sphere = 4 3 ʌU 3 Volume of cone = 1 2 ʌU h 3 Curved surface area of cone = ʌUO Surface area of sphere = 4ʌU 2 r l h r In any triangle ABC The Quadratic Equation The solutions of ax2 + bx + c = 0 where D 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 *P40645A0228* Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in
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speed which was 21 kmph more‚ he would have taken three hours less for the journey. Find the speed (in kmph) at which he covered the distance. (1) 49 (2) 70 (3) 87.5 (4) 770 (Your Answer: 1) 6. In the figure below‚ PQRS is a square. An isosceles triangle is removed from each corner of the square (as shown) so that a rectangle ABCD remains. If diagonal AC measures 24 cm‚ find the area of the shaded region.
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trapezium = 2 (a + b)h a cross section length Volume of a prism = area of cross section × length h b Volume of sphere = 4 r 3 3 Surface area of sphere = 4 r 2 r Volume of cone = 1 r 2h 3 Curved surface area of cone = rl l r h In any triangle ABC b A c a sin A b sin B C a B The Quadratic Equation The solutions of ax 2 + bx + c = 0 where a 0‚ are given by x= −b ± (b 2 − 4ac) 2a Sine Rule c sin C Cosine
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Rotary Inverted Pendulum Model C&DSP Lab. EE@MJU which implies that 1 ¨ ˙ θ= −bc sin(α)α2 − cGθ ˙ ac − b2 cos2 (α) ηm ηg Kt Kg + bd sin(α) cos(α) + c V Rm 1 ˙ b2 sin(α) cos(α)α2 − b cos(α)Gθ ˙ α= ¨ 2 cos2 (α) ac − b η m η g Kt Kg + ad sin(α) + b cos(α) V Rm where a = J + mr2 ‚ b = mLr‚ c = 4 mL2 ‚ d = mgL‚ and 3 Fig. 1. A schematic diagram of the rotary inverted pendulum 2 ηm ηg Kt Km Kg . Rm G=B+ Using the Lagrangian method‚ the equation of motion of rotary inverted pendulum can be derived
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measured by the number of angles that make up that person. As the number of angles decreases the class decreases. Isosceles triangles make up the lowest class‚ because they have the least amount of angles. (7) The people who normally make up this class are the soldiers or the workmen. The next highest class would be the Equilateral Triangles‚ because they are perfect triangles. (7) Then comes Squares because they have 4 angles‚ and so on. (7)There is a way for the next generation to have more angles
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The experiment started out with an inverted T in which the vertical line was changing in length. The object was to click on the moving vertical line when you considered the parallel and vertical lines of the T to be the same length‚ this would stop the vertical line from moving. When you considered the two lines to be the same length you would click the “show results” button and the application would analyze your percentage of how similar the two lines were in size and change in color to reference
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Which is true‚ but does not make the assumption(1 = 2) even one bit less false. As we know‚ falsity implies anything‚ truth in particular. Proof 2 This proof is by E. S. Loomis (Am Math Monthly‚ v. 8‚ n. 11 (1901)‚ 233.) Let ABC be a right triangle whose sides are tangent to the circle O. Since CD = CF‚ BE = BF‚ and AE = AD = r = radius of circle‚ it is easily shown that (CB = a) + 2r = (AC + AB = b + c). And if (1) a + 2r = b + c then (1)² = (2): (2) a² + 4ra + 4r² = b² + 2bc + c².
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questions Real-life money questions Generate a sequence from the nth term Substitution Alternate angles Angle sum of a triangle Properties of special triangles Finding angles of regular polygons Area of circle Circumference of circle Area of compound shapes Rotations Reflections Enlargements Translations Find the mid-point of a line Measuring and drawing angles Drawing triangles Plans and elevations Nets Symmetries Questionnaires and data collection Two-way tables Pie charts Scatter graphs Frequency
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Introduction: “You can learn more from solving one problem in many different ways than you can from solving many different problems‚ each in only one way.” Islamic civilization in the middle ages‚ like all of Europe‚ had a dichotomy between theoretical and practical mathematics. Practical mathematics was the common subject‚ “whereas theoretical and argumentative mathematics were reserved for specialists” (Abedljaouad‚ 2006‚ p. 629). Between the eighth and the fifteenth centuries‚ Islamic civilization
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respectively. (i) Find the co-ordinates of C and D. (ii) Name the figure ACBD and find its area. [3] b) PAQ is a tangent at A to the circumcircle of Δ ABC such that PAQ is parallel to BC‚ prove that ABC is an isosceles triangle. [3] c) A rectangular piece of paper 30 cm long and 21 cm wide is taken. Find the area of the biggest circle that can be cut out from this paper. Also find the area of the paper left after cutting out the
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