Essay Sample on Mathematics The System of Linear Equations

Essay Sample on Mathematics The System of Linear Equations PATTERNS WITHIN SYSTEM OF LINEAR EQUATION A system of linear equation is basically dealt with in the algebra unit. It is a collection of the linear equations involving variables of the same set in the in the equations that are involved. For example a 2Ãâ€"2 system of linear equations includes: x + 2y=10 3x + 4y=15 Here in both the cases the equations only involve two variables that is x and y and no other variable is included. In the example of a 33 system of linear equations it mostly includes the variables x, y and z for example; 2x + y-z =11 x- 2y + 2z =-2 3x-y+2z =5 Where only the three variables are involved There are also various properties of the patterns of the linear systems. We will start with the consistency property. If the systems of the equations have common solutions, then they are said to be consistent. This therefore means that graphically the lines should be straight lines. The independence property is also termed as the linear independence. The systems of equations are usually independent since to start with, they are derived algebraically from others. For example the system 3x+4y =9 and 6x +8y =18. There are different ways of solving the systems of linear equations that includes; The elimination of variables The substitution of variables technique The row reduction method The crammers’ rule The matrix method In the mathematical field, the general linear equation in the x and y is Ax+By=C where both the A and B in the equation are not zeros. The y-intercept in the line is the y-coordinate of that point where graphically, the non-vertical line that is drawn either manually or graphically intersects the y-axis. Also, the x-intercept is the point where the non horizontal line crosses the x-axis. Therefore the most general equation for a line with slope m and the y-intercept passing through b as the y intercept is written as y= mx + b. Therefore, one can easily find the slope and at the same time the y-intercept of any line. For example finding the slope and the y-intercept for 4x+5y=40 Solution: first and foremost, solve the equation for y to put it in the slope intercept format 4x+5y=20 5y=20-4x y=4-4/5x y=-4/5x+4 therefore the slope m=-4/5 and the y intercept is b=4 Consider this 2Ãâ€"2 system of linear equations 4x+3y=7 3x-2y=9 When we examine our first equation 4x+3y=7, there is a pattern in the constants of the equations used. Here 4 is the constant associated with the variable x and it therefore precedes the variable x. Also 3 is a constant that is preceding the variable y and the equation results to 7. In the second equation, 3x-2y=9, the constant 3 precedes our variable x and the constant -2 precedes the variable y making the equation to result to 9. It is also clear that in the two equations, the constants both have a difference of one. Solving the equations simultaneously, we first multiply the first equation by 3 and then multiply the second equation by 4 in order to eliminate the variable x and solve for the variable y. The equation then becomes; 12x+9y=21 12x-8y=36 17y=-15 Therefore solving the equation yields y=-15/17. Putting the value of x in any of the solution to obtain the value of x; 4(x) +3(-15/17) = 21 X=41/17 Graphically the system of equation is solved as This is first done by putting the two equations in the form of y=mx+b. The solution of the equations is by observing the point of intersection of the two lines that are plotted graphically. In this system of equation the solution therefore is (41/17, -15/17) Consider this 2Ãâ€"2 system of linear equations x+2y=3 and 2x-y=-4 The two equations are linear because the unknowns only appear to the first power, no unknown in the denominator of a fraction is in the equations and there are no products of unknowns. Therefore, the most general linear equation is a11x1 + a12x2 ++ a1nxn=b1 a21x1 +a22x2++a2nxn=b2 am1x1+ am2x1 +..+amnxn=bm m With unknowns x1, x2..xn and coefficients a1, a2an . In x+2y=3, the constant is 3 and the unknowns are x and y whereby x= 3-2y and y= (3-x) à ·2. The gradient of the linear equation is -1/2 and the y- intercept is 3/2. The gradient is negative therefore it is negatively sloped. In 2x-y =-4, the constant is -4 and the unknowns are x and y where x= (y-4) à ·2 and y=2x+4. The gradient of the line is 2 and the y- intercept is 4. The gradient is positive and therefore positively sloped. Each of the unknown variables can be solved using the graphical calculator in the matrix calculation area [1 2: 3] and [2 -1: -4] The inverse is The solution therefore is; 1 2: x =3 2 -1: y =-4 1/5 2/5 3 =x 2/5 -1/5 -4 =y The graphic calculator here was used during this step to solve the matrix equation, normally if the equation is Ax= B then the solution is x= A-1B X=-1 y=2 The first function from the graph is sloped from left to right that is it