3 h O B b y c x h C y b x x IBB b3h3 6(b2 h2) 3 Triangle (Origin of axes at centroid) A Ix Ixy bh 2 bh3 36 bh2 (b 72 x Iy 2c) b 3 bh 2 (b 36 IP c y bc h 3 c2) b2 bc c2) bh 2 (h 36 E1 © 2012 Cengage Learning. All Rights Reserved. May not be scanned‚ copied or duplicated‚ or posted to a publicly accessible website‚ in whole or in part. E2 APPENDIX E Properties of Plane Areas 4 y B c B h Triangle (Origin of axes at vertex) Ix Ixy bh3 12 bh2 (3b 24 Iy bh (3b2
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are coprime . A right triangle whose sides form a Pythagorean triple is called a Pythagorean triangle . The name is derived from the Pythagorean theorem ‚ stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2 ; thus‚ Pythagorean triples describe the three integer side lengths of a right triangle. However‚ right triangles with noninteger sides do not form Pythagorean triples. For instance‚ the triangle with sides a = b
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sword‚ only this time the sheath holds the sunlight and the blue sky themselves. And through the light’s revealing‚ the single small incandescent boat in the far distance is readily noticed. Within the sailboats and the waves forms is the shape of triangles. The tops of the houses also have triangular shapes to them. The oval shape of the flying birds resembles the clouds and adds to the skyline a lively repetition that draws the eye towards the lone ship in the distance. As the waves seem to move to
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In mathematics‚ the Pythagorean Theorem — or Pythagoras’ theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas‚ it states: In any right-angled triangle‚ the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). The theorem can be written as an equation relating the lengths
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area of sphere = 4 r 2 r l a a + b2 = c2 4 3 Volume of sphere = h 2 hyp r opp adj adj = hyp cos opp = hyp sin opp = adj tan or sin opp hyp cos adj hyp tan opp adj In any triangle ABC C b a A Sine rule: B c a sin A b sin B c sin C Cosine rule: a2 b2 + c 2 2bc cos A 1 2 Area of triangle ab sin C cross section h lengt Volume of prism = area of cross section length Area of a trapezium = 12 (a + b)h r a Circumference of circle = 2 r Area of circle = r 2 h b r Volume
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smaller outside triangles. The outside triangles are isosceles triangles and all are equal to each other; furthermore‚ the tridecagon can be divided into thirteen isosceles triangles which are also equal to each other. Diamonds are formed from the combined outer and inner triangles. Thirteen diamonds are formed from the divided triskaidecagram and they are equal to each other. In finding the area of a thirteen-pointed star‚ the usual form is getting the area of one of the outer triangles then multiply
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Amongst the lay public of non-mathematicians and non-scientists‚ trigonometry is known chiefly for its application to measurement problems‚ yet is also often used in ways that are far more subtle‚ such as its place in the theory of music; still other uses are more technical‚ such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas‚ including statistics. There is an enormous
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[pic]πr3 Volume of cone [pic]πr2h Surface area of sphere = 4πr2 Curved surface area of cone = πrl [pic] [pic] In any triangle ABC The Quadratic Equation The solutions of ax2+ bx + c = 0 where a ≠ 0‚ are given by x = [pic] Sine Rule [pic] Cosine Rule a2 = b2+ c2– 2bc cos A Area of triangle = [pic]ab sin C Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working.
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TECHNICAL DRAWING APPLICATIONS (65) (Candidates offering Technical Drawing are not eligible to offer Technical Drawing Applications.) Aims: 1. To develop competence among the students to pursue technical courses like Engineering‚ Architecture‚ Draftsmanship Surveying and other professional courses. 2. To understand basic principles of instrumental drawing drawn to scale and to acquire basic skills in the use of traditional drafting methods which would also be helpful in understanding computer aided
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1. If a line y = x + 1 is a tangent to the curve y2= 4x ‚find the point the of contact ? 2. Find the point on the curve y = 2x2– 6x – 4 at which the tangent is parallel to the x – axis 3. Find the slope of tangent for y = tan x + sec x at x = π/4 4. Show that the function f(x) == x3– 6x2 +12x -99 is increasing for all x. 5. Find the maximum and minimum values‚ if any of 6. For the curve y = 3x² + 4x‚ find the slope of the tangent to the curve at the point x = -2. 7. Find
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