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Day 12-Pascals triangle II 100%

Combinatorial Analysis Pascal’s triangle Question:


24/01/2014 www.pdf-archive.com

Parts-of-a-Right-Triangle-and-the-Pythagorean-Theorem 98%

Parts of a Right Triangle and the Pythagorean Theorem  Right Triangle - Triangle with one right angle.


16/02/2017 www.pdf-archive.com

Day 11-Pascals triangle 98%

Combinatorial Analysis Pascal’s triangle By using Pascal’s formula n n−1 n−1 = + k k k−1 and the initial information n = 1, 0 n = 1, n for n ≥ 0, the binomial coefficients can be calculated recursively without using the expression n n!


24/01/2014 www.pdf-archive.com

lawcos 98%

000.1 - The Law of Cosines and Sines c 2010 Treasure Trove of Mathematics The law of cosines and the law of sines are two trigonometric equations commonly applied to find lengths and angles in a general triangle.1 1 The Law of Cosines Suppose we have a triangle labeled by the vertex points A, B, and C, sides a, b and c, and angles α, β, and γ, as shown in Figure 1.


28/07/2011 www.pdf-archive.com

bermuda triangle 97%

The Skeptics SA guide to The Bermuda Triangle The so-called ‘Bermuda Triangle’ is a rather vaguely defined area of the North Atlantic Ocean that has, over time, gained a sinister reputation as being unusually dangerous and mysterious.


20/11/2015 www.pdf-archive.com

CLASS-10-MATHEMATICS-inroduction to Trignometry 96%

Now, if a student is looking at the top of the Minar, a right triangle can be imagined to be made, as shown in Fig 8.1.


05/10/2016 www.pdf-archive.com

triangleineq 95%

000.2 - The Triangle Inequality c 2010 Treasure Trove of Mathematics The Cauchy-Schwarz inequality and the triangle inequality have many theoretical and practical applications including, but not limited to, normed vector spaces, inner product spaces, p-norms and metric spaces.1 We shall see that the Cauchy-Schwarz inequality is helpful in a proof of the triangle inequality.


