Consider the following relational database:
employee(employee-name, street, city)
works(employee-name, company-name, salary)
company(company-name, city)
manages(employee-name, manager-name)
For each of the following queries, give an expression in relational algebra, tuple relational calculus, and domain relational calculus: a. Find the names of all employees who work for First Bank Corporation. b. Find the names and cities of residence of all employees who work for First Bank Corporation. c. Find the names, street address, and cities of residence of all employees who work for First Bank Corporation and earn more than $10,000 per annum d. Find the names of all employees in this database who live in the same city as the company for which they work. e. Find the names of all employees who live in the same city and on the same street as do their managers. f. Find the names of all employees in this database who do not work for First Bank Corporation. g. Find the names of all employees who earn more than every employee of Small Bank Corporation. h. Assume the companies may be located in several cities. Find all companies located in every city in which Small Bank Corporation is located. Answer:

NOTE: If t is a tuple in a relation, we use the notation t[A] to indicate the value t has for attribute A. So t[A] is the same as t.A that we used in the lectures. a. Find the names of all employees who work for First Bank Corporation: i. employee-name(company-name = "First Bank Corporation"(works)) ii. { t | s works (t[employee-name] = s[employee-name] s[company-name] = "First Bank Corporation")} iii. { <p> | c, s (<p, c, s> works c = "First Bank Corporation") } b. Find the names and cities of residence of all employees who work for First Bank Corporation: i. employee-name, city(employee (company-name = "First Bank Corporation"(works))) ii. { t | r employee s works (t[employee-name] =...

...RELATIONALALGEBRA
Query Language
It is a Language in which a user request information from the database. These languages are typically of a level higher than that of the standard programming language. It is divided into either procedural or non-procedural language. In the procedural Language, the user instructs the system to perform the sequence of operation on the database to compute a desired result. In a non-procedural Language, the user describes the information desired without giving a specific procedural for obtaining the information.
RelationalAlgebra Definition
It is a procedure language. It consists of a set of operations that take one or more relations as input and produce a new relation as a result. The fundamental operations of relationalalgebra are select, project, union, set difference, Cartesian product and rename. Other operations are: Set intersection, natural join, division and assignment.
• The basic set of operations for the relational model is known as the relationalalgebra. These operations enable a user to specify basic retrieval requests.
• The result of retrieval is a new relation, which may have been formed from one or more relations. The algebra operations thus produce new relations, which can be further manipulated using operations of the same algebra.
•...

...Cami Petrides
Mrs. Babich
Algebra Period 4
April 1, 2014
Extra Credit Project
12. When you flip a light switch, the light seems to come on almost immediately, giving the impression that the electrons in the wiring move very rapidly.
Part A: In reality, the individual electrons in a wire move very slowly through wires. A typical speed for an electron in a battery circuit is 5.0x10 to the -4th meters per second. How long does it take an electron moving at that speed to travel a wire 1.0 centimeter, or 1.0x10 to the -2nd?
Part B: Electrons move quickly through wires, but electric energy does. It moves at almost the speed of light, 3.0x10 to the 8th meters per second. How long would it take to travel 1.0 centimeters at the speed of light?
Part C: Electrons in an ordinary flashlight can travel a total distance of only several centimeters .suppose the distance an electron can travel in a flashlight circuit is 15 centimeters, or 1.5x10 to the -1st meter. The circumference of the earth is about 4.0x10 to the 7th meters. How many trips around the earth could a pulse of electric energy make at the speed of light in the same time an electron could travel through 15 centimeters of a battery circuit in 5.0x10 to the -4th meters per second?
For part A, the first step is to put (5.0) to the 10th to the -4th. The numerator would be (0.00050) if someone were trying to put 5.0x10 to the -4th in the form it’s supposed to be in. For the second scientific...

...Tuple Relational Calculus ( TRC )
Introduction Procedural Query language query specification involves giving a step by step process of obtaining the query result e.g., relationalalgebra usage calls for detailed knowledge of the operators involved difficult for the use of non-experts Declarative Query language query specification involves giving the logical conditions the results are required to satisfy easy for the use of non-experts
Prof P Sreenivasa Kumar, Department of CS&E, IITM. 1
TRC – a declarative query language
Tuple variable – associated with a relation ( called the range relation ) • takes tuples from the range relation as its values • t: tuple variable over relation r with scheme R(A,B,C ) t.A stands for value of column A etc TRC Query – basic form: { t1.Ai1, t2.Ai2,…tm.Aim | θ } predicate calculus expression involving tuple variables t1, t2,…, tm, tm+1,…,ts - specifies the condition to be satisfied
Prof P Sreenivasa Kumar, Department of CS&E, IITM. 2
An example TRC query
student (rollNo, name, degree, year, sex, deptNo, advisor ) department (deptId, name, hod, phone )
Obtain the rollNo, name of all girl students in the Maths Dept (deptId = 2) {s.rollNo,s.name| student(s)^ s.sex=‘F’^ s.deptNo=2}
attributes required in the result
This predicate is true whenever value of s is a tuple from the student relation, false otherwise In general, if t is a tuple variable with range relation r, r( t ) is taken...

