MIRACLESKILLS.COM OFFERS TRUSTED ADVICE OF TUTORS FOR UNIT 28 FURTHER MATHEMATICS FOR CONSTRUCTION ASSIGNMENT HELP!
Qualification - Higher National Diploma in Construction and the Built Environment
Unit Number - Unit 28
Unit Name - Further Mathematics for Construction
Assignment Title - Further Maths
Learning Outcome 1: Apply instances of number theory in practical construction situations.
Answer: Number theory is applied in construction through concepts such as ratios, divisibility, modular arithmetic, and prime factorisation to ensure accuracy and efficiency in design and material usage. For example, ratios and proportions are used to scale drawings and models to real-life dimensions, while divisibility helps in optimising material cutting to reduce waste. Modular arithmetic is applied in repetitive structural layouts, such as tile patterns or brick bonding, ensuring uniformity and alignment. These applications help construction professionals plan resources efficiently and maintain precision on site.
Learning Outcome 2: Solve systems of linear equations relevant to construction applications using matrix methods
Answer: Matrix methods are used in construction to solve systems of linear equations that arise in structural analysis, cost estimation, and load distribution problems. For instance, simultaneous equations representing forces acting on a structure can be expressed in matrix form and solved using techniques such as Gaussian elimination or inverse matrices. These methods allow engineers to efficiently analyse complex systems with multiple unknowns, ensuring structural stability and accurate decision-making in construction planning.
Learning Outcome 3: Approximate solutions of contextualised examples with graphical and numerical methods
Answer: Graphical and numerical methods are useful in construction when exact solutions are difficult or impractical to obtain. Graphical methods, such as plotting curves, help visualise relationships between variables like load versus deformation. Numerical methods, including iteration and approximation techniques, are used to estimate values such as settlement, stress, or material behaviour under varying conditions. These approaches support informed judgments in real-world construction scenarios where assumptions and approximations are often required.
Learning Outcome 4: Review models of construction systems using ordinary differential equations
Answer: Ordinary differential equations (ODEs) are used to model dynamic construction systems involving change over time, such as heat transfer in buildings, vibration of structures, or fluid flow in drainage systems. By reviewing these models, construction professionals can predict system behaviour, assess performance, and evaluate safety under different conditions. ODE-based models support better design decisions by linking mathematical theory with practical construction applications, enabling more efficient and sustainable solutions.
LO1
Task 1
a. Convert each number into denary,
• 11001.01
• 4D
b. calculate the following in both binary and denary
•11001+1001
Expert Support for Mastering Electrical Circuits - Unit 15, Pearson BTEC Level 3 National Diploma in Applied Science: Achieve Excellence in Electrical Circuit Theory and Application
Task 2
Apply de'Moivre's theorem or otherwise to solve for Zo and C from these expressions given below :
Z0=Z/Y and C=Z*Y
Where:
• Z is a complex number.
• Y is also a complex number.
• Re (Z0) >0 and Re (C) >0
Find Z0 and C when:
Z = 1 + 5 j,Y = 1 - 3 j
Task 3
a. Simplify the following equation:
G = 1 x e j2Π x 2 x ej0.5 x 0.5x e j0.75
b. Express the following expression in complex exponential form:
v=20sin (1000t-30°)
Task 4
Find a formula for cos (3θ) in terms of cos (θ) and sin (θ) using de Moivre's Theorem.
MOST RELIABLE HIGHER NATIONAL DIPLOMA IN CONSTRUCTION AND THE BUILT ENVIRONMENT ASSIGNMENT HELP SERVICE UNDER BUDGET!
LO2
Task 1
1252_Mathematics for Construction.jpg
a) Determine the vector Z when θ = Π/2, Z = Rθ x ( X - Y )
b) Determine the determinant of the matrix Rθ when θ = Π/4
c) Determine the inverse of Rθ When θ = Π/4
d) Solve the following equation for
Task 2
You have been asked by the structural engineering department to find the determinant and inverse of the following matrix
Task 4
You have been asked to the following set of equations that have been obtained from the structural engineering Department and verify your calculations using computer methods
2x2 + x3 = -8
x1 - 2x2 - x3 = 0
- x1 + x2 + 2x3 = 3
LO3
Assignment Brief and Guidance
Task 1
The engineering department has developed the following equation for the bending moment of a beam and you have asked to investigate its behaviour
M ( x) = x3 - 3x2 - 4
The Beam is 4m 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 to
a) Plot the bending moment at 0.5m interval for the range 0 ≤ x ≤ 4m 0 ≤ x ≤ 4 and determine if the bending moment is zero in range 3m ≤ x ≤ 4m
b) Use the graph to estimate where the bending moment is zero
c) Use the bisection method to numerically estimate the exact location where the bending moment is zero
d) Newton-Raphson method to obtain the required location
e) Compare the results of the above method to determine which gives a best solution
Task 2
The following offsets are taken from a chain line to an irregular boundary towards right side of the chain line.
chainage 0 25 50 75 100 125 150
Offset 'm' 3.6 5.0 6.5 5.5 7.3 6.0 4.0
Common distance d =25m
You have been asked to estimate the area using the following methods and compare and comment on their difference and accuracy.
a) Trapezium Rule
b) Simpson's Rule
Task 3
The equation governing a body travelling in a water channel is given by the following equation
dv/dt = 1 - v2
Plot the velocity time graph for the object and determine the final velocity and the time taken to reach this velocity
Master Fundamental Algorithms for Operational Success - Unit 1 Programming Assignment Help, BTEC Higher National Diploma (HND) in Computing: Unlocking Essential Algorithms for Comprehensive Programming Expertise
ENROLL FOR UNIT 28 FURTHER MATHEMATICS FOR CONSTRUCTION ASSIGNMENT HELP SERVICE TO GET QUALITY WRITTEN ASSIGNMENT SOLUTIONS!
LO4
Assignment Brief and Guidance
TASK 1
The equation of catenary is given by the following second order differential equation
y " = 5
x = 0, y = 100
x = 100, y = 100
Solve the above differential equation and plot the curve at 10m intervals.
Task 2
The differential equation governing the motion of a particle is given by the following differential equation
y ''+ 5 y = 0
t = 0, y = 20
Solve the above and plot the results and determine the amplitude and frequency of the oscillations
Task 3
A new series of tests is carried out and the equation modified to
y ''+ 2 y + 5 = 0
y = 20, t = 0
Use Laplace transforms or any other method to solve the new equations and plot the function and comment on the results.
Exploring the Constructional Features and Applications of Transformers - Unit 21 Electric Machines, Higher National Diploma in Mechanical Engineering: Delve into Advanced Transformer Technology and Applications
GET TRUSTED ADVICE OF TUTORS FOR UNIT 28 FURTHER MATHEMATICS FOR CONSTRUCTION ASSIGNMENTS OR DOWNLOAD SOLVED SAMPLE ASSIGNMENTS TO ACHIEVE BETTER GRADES!!