School of Engineering and Information Technology ASSESSMENT COVER SHEET
Student Name PRATAP ADHIKARI
Student ID S268073
Assessment Title Assignment 2
Unit Number and Title HIT 400 Discrete Structures
Lecturer/Tutor Dr. PETER SHAW
Date Submitted 13/10/2014
Date Received
Office use onl
KEEP A COPY
Please be sure to make a copy of your work. If you have submitted assessment work electronically make sure you have a backup copy.
PLAGIARISM
Plagiarism is the presentation of the work of another without acknowledgement. Students may use a limited amount of information and ideas expressed by others but this use must be identified by appropriate referencing.
CONSEQUENCES OF PLAGIARISM
Plagiarism is misconduct as defined
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To solve the recurrence relation, we need to find the quadratic function that is suitable. The n values are input to the function (the ‘x’ values) and the T(n) values are output to the function (the ‘y’ values). From above, we have six set of points(1,1),(2,8),(3,19),(4,34),(5,53) and (6,76).
The standard format of the quadratic equation is ax2+bx+c=y
One method of solving recurrence relation with constant second differences is to write a number of equations and solve it for a,b,c.
We choose three points from the recursive sequence to write a number of three equations.
Using point(1,1) ax2+bx+c=y substitute 1 in for x and 1 in for y We get, a*12+b*1+c=1 a+b+c=1………………eqn(1)
Using point(2,8) ax2+bx+c=y substitute 2 in for x and 8 in for y We get, a*22+b*2+c=8 4a+2b+c=8………………eqn(2) Using point (3,19), ax2+bx+c=y substitute 3 in for x and 19 in for y We get, a*32+b*3+c=19 9a+3b+c=19………………eqn(3)
Solve the system of equations
Subtract equation 1 from equation 2 leaving combined eqn 1.
4a+ 2b +c
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.
For all n we have
T1(k) = T0(k-1) + (d-2){T0(k-2) +(d-2){ T0(k-3) +(d-2)T1(k-n)}}
Let k=n
T1(n) = T0(n-1) + (d-2){T0(n-2) +(d-2){ T0(n-3) +(d-2)T1(n-n)}}
T1(n) = T0(n-1) + (d-2){T0(n-2) +(d-2){ T0(n-3) +(d-2)T1(0)}}
Assume T1(0)=0
T1(n) = T0(n-1) + (d-2){T0(n-2) +(d-2){ T0(n-3) +(d-2)0}}
T1(n) = T0(n-1) + (d-2){T0(n-2) +(d-2)T0(n-3) }
T1(n) = T0(n-1) + (d-2){T0(n-2) +(d-2){ T0(n-3) }
T1(n) = T0(n-1) + (d-2) T0(n-2) +(d-2) (d-2) T0(n-3)
Since (d-2) is a constant (c), Hence the general form would be
T1(n) = c0*T0(n-1) + c1* T0(n-2) +c2*T0(n-3) +………………………
Hence, the recurrence relation is solved
Question 3 (25 Marks)
Draw a DFA diagram that represents a standard Drink machine accepting money
ANS: The following Deterministic Finite Automata (DFA) diagram represents a standard Drink machine which dispenses only one kind of soft drink at the price of $0.30. It accepts only nickels, dimes and quarters and automatically returns change for any amount deposited over $0.30 per drink. The machine has 2 buttons-one for dispensing a drink; the other to return the deposited
Step-Stair Investigation For my GCSE Maths coursework I was asked to investigate the relationship between the stair total and the position of the stair shape on the grid. Secondly I was asked to investigate the relationship further between the stair totals and the other step stairs on other number grids. The number grid below has two examples of 3-step stairs. I will use Algebra as a way to find the relationship between the stair total and the position of the stair on the grid.
Plagiarism is an act in which one person, in essence, steals the work of another and uses it for their own purposes (Cafferty, Serwer). It is an ugly act used these days for many purposes. Many students use the internet to get pre-written essays. Writers will use the internet for source purposes and forget to cite them or use parts of pre-written information.
According to Purdue Owl, Plagiarism “is the uncredited use (both intentional and unintentional) of somebody else's words or ideas.” (Purdue University 2013) Chynette Nealy defines Plagiarism as “presenting someone's words or other creative products as one's own.” (Nealy 2011)
I have decided to find a formula to find the nth term. To help me find
What is Plagiarism? Most students would say that plagiarism is when you copy another person’s work and even use their work as their own. But using terms like “copy” is a way of disguising the seriousness of the issue. To plagiarize means to steal and pass off others ideas as your own, to present a new and original idea from an existing
method can be produced and a graph of the function can be made. From the graph,
Matchstick Staircase Investigation Introduction This investigation is based on the 'number sequence' and I am going to make further more matchstick staircases for this investigation. Investigation to find out the number of matchsticks on the perimeter in a matchstick staircase using the GENERAL RULE. I have drawn 6 matchstick staircases on the graph paper and I am going to put the number of matchsticks on the base, number of matchsticks on the perimeter, total number of matchsticks in a table based on the 6 matchstick staircases. Table to show the number of matchsticks on the base, on the perimeter and the total number of matchsticks. Number of matchsticks on the base Number of matchsticks on the perimeter Total number of matchsticks 1 4 4 2 8 10 3 12 18 4 16 28 5 20 40 6 24 54
Another way of working out the nth term is to use the graph. Using the
3((〖T ̅^y〗_(i-1,j)+ 〖T ̅^y〗_(i,j))/(2 a^2 ))+3 ((〖T ̅^x〗_(i,j-1)+ 〖T ̅^x〗_(i,j))/(2 b^2 )) - (3/(a^2+b^2 )) T ̿_(i,j)=-S ̿_(i,j)/k (2.15)
Plagiarism is taking someone else’s work or idea and using as a benefit by making it look like it has not been copied from some sort of source. Plagiarism can be done unintentionally or intentionally either way it is a serious crime especially in schools and universities because it is known to be a form of cheating.
Plagiarism is something that is not respected, condoned, or accepted in any part of the education process. Not only does it steal someone else’s work, but it robs students of the learning experience they can gain from assignments. Plagiarism is immoral and unethical. According to the dictionary, plagiarism is “The submission of material authored by another person being represented as a student’s own work,” whether that material is paraphrased, completely copied or fragmentally copied. Basically, plagiarism is “to take ideas or writings from another and pass them off as one’s own” (Webster’s New World Dictionary). Plagiarism has been around since humanities first words were written, making it is easy for students to turn to it. Students will
The calculation of n terms in an arithmetic series with initial and final terms being a1 and an correspondingly, can be found with the help of the formula,
Plagiarism is defined by UMUC (2006) as “the intentional or unintentional presentation of another person’s idea or product as one’s own. Plagiarism includes but is not limited to the following: copying verbatim all of part of another’s written work; using phrases, charts, figures, illustration, or mathematical or scientific solutions without citing the source; paraphrasing ideas conclusions or research without citing the source in the text and in reference lists; or using all or part of a literary ...
The true definition of plagiarism is “Using someone else’s ideas or phrasing and representing those ideas or phrasing as our own, either on purpose or through carelessness.”[2] There are many different ways of remedying this problem.
Once you have created your equations you then need to solve them. Nowadays equations are becoming so complex that it will often take vast and powerful super com...