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Step 1: Recognize that a tangent to a circle makes a right angle with the radius at the point of tangency (hereinafter referred to as point T). Hence, the line segment between the center of the circle and the point (4,6) (hereinafter referred to as point A) is the hypotenuse of a right triangle where the legs are the r...
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Ptolemy's Theorem In Trigonometric Delights (Chapter 6), Eli Maor discusses this delightful theorem that is so useful in trigonometry. In case you cannot get a copy of his book, a proof of the theorem and some of its applications are given here. The theorem refers to a quadrilateral inscribed in a circle. As you know, ...
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Area of a circle's perpendicular components Area of a circle's perpendicular components I asked a similar question about gravity, but I would just like to check the math of this first. In the first picture I have a circle of radius r, There is a point p on the circle, and I am first trying to show that the equation bel...
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egg shaped. An ellipse can be drawn by positioning pins at two points, F1 and F2, and loosely tying a length of string between these points, the foci. Using a pencil point to hold the string taut, follow the string to form the shape shown in Figure 19.10. Notice that the distance remains constant. The ellipse also has ...
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Ma3 Shape, space and measures Coordinates Teacher's notes Next steps Extend the problem: for example, given almost all of the coordinates and the name of the resulting shape, find the missing coordinates. Measuring Teacher's notes Measures distance between two dots to the nearest 0.1 cm. Measures angles to the nearest ...
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Geometry Help I need help to find the coordinates of the circumcenter of each triangle. Isosceles triangle CDE with vertices C(0, 6), D(0, –6), and E(12, 0) Thursday, November 15, 2012 at 8:25pm geometry Write a paragraph proof for the following given- AD bisects CB and AD is perpendicular to CB. Prove- triangle ACD = ...
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You can put this solution on YOUR website! There are two very important facts that you must know to do these types of questions. 1. In ANY triangle, the measurements of the three angles must add up to 180. 2. In a RIGHT triangle, one of the angles measures 90 degrees. We have a right triangle with an angle measure of 3...
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Points Points are the basis of all Geometry. There are so many things you can do with the little buggers that the possibilities are endless. Points are zero-dimensional. That basically means that they have no height, length, or width. They are just there. There are four main definitions of a point. They are the dot, th...
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Functions and Analysis The Introduction of Twist (The Skew) in the Mathematics The article define a mathematic entity called twist, which generates, in this way, notion of straight line. Straight line becom thus a twist of eccentricity e = 0, and broken line (zigzag line) is a twist of s = ± 1. Question: What is the r...
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Ah, thanks a bunch Seer, and if it's not too much trouble, can anybody define point and line symmetry? Symmetry, at least bilateral symmetry, which is what you seem to have in mind, is defined as being equal on two parts. Point symmetry is when a pair of points matches perfectly at 90 degree, 180 degree or acute or obt...
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Question 2: Perform induction on the number of line segments within a weakly simple polygon. Suppose that you form the convex hull of the given segments. Together with the segments which have one endpoint touching the hull, you get a weakly simple polygon. This polygon contains some number of segments which don't inter...
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Intersecting Secant-Tangent Theorem If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment. In the circle, is a tangent and is a secant. Th...
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Copy onto cards the following descriptions, one per card: one right angle, one obtuse angle, and two acute angles. Thoroughly mix the three cards. Label the sections of each of two spinners "3," "4," "5," "6," "7," "8." The numbers on these spinners represent the lengths in centimeters of bases of trapezoids. Label equ...
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As they say, be careful what you wish for. The references you want may be found at: In particular, paper 1 and paper 2. Paper 1 gives the basic concepts such as that a linear approximation at the reference point defines most of the keywords and then some projection is applied to that. Paper 2 is all the details of cele...
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Triangles/343272: Is it possible for four lines in a plane to have exactly zero points of intersection? One point? Two points? Three points? Four points? Five points? Six points? Draw a figure to support each of your answer. 1 solutions Answer 245704 by Fombitz(13828) on 2010-09-15 08:56:08 (Show Source): You can put t...
