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Further Analytical Methods for Engineers Essay Example
 Category:Engineering and Construction
 Document type:Assignment
 Level:Undergraduate
 Page:1
 Words:707
Introduction
This paper consist of 5 tasks. In tasks 1 focus was on errors. In tasks 1.2 there was solution of problem involving conversion from binary to octal and hexadecimal number systems. In tasks 1.2 there is also a question on drawing a truth table. The other three tasks majorly involved complex number algebra.
Task (LO 1.1)
, where ) of an ideal gas are obtained using the equation The number of moles (
is the pressure measured in Pascals (Pa),
is the volume measured in cubic metres (m^{3}),
is the universal gas constant (8.31447JK^{1}mol^{1}),
is the temperature measured in Kelvin (K)
In a repeated experiment, the temperature of the gas was measured by a digital meter to the nearest Celsius. The following repeated measurements were obtained :
32C, 33C, 32C, 34C, 32C, 33C, 32C, 32C, 32C, 31C

What is the uncertainty due to the reading error of the digital meter

) or Calculate the uncertainty due to the random error of the repeated measurements (you can either use standard error =

Calculate the mean of the of the repeated measurements and round off to an appropriate number of significant figures

.
and explain the choice of your uncertainty , Conclude on the uncertainty in the temperature measurements i.e. express in the form
The temperature of the gas must be in Kelvin before it is used in the equation . This is obtained by adding 273 to the Celsius temperature. The measured values of the other quantities are:
Pa
cm^{3}
JK^{1}mol^{1}

with its uncertainty given to an appropriate number of significant figures. Calculate the value of
Maximum possible value
Minimum possible value
Uncertainty_{}
Task (LO 1.2)

Convert the binary 1101 1110 1010 1101 into
0 
0 
0 
0 
0 
0 
0 

0 
0 

0 

0 
0 

0 

0 

From the table1 it can be seen that you need 3 cells to represent any possible digit in octal number octal number
We divide the binary numbers into 3 cells to and represent each in octal starting from left. We give each of the 3 cell binomial number its octal equivalent according to table 1.
Thus the octal number =157255

hexadecimal
Hexadecimal 

0 
0 
0 
0 
0 
0 
0 
0 
0 

0 
0 
0 

0 
0 

0 
0 
0 

0 
0 

0 
0 

0 

0 
0 
0 

0 
0 

0 
0 

0 

0 
0 

0 

0 

From the table3 it can be seen that you need 4 cells to represent any possible digit in hexadecimal number
We divide the binary numbers into 4 cells to and represent each in hexadecimal digit starting from left. We give each of the 4 cell binomial number its hexadecimal equivalent according to table 4.
Thus the hexadecimal number is DEAD

Draw a truth table to determine the output states at Z with all possible combinational input states at A, B, C & D.

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Task (LO 1.3)
Two complex numbers are such that and

. and the principal in rectangular (Cartesian) form. Now, findWrite down
Substituting with assigned values

into polar form i.e. in the form and Convert
rad_{}
In polar form _{}
rad_{}
In polar form _{}

in rectangular (Cartesian ) form. . Now, write and the principalFind
_{}Principal
Task (LO 1.4)
using De Moivre’s theorem in rectangular (Cartesian) form. Where m is given by 3 + n modulo 5 and n is your dataset number.Find the m complex roots of the equation
][For example, for n=9 then n modulo 5 = 9 modulo 5 = 4. Therefore 3 + n modulo 5 = 3+4 = 7. And the question would be to find the 7 roots of
2 modulo 5 =7
Therefore 3+nmodulo 5 =3+7=10
_{}From De Moivre’s theorem
Task (LO 1.5)
is the frequency of the alternating power supply, measured in Hertz (Hz). and , where The complex impedance of a circuit containing a resistor of resistance R, inductor of inductance L and a capacitor of capacitance C is given by

to an appropriate number of significant figures the impedance
Making substitutions
to an appropriate number of significant figures
Conclusion
The solution of all the tasks were successfully found