is negatively sloped since the gradient is negative and the second equation is sloped from right to left since the gradient is positive. From the graph the solution of the equations is x and y2. This is read directly from the graph where the two lines intersect. In short, the solution to the system of equation is unique in that there is only one solution set to the system of equations and the solution satisfies the individual equations in the system of equations. Therefore, when x=-1 and y=2. Then -1+ (2Ãâ€"2) =3 and (2Ãâ€"-1) 2 = -4 which satisfy the equations that are given. Another example of linear equations is x+2y =3 3x-5y=9 This is a system of equations since it contains more than one equation. The solution set to the system of linear equation is the set of numbers n and m such that if we let x=n and y=m then we will obtain the result of the right hand side of the equation. For instance ax+by =c, if x=n and y=m then we obtain the result c given a and b are known constants. Each of the unknown variables can be solved using the graphical calculator in the matrix calculation area 1 2: x =3 3 -5: y =9 The inverse of the equation is -5/11 -2/11 -3/11 1/11 The solution therefore is, -5/11 -2/11 3 =x -3/11 1/11 9 =y Therefore xand y The graph of the two equations is as shown below This is so since (3 1) + (2 0) =3 and (33)-(50) = 9 as proven from the equation. Now consider the 2 2 system below x2y=4 5x-y=1/5 In the first equation, x2y=4 f(x) = x/8. Therefore (0, 0) In the second equation, 5x-y=1/5 then f(x) = 5x-1/5. The gradient is 5 and the y intercept is -1/5 The matrix of the equation therefore is [1/8 -1: 0] [5 -1: 1/5] Each of the unknown variables can be solved using the graphical calculator in the matrix calculation area -39/8 39/8: 0 = x -195/8 39/64: 1/5 = y Consider the following two by two system of equation y + 2x=7 y + x/2=3 In the first equation, the line is negatively sloped since y= f(x) = -2x+7. The gradient is -2 which means that the change in x compared to the change in y is -2. The y intercept is 7 and therefore when x=0, y=7 In the second equation, the equation line is also negatively sloped. The equation y= f(x) =-x/2 +3. The gradient is -1/2 and the y- intercept is 3 meaning when x=0, y=3 Each of the unknown variables can be solved using the graphical calculator in the matrix calculation area Therefore the solution to the equation is x=8/3 and y=5/3 The graph of f(x) =-2x+7 and f(x) =-x/2+3 are as follows: From the graph both the linear equations are negatively sloping but that of f(x)= -2x+1 is steeper than that of –x/2 + 3. The equations above are linear equations that results to linear curves and therefore two equations are enough to solve the equations. This two equations result into a square matrix. In the multiplication of matrices for instances, if A is an np matrix and B is a pm, then AB is the product of A and B denoted by AB and AB will be an nm matrix. That is AB exists if and only if number of columns of A is equal to the number of rows of B and that it should be noted that ABBA therefore the matrices do not commute. Therefore in solving the equation for example Ax=B, to find the values of x, the inverse of A is first found then multiplied by B. That is x= A-1B If A is a square matrix, we can find another matrix B known as the inverse of the matrix such that AB=BA=I. The inverse however can be a right inverse or a left inverse most commonly denoted as A-1. If AB=BA=I then A-1= B. Therefore if B exists then A is said to be invertible and non singular matrix. If B does not exist then A is said to be singular matrix. For the solution to be found in the equations, the matrix involved should be non singular. Theorem If A is a non singular matrix then A-1 is unique Proof Let A-1 =B then AB=BA=I Suppose B is not unique, then there exist C such that CB Then CA=AC=I But B=IB therefore (AC) B= (CA) B and thus C (AB) =CI =C Therefore B=C, a contradiction that B is unique An example of invertible matrix can be solved by looking at the following question. Solve the equations -4x-2y=8 and 6x+3y=12 The matrix of the equation is a 22 matrix and therefore the equation can written in the augmented form as shown Any matrix is said to be in reduced row echelon form if it satisfies the following conditions: Any row of all zeros appear at the bottom If a row does not consist of all zeros then its first non zero entity is called a leading 1 and it is one If any two successive rows the leading 1 of the lower is further to the right of the leading 1 of the highest row If a column contains a leading 1 then all the other entries are zero However, each of the unknown variables can be solved using the graphical calculator in the matrix calculation area But the inverse of the matrix does not exist since in fact the determinant is zero (-43) (6-2) =0. Therefore there is no solution to the equation above. Graphically, the lines to the equations are