Quadratic Applications KEY Part 1: Geometry Since area is a square unit‚ often quadratic equations must be used to solve problems involving area. Draw a picture to model each problem. Solve each using any of the following methods: factoring‚ graphing‚ or tables. Show all work. 1. The length of a rectangle is 7 meters more than the width. The area is 60 square meters. Find the length and width. Let x=width and x+7=width
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curve at the point x = -2. 7. Find a point on the curve y = x2– 4x -32 at which tangent is parallel to x-axis. 8. Find a‚ for which f(x) = a(x+sinx)+a is increasing . 9. The side of a square is increasing at 4 cm/minute. At what rate is the area increasing when the side is 8 cm long? 10. Find the point on the curve y =x2-7x+12‚ where the tangent is parallel to x-axis. 11. Find the intevals in which the function f(x) = 2log(x-2) - x2 + 4x + 1is increasing or decreasing. 12. Find
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Box Boxes can be rectangular or cubical. 2 | Chapter 1 Creating Basic 3D Objects To create a box 1 In the drawing area‚ click the Visual Styles viewport label menu and choose Conceptual. 2 On the Tool Sets palette‚ click Modeling tool set ➤ Solids – Create tool group ➤ Solid Primitives flyout ➤ Box. 3 At the Specify first corner prompt‚ click in the drawing area to specify the box’s base point. 4 At the Specify other corner prompt‚ enter @8‚8 to define the opposite corner and press
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of cone = 1 3 r 2h Curved surface area of cone = b rl r3 Surface 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
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decimals in these area students apply their understandings of fractions and fraction models to represent various types of addition | |and subtraction of fractions with unlike denominators. The second standard in which I chose was 3 D shapes. This allows students to relate two-dimensional shapes. It helps them to understand | |and recognize the total number of same sized units of volume that they need to fill a space without gaps or overlaps. They use these shapes and find surface areas and volumes
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A Roll No. • Please check that this questionnaire contains 11 printed pages. • Code A‚ B or C given on the right hand top corner of the questionnaire should be written on the answer sheet in the space provided. • Please check that this questionnaire contains 60 questions. 29th ARYABHATTA INTER-SCHOOL MATHEMATICS COMPETITION – 2012 CLASS - VIII Time Allowed: 2 Hours Max. Marks: 100 _____________________________________________________________________ GENERAL INSTRUCTIONS: 1.
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; use 105Btuhrft2 0F * Allowable velocity at the liquid line is 125 – 450 ft/min; use 287.5 ft/min * For the volumetric flow rate in the coil: V’ = mv V’= (0.739 kg/s) (0.528 m3/kg) V’= 0.391 m3/s = 0.664 ft3/min * For the area of the coil: Acoil = V’v =0.665287.5 Acoil = 2.32 x 10-3 ft2 = 0.335 in2 Dcoil = 0.653 in Steel Pipe Specification | Nominal Size | 1.25 in | Outside Diameter | 1.375 in | Inside Diameter | 1.245 in | Source:
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4πr2 V= Curved surface area‚ A‚ of cylinder of radius r‚ height h. Curved surface area‚ A‚ of cone of radius r‚ sloping edge l. Curved surface area‚ A‚ of sphere of radius r. Volume‚ V‚ of pyramid‚ base area A‚ height h. Volume‚ V‚ of cylinder of radius r‚ height h. Volume‚ V‚ of cone of radius r‚ height h. 1 3 Ah V = πr2h V= 1 3 4 3 πr2h Volume‚ V‚ of sphere of radius r. V= πr3 A a b c = = sin A sin B sin C c b a2 = b2 + c2 – 2bc cos A Area = 1 2 bc sin
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potatoes reacting with Hydrogen Peroxide. In particular I will investigate the effects of changing the surface area of a potato when added to Hydrogen Peroxide. This is because‚ when increasing the surface area of the potatoes it will increase the rate of reaction because there will be more surface area on which particles from the potato and the Hydrogen Peroxide will collide on‚ and with more surface area there would be more particles carrying kinetic energy‚ and by carrying more kinetic energy the chance
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will be used to carry a grand amount of smaller products while cost remain in a stead/safe amount. Mathematical Formulation Below is a list of formulas applied to each question A. Tan = - B. Substitution Area of triangle + Area of rectangle= Area of pentagon C. Differentiation D. The quadratic equation The quadratic formula OR Factorization of the quadratic formula E. Problem solution
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