28/07/2011 www.pdf-archive.com

tables 95%

Node generations 0 23996 1054 52115 41614 175 25153 0 0 144107 Coverage 0 17 6 13 1 4 8 0 0 49 LAO* e n — 12 — 48 — 223 — 887 — 3738 — 93 — 1620 — 3413 — 78 — 4391 — 12277 — 98 — 15681 — 324 — 29885 — 4823 — 735 t 1.00 1.00 1.00 1.20 18.12 1.00 1.74 1.84 1.00 26.36 149.86 1.00 79.48 1.00 27.72 1.44 1.02 Problem fr-p-1-1 fr-p-1-2 fr-p-1-3 fr-p-1-4 fr-p-1-5 fr-p-2-2 fr-p-2-3 fr-p-2-4 fr-p-3-1 fr-p-3-2 fr-p-4-3 fr-p-5-1 fr-p-5-2 fr-p-5-3 fr-p-7-1 fr-p-8-1 fr-p-8-2 LAO* e n — 12 — 48 — 223 — 887 — 3738 — 93 — 1620 — 3413 — 78 — 4391 — 12277 — 98 — 15681 — 324 — 29885 — 4823 — 735 17 / 75 t 1.00 1.00 1.00 1.20 18.12 1.00 1.74 1.84 1.00 26.36 149.86 1.00 79.48 1.00 27.72 1.44 1.02 Coverage Problem fr-p-1-1 fr-p-1-2 fr-p-1-3 fr-p-1-4 fr-p-1-5 fr-p-2-2 fr-p-2-3 fr-p-2-4 fr-p-3-1 fr-p-3-2 fr-p-4-3 fr-p-5-1 fr-p-5-2 fr-p-5-3 fr-p-7-1 fr-p-8-1 fr-p-8-2 first-responders first-responders(75) first-responders-new(91) earth-observation(40) tidyup(10) triangle-tireworld(40) blocksworld(30) faults(55) chain-of-rooms(10) Overall Domain Experiments Total 315.78 inf 17 / 75 23996 38.78 inf 6 / 91 LAO* e — — — — — — t 1.00 1.68 1.08 1.00 1.00 15.88 Problem earth-observation-p02 earth-observation-p03 earth-observation-p06 earth-observation-p08 earth-observation-p11 earth-observation-p14 n 12 1878 757 13 15 4434 LAO* e n — 12 — 1878 — 757 — 13 — 15 — 4434 — 29 — 2660 — 24512 — 10166 — 1061 — 633 — 6324 13 / 40 t 1.00 1.68 1.08 1.00 1.00 15.88 1.00 2.50 497.94 86.14 1.18 1.10 24.62 1054 Coverage Problem earth-observation-p02 earth-observation-p03 earth-observation-p06 earth-observation-p08 earth-observation-p11 earth-observation-p14 earth-observation-p16 earth-observation-p21 earth-observation-p26 earth-observation-p27 earth-observation-p29 earth-observation-p31 earth-observation-p36 earth-observation Coverage Total LAO* e n — 314 — 4659 — 64448 — 1286 — 1259 — 37008 t 1.02 1.34 24.10 1.14 1.10 10.08 n 314 4659 64448 1286 1259 37008 Problem fr-new-p-11-1 fr-new-p-12-1 fr-new-p-14-1 fr-new-p-18-1 fr-new-p-19-1 fr-new-p-20-1 LAO* e — — — — — — 6 / 91 t 1.02 1.34 24.10 1.14 1.10 10.08 Coverage Problem fr-new-p-11-1 fr-new-p-12-1 fr-new-p-14-1 fr-new-p-18-1 fr-new-p-19-1 fr-new-p-20-1 first-responders-new Coverage LAO* e — t 1407.84 1407.84 Problem tidyup-inst-mdp–03 Total Problem blocksworld-p1 blocksworld-p2 blocksworld-p3 blocksworld-p5 blocksworld-p6 blocksworld-p7 t 1.00 1.04 1.00 150.78 4.52 195.70 175 LAO* e n — 34 — 1093 — 49 — 24522 — 5936 — 25725 blocksworld 4 / 40 inf 4.06 Total Coverage LAO* e n — 25 — 148 — 124 — 83 t 1.00 1.00 1.00 1.06 Problem triangle-tireworld-p1 triangle-tireworld-p2 triangle-tireworld-p3 triangle-tireworld-p30 LAO* e n — 25 — 148 — 124 — 83 4 / 40 t 1.00 1.00 1.00 1.06 41614 n 41662 Coverage Problem triangle-tireworld-p1 triangle-tireworld-p2 triangle-tireworld-p3 triangle-tireworld-p30 triangle-tireworld 1 / 10 inf 1 / 10 Coverage 52115 2660 24512 10166 1061 633 6324 LAO* t e n 1407.84 — 41662 13 / 40 inf — — — — — — Coverage Problem tidyup-inst-mdp–03 tidyup 636.12 Total Coverage 2.50 497.94 86.14 1.18 1.10 24.62 earth-observation-p21 earth-observation-p26 earth-observation-p27 earth-observation-p29 earth-observation-p31 earth-observation-p36 0 0 0 / 10 0 Coverage Total LAO* e n t Problem LAO* e n 0 / 10 t Coverage Problem chain-of-rooms 0 0 0 / 55 0 Coverage Total LAO* e n t Problem LAO* e n 0 / 55 t Coverage Problem faults 8 / 30 inf 25153 356.04 Total Coverage LAO* e n — 34 — 1093 — 49 — 24522 — 5936 — 25725 — 34 — 39 t 1.00 1.04 1.00 150.78 4.52 195.70 1.00 1.00 34 39 Problem blocksworld-p1 blocksworld-p2 blocksworld-p3 blocksworld-p5 blocksworld-p6 blocksworld-p7 blocksworld-p9 blocksworld-p10 — — 8 / 30 1.00 1.00 Coverage blocksworld-p9 blocksworld-p10


31/12/2015 www.pdf-archive.com

Defining the Star of David 93%

- Wiktionary Star of David NOUN [SINGULAR] - ​ a star with six points formed by putting a triangle upside down on top of another triangle.


