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
Your Last Name2 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: 6C+4J=600 For the amount of lining used, the linear equation is: 5C+2j=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: 1A linear equation is an equation between two variables which when plotted on a graph would yield a straight line
Your Last Name3 6C+4J=600 5C+2J=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. 6C+4J=600 C=600−4J 6.............equation1 Substitute the value of C into the second linear equation and solve for the number of Jackets J: 5C+2J=360 5[600−4J 6]+2J=360 3000−20J 6+2J=360 3000−20J+12J=2160 −8J=−840 2When 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.
Your Last Name4 J=−840 −8=105Jackets To determine the number of overcoats manufactured we substitute the value of jackets into equation 1 above: C=600−4J 6 C=600−4(105) 6=180 6=30overcoats 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 3According to the rational root theorem a polynomial with rational roots takes the formn dwhere n is the factor of the constant term while d is the leading coefficient.
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