Vector Notation Convert the following vectors to Cartesian form; (2 marks each) 1. 13 m on a bearing of 165° 2. 120 km/h 20° West of North 1. X Y Using soh cah toa X= 13cos(165-90) X= 3.3646475863 X= 3.4m Y= 13sin(165-90) Y= 12.5570357419 Y= 12.6m therefore‚ cartesian vector is [3.4‚-12.6] 2. X Y X=
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ECN601 – Section 003 Syracuse University Fall 2010 Professor Lourenço Paz Math Review 1. Basic algebra and geometry Check out the handouts at : http://www1.maxwell.syr.edu/pa.aspx?id=36507223186 2. Calculus of one variable Let y = axb‚ where a and b are numbers‚ with b different from zero. The derivative of y with respect to x is dy/dx = abxb-1 Examples: y = 2x7‚ dy/dx = 2*7x7-1 = 14x6 y = 5x0.3‚ dy/dx = 5*0.3*x0.3-1 = 1.5x-0.7 Exercises: Calculate dy/dx a) y= 3x2 b) y = 12x0
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entered in a contest. The holding area is made up of 12 identical pens arranged in a two by six grid. If 100 m of fencing is available‚ what dimensions of each pen would maximize the total holding area? State EXACT answer. (from McGraw-Hill Ryerson Calculus & Advanced Functions Pg. 382 #12b) A piece of sheet metal 60 cm by 30 cm is to be used to make a rectangular box with an open top. Squares are to be cut from each corner of the sheet metal‚ the sides folded upward to form the box‚ and then the seams
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rights reserved. Objective Solve applied minimum and maximum problems. Applied Minimum and Maximum Problems 3 4 1 14-Oct-14 Applied Minimum and Maximum Problems Example 1 – Finding Maximum Volume One of the most common applications of calculus involves the determination of minimum and maximum values. A manufacturer wants to design an open box having a square base and a surface area of 108 square inches‚ as shown in Figure 3.53. What dimensions will produce a box with maximum volume?
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Vector Autoregressions By: James H. Stock and Mark W. Watson A Critique Paper presented to The Faculty of the School of Economics De La Salle University - Manila In partial fulfillment Of the course requirements in Advanced Econometrics (ECOMET2) 3rd Term‚ AY 2014 - 2015 Submitted to: Dr. Cesar C. Rufino Submitted by: Arjonillo Jr.‚ Rabboni Francis K. 11148624 V25 March 4‚ 2015 James H. Stock and Mark W. Watson are both professors in Political Economy and Econometrics
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Exercise 7.3 (Solutions) MathCity.org Calculus and Analytic Geometry‚ MATHEMATICS 12 Merging man and maths Available online @ http://www.mathcity.org‚ Version: 1.0.0 Question # 1 ˆ j ˆ (i) u = 3i + ˆ − k ‚ ˆ j ˆ v = 2i − ˆ + k u = (3)2 + (1) 2 + (−1)2 = 9 + 1 + 1 = 11 v = (2) 2 + (−1)2 + (1)2 = 4 + 1 + 1 = 6 ˆ j ˆ u ⋅ v = 3iˆ + ˆ − k ⋅ 2i − ˆ + k j ˆ ( )( ) = (3)(2) + (1)(−1) + (−1)(1) = 6 − 1 − 1 = 4 u ⋅ v = u v cosθ Now ⇒ cosθ = u⋅v u v 4
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Example 5: Student work Maths Exploration Newton-Raphson method Rationale- For this project I chose to research and analyse the Newton-Raphson method‚ where calculus is used to approximate roots. I chose this topic because it looked extremely interesting and the idea of using calculus to approximate roots‚ seemed intriguing. The aim of this exploration is to find out how to use the Newton-Raphson method‚ and in what situations this method is used Explanation of the Newton-Raphson method
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The Campbell’s Soup Lab Argument Writing AP Calculus AB Follow-Up: Suppose you are the owner of Saucy Soup Company. You need to present an argument to your board of directors as to what shape soup can your company should sell. Some things to keep in mind: • ECONOMIC REQUIREMENTS: The product must be cost efficient. • FUNCTIONAL REQUIREMENTS: The product must also be easy for retailers to store and stock on the shelves or the floor‚ and simple to process at a check-out counter
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Wah Cantt STUDENT PROGRESS REPORT Name: Arooj Safdar Reg. No: CIIT/SP12-BS(CS)-065/WAH Degree Incomplete Course No. Course Title Credite Hours Marks LG EEE121 Electric Circuits Analysis I 4 85 A- MTH104 Calculus and Analytic Geometry 3 85 A- MGT101 Introduction to Management 3 81 B+ HUM100 English Comprehension
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TRIGONOMETRY EXPLORATION by Willy Wibamanto 1. The graphs y= and y= intersect at the origin. 2. The graphs intersect at the origin. 3. As the degree of the polynomial increases‚ the graphs are approaching y=sin (x). 4. As the degree of the polynomial increases‚ the graphs are moving away from y=cos (x). 5a. When y = sin (1)‚ y = 0.841. Using the Taylor series with two terms‚ y = 0.830. When y = sin (5)‚ y = -0.958. Using the Taylor series with two terms‚ y = - 15
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