04/06/2016 www.pdf-archive.com

math words 92%

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double, draw, element, elevation, ellipse, empty set, endpoint, equal, equation, equiangular, equilateral, estimate, evaluate, even, expand, exponent, expression, extraneous root, factor, factor tree, factorial, first, floating decimal, focus, formula, fraction, fraction bar, function, fundamental, gamma, geometry, googol, graph, greater than, guess and test, half, height, heptagon, hexagon, histogram, horizontal, hundredth, hyperbola, hypotenuse, identity, if and only if, imaginary, improper, index, infinity, inscribed, integer, integral, intersect, inverse, irrational, isosceles, joint, last, leg, length, less than, line, line graph, linear combination, log, logarithm, logistic, mathematics, matrix, maximum, mean, measure, median, midpoint, minimum, minus, minute, mixed, mode, monomial, multiple, multiply, nand, natural, negative, nonagon, nor, not, null set, number, number line, numerator, obtuse, octagon, odd, one-to-one, operation, opposite, or, ordinate, origin, orthogonal, oval, 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Using Polar Coordinates, Argand Plane, Argument of a Complex Number, Argument of a Function, Argument of a Vector, Arithmetic, Arithmetic Mean, Arithmetic Progression, Arithmetic Sequence, Arithmetic Series, Arm of an Angle, Arm of a Right Triangle, ASA Congruence, Associative, Asymptote, Augmented Matrix, Average, Average Rate of Change, Average Value of a Function, Axes, Axiom, Axis of a Cylinder, Axis of Reflection, Axis of Rotation, Axis of Symmetry, Axis of Symmetry of a Parabola, Back Substitution, Base (Geometry), Base of an Exponential Expression, Base of an Isosceles Triangle, Base of a Trapezoid, Base of a Triangle, Bearing, Bernoulli Trials, Beta (Β β), Between, Biconditional, Binomial, Binomial Coefficients, Binomial Coefficients in Pascal's Triangle, Binomial Probability Formula, Binomial Theorem, Bisect, Bisector, Boundary Value Problem, Bounded Function, Bounded Sequence, Bounded Set of Geometric Points, Bounded Set of Numbers, Bounds of Integration, Box, Box and Whisker 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Degree Taylor Polynomial, nth Derivative, nth Partial Sum, nth Root, nth Root Rules, n-tuple, Nu (Ν ν), Null Set, Number Line, Numerator, Oblate Spheroid, Oblique, Oblique Asymptote, Oblique Cone, Oblique Cylinder, Oblique Prism, Oblique Pyramid, Obtuse Angle, Obtuse Triangle, Octagon, Octahedron, Octants, Odd/Even Identities, Odd Function, Odd Number, Odds, Odds Against, Odds in Favor, Odds in Gambling, Omega (Ω ω), Omicron (Ο ο), One Dimension, One-Sided Limit, One-to-One Function, Open Interval, Operations on Functions, Opposite Reciprocal, Order of a Differential Equation, Ordered Pair, Ordered Triple, Ordinal Numbers, Ordinary Differential Equation, Ordinate, Origin, Orthocenter, Orthogonal, Outcome, Outlier, Oval, Overdetermined System of Equations, p-series, Paired Data, Pappus’s Theorem, Parabola, Parallel Cross Sections, Parallel Lines, Parallel Planes, Parallel Postulate, Parallelepiped, Parallelogram, Parameter (algebra), Parametric Derivative Formulas, Parametric Equations, Parametric Integral Formula, Parametrize, Parent Functions, Parentheses, Partial Derivative, Partial Differential Equation, Partial Fractions, Partial Sum of a Series, Partition of an Interval, Partition of a Positive Integer, Partition of a Set, Pascal's Triangle, Pentagon, Per Annum, Percentile, Perfect Number, Perfect