[pic] Design of rural road segment. Table of contents 1. Scope of design exercise. 3 2. Design data. 3 3. Horizontal road alignment. 3 3.1. Length of straight segments and angels of deflection. 3 3.2. Horizontal curves. 4 3.2.1. Calculation of curve length and tangent length. 4 3.3. Road chainage. 5 3.4. Determination of lane widening on curves. 5 4. Vertical road alignment. 6 4.1. Calculation of characteristic points on the road
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1. | Define each term and write the formula if needed | a) Amplitude Amplitude is half the distance between the minimum and maximum values of the range of a periodic function with a bounded range. b) Period A function whose value is repeated at constant intervals‚ such as sin x. c) Area of a sector Area = (1/2 )(r^2)(θ) radians = (θ/360)( π r^2) degrees d) Micron A unit of length equal to one millionth of a meter. e) Area of a minor segment
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MT105a Study Notes – J.Fenech Chapter 1/2 – Basics 1. Basic notations 1.1. Sum of: ∑ 1.2. Product of: ∏ 2. Sets A = {1‚2‚3} describes the set A containing members 1‚ 2‚ and 3. A={n | n is a whole number and 1≤n≤3} x A denotes that x is a member of set A S T denotes that S is a subset of T A B is the set whose members belong to either set A‚ set B or both i.e. A B = {x | x A or x B} A B is the intersection of 2 sets where A B = {x | x A and x B} denotes an empty
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> # Ho’s Maple Lab Test Solution: Semester 1 2012 (1) # Question 1; > evalf(100*sin(95)‚38); 68.326171473612098369957981656827095404 > # Queston 2; > f:=x->3*sin(1/4*x^4)-sin(3/4*x)^4; (2) > # Find 1st derivative; > D(f); (3) > # Find turning/stationary point in the interval [1‚2]‚ 1st derivative expression = 0‚ 10 significant figures!; > evalf(fsolve(3*cos((1/4)*x^4)*x^3-3*sin((3/4)*x)^3*cos((3/4)*x)= 0‚x=1..2)‚10); 1.562756908 (4) > # Find 2nd derivative at x= 1.562756908; 10 significant
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π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle’s circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle’s area to the square of its radius. It is approximately equal to 3.141593 in the usual decimal notation (see the table for its representation in some other bases). The constant is also known as Archimedes Constant‚ although this name is rather uncommon in modern‚ western‚ English-speaking contexts. Many formulae
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Newton’s Method: A Computer Project Newton’s Method is used to find the root of an equation provided that the function f[x] is equal to zero. Newton Method is an equation created before the days of calculators and was used to find approximate roots to numbers. The roots of the function are where the function crosses the x axis. The basic principle behind Newton’s Method is that the root can be found by subtracting the function divided by its derivative from the initial guess of the
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FKB20203 Engineering Technology Mathematics 2 Lecture 2: Limits and Continuity Lecturer: Norhayati binti Bakri ( (norhayatibakri@mfi.unikl.edu.my) WEEK 2 Objective: To evaluate limits of a function graphically and algebraically To determine the continuity of a function at a point Limits (a) (b) A 1. in everyday life in mathematics Limits – Graphical Approach Examples f(x) = x + 2 x+2 ‚ x ≠ 2 h(x) = ‚ x=2 3 7 6 5 4 3 2 1 0 1 2 3 4 5 -3 -2 -1 0 1 2 3 4 5 g(x) = x2 − 4 x
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The purpose of this project is to solve the game of Light’s Out! by using basic knowledge of Linear algebra including matrix addition‚ vector spaces‚ linear combinations‚ and row reducing to reduced echelon form. | Lights Out! is an electronic game that was released by Tiger Toys in 1995. It is also now a flash game online. The game consists of a 5x5 grid of lights. When the game stats a set of lights are switched to on randomly or in a pattern. Pressing one light will toggle it and the lights
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Philippine Normal University Taft Avenue‚ Manila S.Y. 2013-2014 GRAPH OF COSINE FUNCTION (Semi - Detailed Lesson Plan) Submitted by: Rañola‚ Rachel L. III – 18 BSE Mathematics Submitted to: Prof. Imperio FIELD STUDY PROFESSOR September 13‚ 2013 I. TOPIC: GRAPHING COSINE FUNCTION Subtopic: Properties of Cosine Function Shifting of the graph References: 1. Advance Algebra‚ Trigonometry and Statistics
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MATH 152 MIDTERM I 02.11.2012 P1 P2 P3 Name&Surname: Student ID: TOTAL Instructions. Show all your work. Cell phones are strictly forbidden. Exam Duration : 70 min. 1. Show that 1 p n (ln n) n=2 converges if and only if p > 1: Solution: Apply integral test: Z Z ln R 1 X R 2 1 p dx x (ln x) p=1 p 6= 1 let ln (x) = u then ln 2 so that when p = 1 and p < 1 integral diverges by letting R ! 1‚ so does the series. When p > 1 then integral converges to ! 1 p 1 p 1 p (ln R) (ln 2) (ln
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