parallel and never intersect therefore there is no solution to the problems From the graph, it is clear that the two lines are parallel and are never to intersect and therefore this means that the equations do not have a solution. In some cases, the system will have many solutions in the algebraic sense, however geometrically, the lines will collide and look like there is only one line and therefore all the points along that line are indeed solutions to the equation. For example the equation -2x+y=8 and -4x+2y= 16 matrix to the equation is One of the solutions is x=0 and y=-4 and many other solutions. The matrix does not have an inverse as shown by the graphical calculator in the matrix calculation area since the determinant of the matrix is zero. This means that the solution of the equation is not one hence the equation has many solutions. In general, given any systems of linear equation with two unknown solution, the two lines will graphically intersect at one point. The point of intersection is the solution to the systems of linear equations. Also, the lines can be parallel to each other meaning that the system does not have any solution and finally the lines can collide and the solution to the system is not unique that is there are many solutions to the system of linear equations. The system with many solutions can be presented in the graph below using the equation given above. Note that: -4x+2y=16 2 {(-2x+y) =8} and therefore one equation is a multiple of the other which basically means that the equation is more or less the same. Remember that a system such as 2x-3y=7 and x+7y=11 can be written in the form = It is normally represented as Am=b where A= , b= and m= If b=0, then the system Am= b has m=0 as a trivial solution but if A-1 exists then m=0 is the only solution to the system. There is also the possibility of graphing those equations with piecewise defined functions. For instance there are functions such as |x| = In our example, we will graph one of the most commonly used piecewise defined functions. f (x) = In this case, the entire function is considered as one function in who’s the domain is the real numbers. APPLICATION OF LINEAR FUNCTIONS There are times when the solutions for the complicated functions cannot easily be obtained. This lead to the use of the linear equations that is the equations that are to only one degree to be used in the approximation of the complicated functions since they gives some little bit of accuracy and the linear functions are easy to work with. This is basically known as linearization. This is mostly used in conjunction with the differential functions. Here if the function, normally denoted as f is differentiable at x=a, then in this case the approximation function denoted as L(x) = f (a) +f’ (a) (x-a) is now what is known as the linearization of the function f at a. For example we will try to find the linearization of the function f(x) = at x=0 The above graph is now the linearization of the function at x=o and x=3. We now know that f’(x) =1/2(1+x)-1/2. We will therefore see that f (0) =1 and also that f’ (0) =1/2. Therefore this concludes that the linearization will therefore be: L(x) = 1+1/2(x-0) = 1+x/2 These are some of the general applications of the linear equations/functions and many other that are dealt with at the higher level of the course work Theorem in the solution of system of equation If A is invertible, then there is only one solution to Am=b which is the unique solution Proof Let w be any solution such that wA-1b That is Aw=b but since A is invertible A-1 exists that is Aw=b Therefore multiplying both sides to the left with A-1 we have A-1Aw = A-1b I w = A-1b w = A-1b which is a contradiction and therefore A-1b is the only solution to the system Next there are equations that are to the second degree and the linear equations are used to find the gradients at particular points through the use of the tangent line and the normal lines to the equations that are being considered in this case. These equations mostly include the parabolas and other quadratic equations among others. Though our main interest is not the parabolas and such equations, the linear equations are particularly used here to serve various mathematical purposes. The parabola for instance is a set that usually consist of all points in a plane that is equal in distance sense from a point that is given and also a given line. Mostly the parabolas will have a graph of equations of the form y= ax2+bx+c. We will for instance plot a graph of y=x2. In this case the graph is a simple graph that is curved in u shape. But mathematically, we may want to find the gradient of the graph at particular points. We will therefore use the current technology for graph plotting to plot both the graphs as shown; The tangent line is used to find the gradient of the curve at that particular point. The graph shown is a curve with the equation y=x2. The axis of