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Diploma in Construction and Built Environment PDF

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Added on  2021-12-13

Diploma in Construction and Built Environment PDF

   Added on 2021-12-13

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HE School of Construction and Built Environment
Higher National Diploma in Construction and Built Environment
Building Services Engineering and Civil Engineering
Your Name
Applied Mathematics for Complex Engineering Problem
Lecturer’s Name
Date
Diploma in Construction and Built Environment PDF_1
Your Last Name 2
Task 1
Problem statement
The amount of cloth and lining used by the industrial tailor limited for a single overcoat
is 6m and 5m respectively. The amount of cloth and lining for a single jacket is 4m and 2m
respectively. We are required to determine the number of jackets and overcoats that are
manufactured in a week If the company uses 600m of cloth and 360m of lining every weak for
the manufacture of the jackets and overcoats.
Solution
Step 1
Formulate the linear equation for the cloth and lining needed for the manufacture of
cloths and overcoats in a week.1
For the amount of cloth used, the linear equation is:
6 C+ 4 J =600
For the amount of lining used, the linear equation is:
5 C+2 j=360
C represents the overcoats while J represent the Jackets manufactured in a week.
Step 2
Write the linear equation in simultaneous form as below:
1 A linear equation is an equation between two variables which when plotted on a graph would
yield a straight line
Diploma in Construction and Built Environment PDF_2
Your Last Name 3
6 C+ 4 J =600
5C +2 J =360
Step 3
Solve the simultaneous equation using the substitution method to obtain the number of coats and
jackets manufactured in a week.2
Using the first linear equation make the number of overcoats C the subject.
6 C+ 4 J =600
C= 6004 J
6 ... ... ... ... . equation 1
Substitute the value of C into the second linear equation and solve for the number of Jackets J:
5 C+2 J=360
5 [ 6004 J
6 ]+2 J =360
300020 J
6 + 2 J =360
300020 J +12 J=2160
8 J=840
2 When a set of equations have two or more unknowns, they cannot have a unique solution.
Therefore, to determine the value of the unknowns more than one set of linear equation
determined by the number of unknowns are required to be solved simultaneously. Simultaneous
equations can be solved through substitution method, elimination method, linear line graphs or
matrix method.
Diploma in Construction and Built Environment PDF_3
Your Last Name 4
J=840
8 =105 Jackets
To determine the number of overcoats manufactured we substitute the value of jackets into
equation 1 above:
C= 6004 J
6
C= 6004(105)
6 = 180
6 =30 overcoats
Hence, the number of Jackets manufactured in a week is 105 jackets, while the number of
overcoats manufactured in a week is 30 overcoats.
Task 2
We explain the steps needed to reduce a cubic equation to linear equation and solve two
cubic equations below to find the values of x in each case
Solution
Part A
Steps
i. Apply the rational root theorem to determine the factors of the constant term and the
leading coefficient of the cubic function.3
3 According to the rational root theorem a polynomial with rational roots takes the form n
d where
n is the factor of the constant term while d is the leading coefficient.
Diploma in Construction and Built Environment PDF_4

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