of tank will be empty in 1hr the entire tank will be empty in 3 hrs. (Marks: 3.0‚ Negative Marks : 0.0). 3. In the above figure‚ "CD " is the diameter‚ PQSR is a square and a of the square‚ if area of the biggest triangle is 36 sq. cm is : is an isosceles triangle. The area (A). (C). 12 sq. cm 24
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“Platonic Solids”. Till now many breath-taking huge structures are inspired by these polyhedrons. It is also found in nature in micro-organisms‚ crystals‚ molecules and many other forms. Even these solids are made of 2D shapes‚ especially 3 shapes: the triangle‚ the square‚ and pentagon polygons. These 3 simple shapes give those solids a unique symmetry impossible to find in any other polyhedron. Every shape has a concept behind it that affects the eye and brain when subjected to it‚ and imprints this concept
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Polynomials UNIT III. Geometry A. Points‚ Lines‚ Planes and Space -Points on a Line -Distance Between Two Points -Postulates on Points and Lines -Convex Sets -Theorems on Points and Lines B. Shapes -Triangles Properties of Triangles Triangle Congruence Isoscleles Triangle Congruent Right Triangles -Polygons Polygon Sum Parallelograms Properties of Special Prallelograms Properties of Trapezoid and Kites Midsegments -Circles Arcs and Angles Chord Properties Properties of Chors‚ Secants
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△ABD ≅ △CBD 28. Critical Thinking Draw two triangles that are not congruent but have an area of 4 cm 2 each. 29. � /////ERROR ANALYSIS///// Given △MPQ ≅ △EDF. Two solutions for finding m∠E are shown. Which is incorrect? Explain the error. ��� � � � � � � � ������������������������� ������������������������� ���������� ��������������������������� ������������������������ ���������������������� 30. Write About It Given the diagram of the triangles‚ is there enough information to prove that
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b)h h 2 b Volume of prism = area of cross-section × length crosssection h lengt r 4 Volume of sphere = – πr3 3 Surface area of sphere = 4 π r 2 1 Volume of cone = – πr2 h 3 l h Curved surface area of cone = π rl r In any triangle ABC C 1 Area of triangle = 2 ab sin C Sine rule a sin A = b sin B = b a c sin C A c B Cosine rule a 2 = b 2 + c 2 – 2bc cos A The Quadratic Equation The solutions of ax 2 + bx + c = 0‚ where a ≠ 0‚ are given by x= (02) – b ± √ (b2 – 4ac) 2a
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which means that they are equivalent circles. Therefore‚ in the ΔAOP’‚ AO=AP. When a triangle has two equivalent sides‚ it is an isosceles triangle. By that logic‚ ∠O=∠P’. Now‚ I looked at the triangle that is already drawn in the above figure‚ ΔAOP. We know that this triangle is also isosceles because OP=AP. By that logic‚ ∠A=∠O. Using the law of cosines c^2=a^2+b^2-2abcos(C)‚ which works for any triangle‚ I assigned θ to ∠O and determined that cos(θ)=1/(2*OP). Then‚ using the law of sines
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APPLICATION OF SINE LAW The shorter diagonal of a parallelogram is 5.2 m. Find the perimeter of the parallelogram if the angles between the sides and the diagonal are 40o and 30o10’. From the top of a 150 m lighthouse‚ the angles of depression of two boats on the shore are 20o and 50o‚ respectively. If they are due north of the observation point‚ find the distance between them. SOLUTION Solved for a 150/sin50 = a/sin90 a = (150 sin90)/sin50
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1. The street of a city are arranged like the lines of a chessboard ‚ there are m street running north and south and n east and west . Find the no. ways in which a man can travel from N.W to the S.E corner‚ going by the shortest possible distance. 2. How many different arrangement can be made out of the letters in the ex-pression a^3b^2c^4 when written at full length? Ans. 1260. 3. How many 7-digit numbers exist which are divisible by 9 and whose last but one digit is 5? 4. You continue
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work a rough feeling by the lines being smooth and pointy. The texture in this piece of work is rough by the shapes created and the lines are smooth but also pointy that gives it a rough feeling and Jen Stark could of made this by making several triangles all the same size and kept sticking them together
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The use of questioning and paired work in Mathematics Traditionally‚ mathematics and language-based subjects have been seen as occurring on opposite sides of a great divide. However‚ in recent years teachers have realised the importance of talk across the curriculum including mathematics. This is supported by the DfEE (1999a‚ p11) who state that ‘high quality interactive teaching is oral‚ interactive and lively. It is a two way process in which pupils are expected to play an interactive role by
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