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Ellipse Ellipse is one of the easiest topics in the Conic Sections of Co-ordinate Geometry in Mathematics. "Ellipse" is defined as the locus of a point which moves such that the ratio of its distance (Eccentricity) from a fixed point (Locus) and a fixed line (Directrix) is less than one i.e. a point moves such that its...
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What is geometry? A dictionary might say it is the study of shapes and configurations. An even better dictionary might say it is the study of figures in a space of a given number of dimensions and of a given type. A comic might say life is pointless without geometry (and you may or may not get it). But I want you to th...
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first one i dont see a diagram.....GMAT/MBA Expert they ask for a length, so statement 2 is not going to be useful - it gives us an angle only, and you can have a triangle of any size, teeny-tiny to huge, with those angles. So, ACE. AD is 6. <BAD is x. <BCD is 2x. <BCD is 2x. They want to know side BC. <BDC is what's c...
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While I had been teaching math in the classroom prior to our geometry unit, this unit was the first unit that I introduced and carried through completely. Obviously, I wanted to adhere to the curriculum of the school, but I was interested in working within this curriculum to design a more hands-on experience. The unit ...
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Latitudes are imaginary lines running parallel to the equator and longitudes are imaginary lines running parallel to the prime meridian and perpendicular to the equator. Latitude and longitude are used to reference a specific point on Earth. Lines of latitude and longitude are equally spaced and their values are the an...
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And while I'm at it please could you explain how, if you know 1 side of a right angled triangle e.g. 5 (ie. commonly memorised 5,12,13) and you know it's the shortest side, why you cannot automatically know the other sides will be 12 and 13? Bottom two paragraphs: Let's say the sides can be represented in terms of x, 2...
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Given a line and a point not on the line, there exist(s) ____________ through the given point and parallel to the given line. a) exactly one line (Euclidean) b) no lines (spherical) c) infinitely many lines (hyperbolic) Euclid's fifth postulate is ____________. a) true (Euclidean) b) false (spherical) c) false (hyperbo...
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Great circles are the "straight lines" of spherical geometry. This is a consequence of the properties of a sphere, in which the shortest distances on the surface are great circle routes. Such curves are said to be "intrinsically" straight. (Note, however, that intrinsically straight and shortest are not necessarily ide...
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What exactly do you mean by 'the shortest distance'? What are you trying to doThe shortest distance will either be a horizontal or vertical line (in which case any of a range of points can be used as the endpoints of the line), or a line connecting two of the corners. If your x coordinates overlap, then the distance is...
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Question: I am going to try out for the ARML math team in a few weeks and I have noticed a type of problem which seems to appear on the tryouts with some regularity. The problem will require the evaluation of an expression with trigonometry functions such as (sin 25)(sin 35)(sin 85). We are not allowed to use calculato...
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I want to calculate the angle a line makes with the positive x-axis in a clockwise direction. It's a lot like a bearing except instead of North, I want the angle it makes with positive x-axis. The image illustrates what I'm after. Below is the code I wrote to achieve this. It works fine but I am just wondering if there...
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Wendy - The details are nice, but the general form looks squashed. I'm sure you know, but you need to analyze carefully for the time being; with more practice, you will apply it intuitively :thumbsup:. All lines of a set of parallel lines vanish to the same point. Here are the 4 box still life's. Two copies as I had to...
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To calculate the distance between two atoms:Click/Enter these atoms. Clicking them will input their names into the dialog box. Click Execute to calculate the distance. Bond Angle Structure > Bond angle. To measure a bond angle, three atoms need to be selected so that the angle can be measured between them. A dialog box...
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Polar coordinates With this calculator you can convert cartesian coordinates of a point into polar coordinates and vice versa. The cartesian coordinates of a point are the value of the abscissa x an the ordinate y. The polar coordinates are the radius r for the distance between the point and the pole (the origin of the...
