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Mathematical equations

Project description

The Brief

a) Simplify as a single fraction: 4/(2x+1)- 2/(x+3)

(5 marks)

b) Express as the sum of partial fractions (5×-4)/((x-2)(x+1))

(10 marks)

c) Find the simultaneous solutions to:

y=4x^2+7x+4 and y=x+2

analytically and graphically (plot in the range -2=x=1)

(10 marks)

d) The velocity of an accelerating object was measured over equal time periods.

t (sec) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

v (m.s) 20.0 23.1 26.2 29.8 33.0 36.0 39.5 42.2 45.5 49.0 52.2

Draw a graph of the results and determine a relationship between v and t.

Check the relationship using regression

Compare the relationship obtained with standard equations of motion and determine the initial velocity and acceleration of the object

(10 marks)

e) An object starts from rest and accelerates uniformly. The distance travelled in equal time intervals is measured, and the results tabulated.

t (sec) 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

s (m) 0 14.8 59.7 136 240 375 535 740 965 1210 1500

Draw a graph of the results in a software package such as Excel

Use a trendline to obtain a relationship between s and t.

Verify the relationship by converting the plot to a straight line graph

Estimate the distance travelled in 12 seconds

(15 marks)

Reading Materials

Module lecture and support notes.

See also module reading list.

Note: These sources are guides only to commonly available material. Students will also be expected to consult other relevant source material.

Stroud, K and Booth, D (2011) Advanced Engineering Mathematics Palgrave Macmillan

Submission Requirements

The assignment will need to be the equivalent of 800 words in length, plus diagrams, and conform to the appropriate written assignment standard.



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