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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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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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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construction of those buildings. Understanding how to solve math problems becomes easier as one learns math terminology. Below is a list of many common math terms and their definitions. Acute angle – An angle which measures below 90°. Acute triangle – A triangle containing only acute angles. Additive inverse – The opposite of a number or its negative. A number plus its additive inverse equals 0. Adjacent angles – Angles with a common side and vertex. Angle – Created by two rays and containing an
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above triangle and find the value of B‚ b‚ and c. A. A+B+C=180 B. A+C=48+97=145 C. B=180-145=35 2. Two sides and an angle (SSA) of a triangle are given. Determine if the given measurements produce one triangle‚ two triangles‚ or no triangle at all. Sin B)/5=sin70/7 Sin B/5=0.9397/7 Sin B=0.6712 then B=42 or 138〗 B = 138 is impossible since 138 + 70 = 208 and exceeds 180 B=42 since 42+70 = 112 and less than 180 C = 180 – 112 = 68 There’s only one triangle 3
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w w w e tr .X m eP e ap UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level .c rs om * 4 2 8 5 4 9 6 3 4 3 * MATHEMATICS (SYLLABUS D) Paper 1 Candidates answer on the Question Paper. Additional Materials: Geometrical instruments 4024/12 October/November 2012 2 hours READ THESE INSTRUCTIONS FIRST Write your Centre number‚ candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any
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Math Exam Notes Unit 1 The Method of Substitution -Solving a linear system by substituting for one variable from one equation into the other equation -To solve a linear system by substitution: Step 1: Solve one of the equations for one variable in terms of the other variable Step 2: Substitute the expression from step 1 into the other equation and solve for the remaining variable Step 3: Substitute back into one of the original equations to find the value of the other variable Step
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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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into four congruent isosceles triangles (Two angles are 45 degree). Square is a special rectangle. 2. Equilateral Triangle An acute triangle with all angles and sides congruent‚ the angle is 60 degree. It is also known as the isosceles triangle with one 60 degree angle. The sum of two sides is greater of the third side and the difference of two sides is smaller than the third one. Each bisector‚ altitude and angular bisector of a side is coincident. Equilateral triangle is a symmetrical figure and
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