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as we have seen, all lines that pass through the center of projection are represented as a point, the representation of this line is the intersection of line 9 with the picture plane. This intersection is D1 for line 9 is parallel to the diagonals that converge at that point. Now consider the triangle O VD1. Because it...
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We'll each eat through the Radius, To the center where we get a Lady and Tramp kiss. The distance from one side, through the middle to the other side Is the Diameter, so never say die. Perimeter, distance around a circle is 2 pi R. Area is pi R squared, How much space is in there, do you care? Well I sure hope you do, ...
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rangian Points'm not sure what you use to conceptualize things, but basically, we're just looking for orbits that keep everything in the same orientation. So, If M1 is many orders of magnitude larger than M2, L1 & L2 are practically on M2. If M1 = M2, L1 is midway between them, and L2 is somewhere giving it a one (year...
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The name geometry comes from two Greek words meaning "earth" and "to measure". The ancient Egyptians used geometry to measure their fields and find the boundaries of their land. Euclidean geometry was organized in about 300 B.C. by a Greek mathematician named Euclid. He arranged mathematical propositions into thirteen ...
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As the difference of affine points, x and y are vectors in the euclidean image plane. Perpendicularity is preserved when (Sx)^T(Sy) = 0, and aspect ratio is preserved if [(Sx)^T(Sx)]/[(Sy)^T(Sy)] = w²/h². Question: What condition preserves the aspect ratio of these vectors? Answer: [(Sx)^T(Sx)]/[(Sy)^T(Sy)] = w²/h²
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i need calculus help asap AloofGhost257 asked 1) One side of a right triangle is known to be 36 cm long and the opposite angle is measured as 30°, with a possible error of ±1°. (a) Use differentials to estimate the error in computing the length of the hypotenuse. (Round your answer to two decimal places.) Answer in CM ...
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Now, let's get two-dimensional here. We'll start with the easy case, which is when the points line up. In that case, we can use the same rule, right? For instance, let's look at (4,3) and (10,3). How far apart are they? Same as before—6. We can just count, or we can just subtract, because the y-coordinates are the same...
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Mathematical Properties of the Golden Ratio The Golden Ratio, Φ, is an irrational number that has the following unique properties: Taking the reciprocal of Φ and adding one yields Φ. phi=1/phi+1, or Φ=1/Φ+1. Φ squared equals itself plus one. In other words, Phi^2 =Phi+1, or Φ^2=Φ+1. These characteristics are indeed ver...
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To identifying poles, find two great circles that intersect with the desired pole point. Find the zone directions of these great circles by finding two planes in them (not planes that are diametrically opposed, as these contain all possible planes), and take the cross product of those plane directions. Then take the cr...
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Autograph Activity - Angles in the Same Segment An Autograph Player activity to illustrate The Angles in the Same Segment circle theorem. You can use this activity on the interactive whiteboard, or for your students to investigate on their own. Autograph does not need to be installed to use this activity (so your stude...
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For every whole number n greater than or equal to 3, it is possible to have a regular polygon with n sides. So far we've seen the equilateral triangle ( n = 3), the square ( n = 4), the regular pentagon ( n = 5), the regular hexagon ( n = 6), and the regular octagon ( n = 8). There can exist a regular polygon with 1000...
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important thing where i got stuck... i found this on another site..its really help full. I feel we are not supposed to take the literal meaning of the term "cord" {lineseg that lies inside the cirlce with its ends lieing on the circle"} [color=#FF4040]as its meaning but as a piece of wire/some material that goes around...
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The compass can be opened arbitrarily wide, but (unlike some real compasses) it has no markings on it. A compass or pair of compasses is a Technical drawing instrument that can be used for inscribing Circles or arcs They can also be used as It can only be opened to widths that have already been constructed, and it coll...
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Archimedes and Apollonius gave constructions involving the use of a markable ruler. Archimedes of Syracuse ( Greek:) ( c. 287&nbspBC – c 212&nbspBC was a Greek mathematician, Physicist, Engineer This would permit them, for example, to take a line segment, two lines (or circles), and a point; and then draw a line which ...
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