...Relational Counselling: History and Theories Essay One
Relational model of counselling is a synthesis of both humanistic and psychodynamic theories. A central defining assumption of this approach is the importance of relations in the development of self, especially childhood and infancy. Environmental factors also play a crucial part (Stephen Mitchell 1988, 1993: Greenberg & Mitchell 1993). The relational approach looks at the sum total of an individual’s relationships from early childhood through to adulthood, i.e. the present. In this essay there will discussion on how counselling relationship is influenced by worldviews. This will also include indigenous worldview, my own worldview and how this might influence my own counselling practice.
In order to develop the restorative partnership, an environment of convenience ought to be set up. Rely on as well as peace of mind come to be common as well as essential arrangement need to happen. Customer and also counsellor could most ideal collaborate with a specific focus on clear contracting as well as clear specifying of limits (Kahn 1991). Throughout a specific life expectancy individual advancement will certainly be impacted by the connections with people and also items. An individual's feeling of self creates via connections with others (Rogers. 1961, Winnicott. 1990: Stern. 1985: Brazelton & Cramer. 1991).
If counsellors are to supply appropriate support to the clients they...

...PROFILE
INTRODUCTION:
CorporationBank, founded in 1906 in Udupi, Karnataka state, India, is one of the Indian Banks in Public Sector Undertaking. The body was founded with an initial capital of Rs. 5000 (US$ 100), and first day’s canvassed resources of less than one US$ 1, has currently (31 march 2004) 11,325 full time employees, and operates from several branches in India.
The Bank is a public sector unit with 57.17% of share capital held by the Government of India. The Bank came out with its Initial Public Offer (IPO) in October 1997 and 37.87% of Share Capital is presently held by the Public and Financial Institutions. The Bank’s Net Worth stood at Rs. 3, 054.92 crores as on 31 March 2005.
HISTORY:
CorporationBank, the oldest banking institution in the erstwhile undivided Dakshina Kannada District of Karnataka and one of the oldest banks in India, was founded in 1906 in the Temple Town of Udupi, by a small group of philanthropists’ led by Khan Bahadur Haji, Abdulla Haji, Kasim Saheeb Bahadur. The need to start this bank was felt because there was no such facility at Udupi, an important trading centre next to Mangalore in Dakshina Kannada District.
The indigenous banking was largely in the hands of a few rich private individuals and something had to be done provide relief to the common man from the clutches of the...

...Name/Student Number:
Algebra 2 Final Exam
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Simplify the trigonometric expression.
1.
a.
b.
c.
d.
Answer B
In , is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.
2.
a = 3, c = 19
a.
= 9.1°, = 80.9°, b = 18.8
c.
= 14.5°, = 75.5°, b = 18.8
b.
= 80.9°, = 9.1°, b = 18.8
d.
= 75.5°, = 14.5°, b = 18.8
Answer A
3.
What is the simplified form of sin(x + p)?
a.
cos x
b.
sin x
c.
–sin x
d.
–cos x
Answer C
Rewrite the expression as a trigonometric function of a single angle measure.
4.
a.
b.
c.
d.
Answer A
Short Answer
5.
Consider the sequence 1, , , , ,...
a.
Describe the pattern formed in the sequence.
b.
Find the next three terms.
6.
Consider the sequence 16, –8, 4, –2, 1, ...
a.
Describe the pattern formed in the sequence.
b.
Find the next three terms.
7.
Consider the graph of the cosine function shown below.
a. Find the period and amplitude of the cosine function.
b. At what values of for do the maximum value(s), minimum values(s), and zeros occur?
Verify the identity. Justify each step.
8.
sinΘ/cosΘ+cosΘ/sinΘ
sin^20+cos^2Θ/sinΘcosΘ
1/sinΘcosΘ
9.
Verify the identity...

...Algebra is a way of working with numbers and signs to answer a mathematical problem (a question using numbers)
As a single word, "algebra" can mean[1]:
* Use of letters and symbols to represent values and their relations, especially for solving equations. This is also called "Elementary algebra". Historically, this was the meaning in pure mathematics too, like seen in "fundamental theorem of algebra", but not now.
* In modern pure mathematics,
* a major branch of mathematics which studies relations and operations. It's sometimes called abstract algebra, or "modern algebra" to distinguish it from elementary algebra.
* a mathematical structure as a "linear" ring, is also called "algebra," or sometimes "algebra over a field", to distinguish it from its generalizations.
A variable is a letter or symbol that takes place of a number in Algebra. Common symbols used are a, x, y, θ, and λ. The letters x and y are commonly used, but remember that any other symbols would work just as well.
Variables are used in algebra as placeholders for unknown numbers. If you see "3 + x", don't panic! All this means is that we are adding a number who's value we don't yet know.
Term: A term is a number or a variable or the product of a number and a variable(s).
An expression is two or more terms, with operations...

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