Maths Construction - Essay Example

Maths assignment – Construction By and Couse al Affiliation Department LO1 a) You have been contracted as a mathematical consultant to solve and confirm a number of mathematical problems/solutions for projects on a major contract. A building services engineer is to design a water tank for a project. The tank has a rectangular area of 26.5 m2. With the design specifics of the width being 3.2m shorter than the length, calculate the length and width to 3 significant figures for resource requirements.

Let x be the lengthen Solving the quadratic equation using the quadratic formula yield: = The answer isLength is 6.99mWidth is (6.99-3.20) =3.79 MB) A can company has cylindrical cans with a surface area of 225cm2. Find the radius of each cylinder given it has a height of 8.25cm. Give your answers in m to 2dp. Solving the quadratic equation using the quadratic formula yields: = x=3.142 or -11.392The answer is 3.14c) Company Building Control design produces resistors by specification. The resistance R is given by R= R0 (1+αt).

R0 is the resistance at temperature 0⁰C and α is a constant. At 50⁰C the resistance is found to be 25.6 ohms and at 95⁰C the resistance is 36.2 ohms respectively. Find R0 and α both algebraically and using graphical methods. Using graphical methods determines the resistance at 72⁰C. R0+αt=RSolve the equation by elimination method: Subtract the two equations to eliminate R0R0+50α=25.6R0+95α=36.245α=10.6α=0.2355R0=25.6-50αR0=13.822Draw a table with at least two points satisfying the two equations and draw the resulting graph: R37.37732.66629.

955t1008060From the graph it can be shown that 72 oc corresponds to approximately 31 of the same results can be proved by: Insert 72 °c into the equation R= 0.2356(72) + 13.822= 30.79 The answer is 30.79 ohms) As an employee of company JR Construction, you have received a letter regarding the project your company is working on. It has a penalty clause that states the contractor will forfeit a certain sum of money each day for late completion. (I.e. The contractor gets paid the value of the original contract less any sum forfeit).

If she is 5 days late, she receives £4250 and if she is 12 days late she receives £2120. Calculate the daily forfeit and determine the original contract value. Use both algebraic and matrix methods to solve this. Let the value of the original contract be x and the penalty be ySolving by elimination yields By matrix methodThe matrix will be Determinant is The inverse of the matrix isSolving the simultaneous equation using matrix method result to: Multiply the matrix with its inverse on both sides Perform algebraic operations of the matrices= £ 304.

28 The answer is: Constant pay is £5771.4Penalty per day is £304.3e) Excel Electrical specializes in the batch production of electrical switchgear used in building services installations. The company has been asked to tender for equipment to be fitted in several hundred new stores planned by Setco Supermarkets. Data is available from ten previous production runs of components. PRODUCTION units total Costs (Y (£10) 9 132 11 157 14 196 15 208 16 221 20 272 21 285 25 335 32 424 38 501 a) Investigate graphically whether it is reasonable to assume that there is a linear relationship between the variables, present and explain your conclusions.

Yes, there exists a linear relationship between the two variables. The graph is a straight line. b) From your graph, determine the equation linking the two variablesThe gradient of the graph is approximately: y-intercept is 17.5The equation ISC) Outline and apply an alternative means of assessing whether or not a linear relationship exists between the variables and determining the equation linking the two variables. Present and explain your conclusions. (Singh & Baker, 2007, p. 59) The alternative is to draw a scatter plot and extract the regression line relating to the two variables.

The equation relating to the two variables is y=12.716x+17.516