Square, Perimeter, Period of a Periodic Function, Period of Periodic Motion, Periodic Function, Periodic Motion, Periodicity Identities, Permutation, Permutation Formula, Perpendicular, Perpendicular Bisector, Phase Shift, Phi (Φ φ), Pi (Π π), Piecewise Continuous Function, Piecewise Function, Pinching Theorem, Plane, Plane Figure, Plane Geometry, Platonic Solids, Plus/Minus Identities, Point, Point of Division Formula, Point of Symmetry, Point-Slope Equation of a Line, Polar Angle of a Complex Number, Polar Axis, Polar Conversion Formulas, Polar Coordinates, Polar Curves, Polar Derivative Formulas, Polar Equation, Polar Form of a Complex Number, Polar Integral Formula, Polar-Rectangular Conversion Formulas, Polygon, Polygon Interior, Polyhedron, Polynomial, Polynomial Facts, Polynomial Long Division, Population, Positive Direction, Positive Number, Positive Series, Positively Associated Data, Postulate, Power, Power Rule, Power Series, Power Series Convergence, Precision, Pre-Image of a Transformation, Prime Factorization, Prime Number, Principal, Prism, Probability, Product, Product Rule, Product to Sum Identities, Projectile Motion, Prolate Spheroid, Proof by Contradiction, Proper Fraction, Proper Rational Expression, Proper Subset, Properties of Equality, Proportional, Psi (Ψ ψ), Pure Imaginary Numbers, Pyramid, Pythagorean Identities, Pythagorean Theorem, Pythagorean Triple, Q1, Q3, QED, Quadrangle, Quadrantal Angle, Quadrants, Quadratic, Quadratic Equation, Quadratic Formula, Quadratic Polynomial, Quadrilateral, Quadruple, Quartic Polynomial, Quartiles, Quintic Polynomial, Quintiles, Quintuple, Quotient, Quotient Rule, Radian, Radical, Radical Rules, Radicand, Radius of a Circle or Sphere, Radius of Convergence, Range, Ratio, Ratio Identities, Ratio Test, Rational Equation, Rational Exponents, Rational Expression, Rational Function, Rational Numbers, Rational Root Theorem, Rational Zero Theorem, Rationalizing Substitutions, Rationalizing the Denominator, Ray, Real Numbers, Real Part, Reciprocal, Reciprocal Identities, Reciprocal Rule, Rectangle, Rectangular Coordinates, Rectangular Form, Rectangular Parallelepiped, Recursive Formula of a Sequence, Reduce a Fraction, Reduced Row-Echelon Form of a Matrix, Reference Angle, Reflection, Reflexive Property, Regression, Regression Equation, Regression Line, Regular Dodecahedron, Regular Hexahedron, Regular Icosahedron, Regular Octahedron, Regular Polygon, Regular Polyhedra, Regular Prism, Regular Pyramid, Regular Right Prism, Regular Right Pyramid, Regular Tetrahedron, Related Rates, Relation, Relative Maximum, Relative Minimum, Relatively Prime, Remainder, Remainder of a Series, Remainder Theorem, Removable Discontinuity, Residual, Restricted Domain, Restricted Function, Rho (Ρ ρ), Rhombus, Riemann Sum, Riemannian Geometry, Right Angle, Right Circular Cone, Right Circular Cylinder, Right Cone, Right Cylinder, Right Prism, Right Pyramid, Right Regular Prism, Right Regular Pyramid, Right Square Parallelepiped, Right Square Prism, Right Triangle, RMS, Rolle's Theorem, Root Mean Square, Root of an Equation, Root of a Number, Root Rules, Root Test, Rose Curve, Rotation, Rounding a Number, Row-Echelon Form of a Matrix, Row of a Matrix, Row Operations, Row


31/07/2011 www.pdf-archive.com

GoNoodle Classroom Kit 92%

FO LD ER H E FO LD H ER E GLUE HERE GLUE HERE Where it says Fold the yellow “FOLD HERE”, triangle so that fold the green it’s on top of the triangle down green triangle, so that it’s behind and it makes a ER H H E ER pocket.


