The Parabola What is a Parabola? A quadratic expression is an expression in which the highest power of is 2. Consider the following: The above equations are all quadratic expressions as the highest power of is 2. When a quadratic function is graphed‚ the resulting curve is called a parabola‚ as demonstrated in figures 1 and 2. Real Life Application A quadratic function and parabola can be used when undertaking a new business venture to determine the optimum sales price of a particular
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MA1506 TUTORIAL 1 1. Solve the following differential equations: (a) x(x + 1)y = 1 (b) (sec(x))y = cos(5x) (c) y = e(x−3y) (d) (1 + y)y + (1 − 2x)y 2 = 0 Use www.graphmatica.com to sketch the functions you found as solutions of [a]-[d]‚ if y = 1/2 at x = 1. Graphmatica can also directly sketch the graph if you insert the equation itself; for example‚ in [a] you just enter x(x + 1)dy = 1 {1‚ 1/2}. [curly brackets for the initial conditions‚ with x followed by y.] Here dy represents
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DEPARTMENT OF MATHEMATICS NAME: Chen Haiwei Student Id: 42416302 FACULTY OF SCIENCE MATH123 S212 Mathematics 123 Tutorial Week 3 Tutorial Group: You must hand in this sheet at your tutorial class. Do not hand in your worked solutions‚ you should keep these for your own reference. MATH123 Mathematics 123 S212 2012 Tutorial Week 3 1. Simplify each of the following expressions‚ to obtain equivalent expressions‚ and reducing the complexity of denominators wherever possible. Show all your
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MAT 117 /MAT117 Course Algebra 1B MAT 117 /MAT117 Week 9 Discussion Question Version 8 Week 9 DQ If your neighbor asked you to explain what you learned in this course‚ what would you tell her? RESPONSE If my neighbor asked me what I learned in this math course‚ I would tell her "probably the same thing your kids are learning in school." As our generations progress‚ so does the advancement of the math that is taught to our kids in school. What I mean is‚ what may be considered
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Homework description: The following three degree monic polynomial has three real roots. f(x)=x3+2.3x2+0.32x-0.56 a. For finding the real roots ‚ Cardano’s Method[1] can be used To reduce the degree of the equation ‚these operations are done‚ a=1 ‚ b=2.3‚ c=0.32 ‚ d=-0.56 If we write y+r ‚ instead of x (x=y+r) y3 +(3r+2.3)y2+3r2+4.6r+0.32y+r3+2.3r2+0.32r-0.56=0 If we choose r=-2.33 Equation becomes this form; y3+my+n=0 m=3ac-b23a2 n=2b3-9abc-27a2d27a3 m=-1.44333…
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Problems with at least one algorithm that solves the problem in polynomial time wrt to l h bl i l i l i the input size. • Polynomial time Polynomial time – The number of steps needed relates polynomially to the size of the input. to the size of the input – O(n2)‚ O(n9)‚ O(nc)‚ where c is a constant. – but NOT O(n!) O(2n) when n is the size of the but NOT O(n!)‚ O(2 )‚ when n is the size of the input. 6 P class‚ wrt Turing Machines P class wrt Turing Machines • Problems solvable in polynomial time using a Deterministic Turing Machine (DTM) belong to
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the size n becomes large (you may use the file splinemat.m)? 6. A parabolic runout spline is the interpolating function you get by changing the condition f ′′ (x1 ) = f ′′ (xn ) = 0 to the condition that p1 (x) and pn−1 (x) should be quadratic polynomials (that is‚ a1 = an−1 = 0). Modify the file splinemat.m so that it computes the matrix relevant to this modified problem. Call the modified file splinematpr.m. (Hand in a a print-out of the modified file and an explanation of your changes.) Use your
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solving boundary value problems. This course serves as a basis of the applications for differential equations‚ Fourier series and Laplace transform in various branches of engineering and sciences. This course emphasizes the role of orthogonal polynomials in dealing with Sturm-Liouville problems. 2. Text Book: Simmons G.F.‚ Differential Equations with Applications and Historical Notes‚ TMH Edition 2003‚ Twelfth reprint 2008 Reference Book: 1. Kreider D.L. and Others: An Introduction to Linear
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FERGUSON AND BEZIER CURVES Palash Luthra Sachin Maheshwari Netaji Subhas Institute of Technology New Delhi-110078 India 1. CURVES-DEFINITION 2. NEED OF CURVES March 2013 A line or outline that gradually deviates from being straight for some or all of its length. Curves play a very significant role in CAD modeling‚ especially‚ for generating a wireframe model‚ which is the simplest form for representing a model. We can display an object on a monitor screen in three different computer-model forms:
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outside c) on d) as vertex of viii) Sutherland – Hodgman algorithm is used for _______________. a) line clipping b) point clipping c) polygon clipping d) hybrid clipping d) Newton polynomials d) animation ix) The blending functions of Bezier curves are_______________. a) Splines b) Bernstein polynomials c) Lagrangian polynomials x) Z-buffer algorithm is used for _______________. a) frame buffer removal b) visible surface detection xi) Refresh rate is
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