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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 2 Examinations 2008/
Module Title: Technological Mathematics 1
Module Code: MATH
School: School of Mechanical & Process Engineering School of Manufacturing, Biomedical & Facilities Engineering
Programme Title: Bachelor of Engineering in Mechanical Engineering – Year Bachelor of Engineering in Biomedical Engineering – Year Bachelor of Engineering in Building Services Engineering – Year
Programme Code: ESENT_8_Y EBSEN_7_Y EBIME_7_Y EMECH_7_Y
External Examiner(s): Dr Brendan O Regan Internal Examiner(s): Ms H. Lordan, Dr V. Morari, Mr G. O Driscoll
Instructions: Answer Q1 (compulsory – 40 Marks) and 2 other questions (30 Marks each)
Duration: 2 Hours
Sitting: Summer 2009
Requirements for this examination: Mathematical Tables
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper.
- Answer each of the following:
(i) Given the formula 2 15 4
T
P
ku π
, evaluate P when T = 1.45 × 105 ,
u = 1.21 × 103 and k = 5.7 × 10 −^2 (5 marks)
(ii) Solve for x : log 5 ( x + 3 ) + log 5 ( x − 4 ) = 2 log 5 ( x − 1 )
(5 marks)
(iii) Express the following as the sum of two partial fractions:
x x x
(5 marks)
(iv) Solve the equation:
4 x 5 x
(5 marks)
(v) Use the data in the following table to find values for a and b in the
relationship (^2)
a R b d
(5 marks)
(vi) Given that the law relating T and t is T = 40 e − t^1500 find the value of T when t = 240 and the value of t when T =26. (5 marks)
(vii) Solve for x : 3sin ( x + 25 o )^ =1.8 ( 00 ≤ x ≤ 3600 )
(5 marks)
(viii) What is a radian? Convert (a) 12 18o^ ′to radians (b) 1.45 radians to degrees and minutes
d 2 8 R 40 190
4 (a) Express the following in linear form, indicating what you would plot along each axis and what each represents:
(i) (^2)
a y bx x
= + where a and b are constants.
(ii)
2
c y = Kex where K and c are constants? (10 marks)
(b) The power dissipated by a resistor was measured for various values of current flowing in the resistor and the results are shown:
I (amps) 1.0 1.5 2.5 4.0 5.5 7. P (watts) 50 112 310 800 1510 2450
The variables I and P obey a law of the form P = RIn where R and n are constants. By plotting a suitable graph, find the values for (^) R and n. (20 marks)
5 (a) A triangle ABC has side a = 10 cm, b = 3.5 cmand angle between
them ∠ ACB = 670. Determine the other side and remaining two angles. (7 marks)
(b) An alternating voltage V (volts)with respect to the time t (seconds)is given by the equation V t ( ) = 54sin(250 π t +0.240) (i) Determine the value of (^) V t ( ) at the time (^) t =0 seconds. (ii) Determine the value of V t ( ) at the time t =40 seconds. (iii) Determine the time when V t ( ) reaches 20 volts. (iv) Determine the time when V t ( ) is first a maximum. (14 marks)
(c) Solve the following trigonometric equation for 0 ≤ A ≤ 2 π:
1 + cos A = sin^2 A.