24/06/2016 www.pdf-archive.com

2005 - 2006 Workouts Answers 91%

(Since we were working with an isosceles right triangle, we also could see that the diagonal path was equal to 90 2 ≈ 127.28 feet since the hypotenuse of a 45-45-90 triangle is the product of the length of the leg and 2 .) Because we have a formula for the diagonal path, we could check if our answer would remain the same for a square plaza of any size.


12/08/2016 www.pdf-archive.com

4024 s14 qp 11 91%

4 In the triangle PQR, PQ = 5 cm, QR = 7 cm and PR = 9 cm.


11/06/2016 www.pdf-archive.com

2017-Annual-Report-on-the-Triangle-NC 90%

Todd Harrison, Broker Todd-Harrison.kw.com | 919.274.5532 Annual Report on the Triangle Region Housing Market FOR RESIDENTIAL REAL ESTATE ACTIVITY IN THE ENTIRE TRIANGLE REGION Data is refreshed regularly to capture changes in market activity.


25/01/2018 www.pdf-archive.com

gauntlet 90%

This will put you behind your shooter partner, and you will need to shoot the next triangle from a distance after the runner calls it out.


10/10/2017 www.pdf-archive.com

Work in Evidence of Talent 90%

This sequence is derived by starting with a single object, and adding rows of increasing numbers of such objects in the form of an equilateral triangle.


04/01/2017 www.pdf-archive.com

Trialgle-comercial Tyre-2015 89%

Product Catalogue Commercial Tires Bus Truck www.triangle.com.cn Sustainable Development Sustainable development is an integral part of our daily business activities.


31/08/2015 www.pdf-archive.com

34. constructions 89%

Soit ABC un triangle non plat.


25/04/2015 www.pdf-archive.com

7048 w12 ms 1 87%

Page 2 1 Mark Scheme GCE O LEVEL – October/November 2012 Syllabus 7048 Paper 01 (a) 500 660 / 700 2 1 1 1 [3] (b) (i) Front view Stand Height 100 mm (accept 115) Width 70 mm (accept 66) Three horizontal shelves [1] or one complete width shelf + two half width shelves showing 2 mm thick [2] One vertical information board to O/L [1] or 50mm high from the top shelf showing 2 mm thick [2] 1 1 2 2 [6] (ii) End view Height to candidate FE Width at base 50 mm Triangle at base (30 mm high x 50 mm) Three horizontal shelves (15 mm wide) projected from candidate FE (accept protrusion) Information board (50 mm x 30 mm) 1 1 1 1 1 [5] (iii) Plan view Base (70 mm x 50 mm) or to candidate solution Information board central Shelf along length of base (15 mm wide) 30 mm wide Information board 1 1 1 1 [4] (c) 60 mm x 100 mm rectangle Centre triangle [1] and two outer triangles [1] (to overlay) or 1 mark if triangles added incorrectly 30 mm diameter circle Ellipse 50 mm x 30 mm [1] and profile to overlay/ candidate solution [1] Slot to overlay (15 mm x 4 mm) 1 2 1 2 1 [7] © Cambridge International Examinations 2012 Page 3 Mark Scheme GCE O LEVEL – October/November 2012 Syllabus 7048 Paper 01 (d) (i) One piece development (net) (at least 5 surfaces – two triangles and three rectangles) or workable solution 4 x Fold lines shown -- · · -- or - - - Slot evident in top 1 1 1 [3] (ii) Sectional view of foam board (two lines + hatching) ‘V’ slot 1 1 [2] [30] © Cambridge International Examinations 2012 Page 4 2 Mark Scheme GCE O LEVEL – October/November 2012 Syllabus 7048 Paper 01 (a) Front view completed - eaves line to VP2 [1] and the corner vertical [1] End completed by adding one line to VP1 [1] and one vertical line [1] to determine back Roof completed by adding triangular end [1] ridge of roof line to VP2 [1] and R/H end of roof [1] Details at least one window [1] 2 2 3 1 [8] (b) One piece development (net) with six or seven surfaces if base included Workable development (net) to make the display stand Indication of windows (at least two – front and end) Sufficient glue tabs to hold development together Minimum 4× fold lines shown -- · · -- or - - - - 1 1 1 1 1 [5] (c) Four further process boxes added Finish box added Appropriate simplified text added [1] and stages in the correct order [1] (score and cut out can be reversed) Arrows added between boxes 1 1 2 1 [5] (d) Planometric 30 / 60 (accept 45 / 45) base drawn Exhibition stands shown [1] or exhibition stands shown three dimensionally [2] or all six exhibition stands, including pitched roofs, as shown in arrangement given [3] Position of ‘Sun King’ stand shown / located Position of information Tower shown Planometric cylinder drawn Entrance and Exit shown 1 3 1 1 1 1 [8] (e) Sketches [1] and notes [1] show a mechanism Allows the words ‘Sun King’ to be displayed in three colours [1] or mechanism will clearly allow the words ‘Sun King’ to displayed in three different colours [2] 2 2 [4] [30] © Cambridge International Examinations 2012 Page 5 3 Mark Scheme GCE O LEVEL – October/November 2012 Syllabus 7048 Paper 01 (a) Do not award marks when the sentences are used to convey the message.


