ASSIGNMENT APPLIED MATHEMATICS 1 AUTUMN 2020 Module Title Applied Mathematics 1 Module Code 4HX506 Module Leader Maan Al-Radhi Issue Date 25th Nov, 2020 Submission Date 31st December, 2020 Weighing 50% IV: Dr V. O. Oke Learning Outcomes Select and evaluate the correct mathematical techniques for a range of construction and civil engineering problems. Analyse and model construction and civil engineering situations using a range of mathematical methods. Analyse and demonstrate ability to evaluate construction and civil engineering situations using statistical analysis techniques. Ability to demonstrate knowledge and understanding of the above under constraint conditions. Introduction You have been appointed to prepare an initial conceptual design and implementation of a bridge crossing a local a stream near the expressway that links an international airport in the major city in the UK. The Client who is a local authority needs the bride to carry a carriageway8m wide with side walkways 2.4m each.The structural design should take in consideration the aesthetical and environmental aspect of the design. Assignment Requirement On behalf of the client, you are tasked with the responsibility of preparing the all design mathematical calculations for the mathematical model to be used in proposed 3 options and forms, include construction information package that will allow the construction team to build the project. The package of information required includes the following: Select the correct mathematical techniques to evaluate a number of options.Analysis and model construction and civil engineering situations.Consideration of appropriate constraints involved.Evaluation and choice of the variousstatistical and analytical techniques.Ability to demonstrate knowledge of various mathematical techniques in developing the solution. Submission Requirements There will be two types of submission: -Submission of the main module assignment will be on the 31 Dec 2020, end of the autumn term. – Mathematical Exam Test covering large part of the learning outcomes mentioned above and shall be taken mid-January 2021. LO 1: Select and evaluate the correct mathematical technique for a range of construction and civil engineering problems. Total Marks 25 Task1 (A) 1.1 In the triangle ABC, A=53⁰, B=61⁰ and the length a= 12.6 cm. Find the Unknown sides of the triangle below. 5 Marks (B) Identify which one of the following are the sine and cosine of the angle θ in the right-angled triangle DEF below? -(a) 8/17 -(b) 17/8 -(c) 17/15 D -(d) 15/17 17 15 E F 5 Marks Task 2 (a) State the amplitude and period of the waveform: y= 4cos(2θ+ 45o) And sketch the curve between 0oand360°. 5 Marks (b) State the amplitude and period of the wave form y= 6sin(t– 30o) And sketch the curve between 0oand 360o. 5 Marks (c) Prove the trigonometric identity: 5 Marks sin2x(secx+ cosecx)= 1+ tanx cosxtanx LO2 Analyse and model civil engineering situations using range mathematical methods Total 25 Marks Task 1 The following offsets are taken from a chain line to an irregular boundary towards right side of the chain line. 8 Marks chainage0255075100125150Offset ‘m’3.65.06.57.57.36.04.0 Common distance d =25mYou have been asked to estimate the area using the following methods and compare and comment on their difference and accuracy.Trapezium RuleSimpson’s Rule Mid Ordinate Rule 2. Solve the following logarithmic equation showing clearly each of the key steps and indicating why each is necessary : 5 Marks determine the determinant of 3×3 matrix : 3 Marks Determine the inverse of the above matrix and en-route identify the ad-joint, some cofactors, of the same 3×3 matrix (above) 4 Marks Task 2 (a) Solve the following Indicial equations (32)x2 X (3)(2x-3) = 27 and (42)x2 X (4)(2x-3) = 64 Determine for each equation the value for the (x) 5 Marks LO3 Analyse and demonstrate ability to evaluate construction and civil engineering situation using statistical Analysis techniques. Total 25 Marks Task 1 Concrete blocks are tested and it is found that, on average, 7.1% fail to meet the required specification. For a batch of 9 blocks, (a) Determine the probabilities that (a) three blocks and 2 Marks (b) Less than four blocks will fail to meet the specification 3 Marks Task 2 You have been asked to investigate the following data for a large building services company Revenue Number of customers Number of customers January July Less than 5 27 22 5and less than 10 38 39 10 and less than 15 40 69 15 and less than 20 22 41 20 and less than 30 13 20 30 and less than 40 4 5 Produce a histogram for each of the distributions scaled such that the area of each rectangle representsfrequency density and find the mode 4 Marks b) Produce a cumulative frequency curve for each of the distributions and find the median and interquartile range 3 Marks c) For each distribution find the: the mean the range the standard deviation 5 Marks Task 3 In an experiment to determine the relationship between force and momentum, a force X, is applied to a mass, by placing the mass on an inclined plane, and the time, Y, for the velocity to change f rom u m/s to v m/s is measured. The results obtained are as follows: Force (N) 11.4 18.7 11.7 12.3 14.7 18.8 19.6 Time (s) 0.56 0.35 0.55 0.52 0.43 0.34 0.31 Determine the equation of the regression line of time on force, assuming a linear relationship between the quantities, correct to 3 significant figures. 8 Marks LO 4 Ability to demonstrate knowledge and understanding of the above outcomes under constraint conditions: Total 25 Marks Task 1 Determine the surface area generated by a line 350mm long rotating around the x-axis at a distance of 400.0mm using Pappus theorem. And sketch the shape. 350 mmmmmmmmm + Y 400 mm +X -X 100 -Y 3Marks Task 2 1.The engineering department has developed the following equation for the bending moment of a beam and you have asked to investigate its behaviourThe Beam is 4.2m long and the design team suspect the is problem if the bending moment is zero in the range between 3-4m and you have been asked toPlot the bending moment at 0.25m interval for the range and determine if the bending moment is zero in rangeUse the graph to estimate where the bending moment is zeroNewton-Raphson method to obtain the required locationCompare the results of the above method to determine which gives a best solution 10 Marks Task 3 Using the following integration formulas below calculate the centroid and first moment of area for the triangle below: Y y=2x-1 X=2 Y=-x+2 -X X 1 2 -Y 4 Marks Having calculated the first Moment of area; calculate the second moment of area (known commonly as moment of Inertia. 4 Marks Task 4 Determine the volume area generated by a rectangle 300X200 mm rotating around the x-axis at a distance of 400.0mm using Pappus theorem. And sketch the shape. 300×200 mmmmmmmmm Y 400mm Y X 200 4Marks

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