10/06/2016 www.pdf-archive.com

Geometry (Post Paper 1) 87%

Edexcel Higher Geometry Checklist Alternate and corresponding angles Area of a circle Areas of composite shapes Areas of triangles, trapezia and parallelograms Bearings Circle terminology Circumference of a circle Congruent triangles Enlargements and fractional SF Perimeter of 2D shapes Plans and elevations Polygons Solve geometrical problems Vector arithmetic Volume of prisms Arc lengths and sectors Derive triangle results Enlargements and negative SF Loci Pythagoras Similarity and Congruence Standard constructions Surface Area Trigonometric ratios Volume Combined transformations Congruence and Similarity Standard trigonometric ratios Area of a triangle Cosine Rule Pythagoras and trig 2D and 3D Sine Rule Circle theorems Vector arguments and proof Green Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Geometry Title Amber 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 7 7 7 7 8 8 Area Red Approx.


25/05/2017 www.pdf-archive.com

godbuilding ritual 86%

place the peach pit in the upper left hand corner triangle.


06/02/2016 www.pdf-archive.com

November 2012 2H 85%

Volume of prism = area of cross section × length Area of trapezium = 1 (a + b)h 2 a cross section h b h lengt Volume of sphere = 4 3 3 Volume of cone = 1 2 h 3 Curved surface area of cone = Surface area of sphere = 4 2 r l h r In any triangle ABC The Quadratic Equation The solutions of ax2 + bx + c = 0 where 0, are given by C b A Sine Rule a x= B c −b ± (b 2 − 4ac) 2a a b c = = sin A sin B sin C Cosine Rule a2 = b2 + c 2 – 2bc cos A Area of triangle = 2 1 ab sin C 2 *P40675A0228* Answer ALL questions.


08/03/2014 www.pdf-archive.com

FBI-pedophile-symbols 85%

(U) The BoyLover logo (BLogo) is a small blue spiral-shaped triangle surrounded by a larger triangle, whereby the small triangle represents a small boy and the larger triangle represents an adult man.2 A variation of the BLogo is the Little Boy Lover logo (LBLogo), which also embodies a small spiral-shaped triangle within a larger triangle;


07/11/2016 www.pdf-archive.com

CLASS-10-MATHEMATICS-Trignometry exercise 85%

In triangle ABC, right-angled at B, if tan A = find the value of:


06/10/2016 www.pdf-archive.com