the parabola is the y-axis that is it is the axis of symmetry.lso, the vertex of the parabola as seen from the graph is at the origin. The parabola is seen to open upwards when the values of the constant are positive and increasing and open up downwards if the values of the constant are negatively increasing. Now if we consider the 33 matrix system, there are 3 variables that are involved, we will concentrate on the variables x, y and z. For instance, let as consider the matrix below 2x+y-z=11: Here the constants are 2 that precede the variable x, 1 that precedes the variable y and -1 that precedes the variable z. The system can be solved using the usual matrix method, the elimination method or the use of a three dimension matrices. When we deal with the matrix method the graphing calculator here is used to find the inverse of the matrix. The system of equations can be basically being written as; M X=A Using the graphing calculator to find the inverse of the matrix will yield X= M-1A X= And therefore the solution to the equation becomes X = In this type of system, there are also the possibility of obtaining a unique solution, the; possibility of many solution and the option of no solution. The possibility of many solutions or no solution is as a result of having a singular matrix that is a matrix with a zero determinant. For example looking at the following system of solution x+2y+3z=4 4x+6y+8z=10 2x+y=-1 The determinant of the matrix is zero and therefore there can be the case where there are many solutions and graphically in a three dimension graph, the lines are common or the case where there are is no solution and the lines are parallel to each other. We can also use our technology to create a family of linear equations that are usually similar in characteristics. On the same set of the axis, we usually display the equations and evaluate them mathematically. The family of curves will include several lines which usually have a wide range of equations. This can be represented as; The family of linear equations above all have different gradients fro negative to zero to positive. In a 33 matrix, the solution can also be obtained geometrically and algebraically. This is so because the graph of the equations can be plotted in the graph especially with the current technologies and calculators and it can be done algebraically through various methods which include the elimination methods and the current modern methods. Therefore the 33 matrix can be dealt with in the same manner as the 22 matrix. There are many ways of proving mathematical theorems and terms such as the contradiction method, proving by induction and many others in the above matrix we have used the contradiction method. In the 33 matrix, we are going to basically see how to prove by induction the conjectures that are involved. Conjectures in mathematics are some of the propositions and they are easily not disapproved since they are believed to be true For instance the sequence an= n (n-1) is the sequence such that a1= 1*0 a2= 2*1 : : an= n*(n-1) When we sum up the sequence of the first n numbers we obtain a series and therefore sn= a1+a2++an. Therefore; S1=0 S2=2 Sn= Sn-1+an Next, the difference between successive sums is made until the constant term in the series is obtained so long as the nth term n0, This will result to a polynomial of the third degree in order for the constant terms to be obtained in that the equation for the series will therefore be Sn = Ax3+Bx2+Cx+D where A,B,C and D are constants that are and xâ ± ¤ Now replacing x in the equation with the natural numbers 1,2,3,4,5.. we get the A+B+C+D=0 8A+4B+2C+D=2 27A+9B+3C+D=8 64A+16B+4C+D=20 This is a four equation system since there are four different unknown variables. Therefore we will use the graphing calculator to find the solutions to the unknown variables 1 1 1 1: 0 8 4 2 1: 2 27 9 3 1: 8 64 16 4 1: 20 We will find that A=1/3, B=0, C=-1/3 and D=0 Sn=1/3 x3-1/3 x The graph for the equation is therefore as follows Proving the equation by the induction method therefore will be (for n0); For n=1: =1/3*13 1/3* 1 =0 For n=3: =1/3*33 -1/3*3 =8 For n=5: =1/3*53 1/3*5 =40 Therefore we can assume that the equation is true for all values of natural number that is n0, We therefore assume that the equation is true for n=k Therefore for n=n+1, Sk+1= Sk+ (k+1)*k =1/3k3 -1/3k +k2 +k =1/3(k+1)3 -1/3(k+1) Since the expression is true for n=k+1 is true, the equation is true by induction. In the mathematical sense, a function of a polynomial p is normally written as p(x) =anxn+an-1+.+a1 x+ a0. In this case the n are non negative integers and the a’s are the coefficients of the polynomial itself. Usually all the polynomials have the domain of (-, ). In this case we can say that the linear functions themselves are polynomials of degree one while the quadratic functions are polynomials of the second degree and so on. As with our 33 matrix, the polynomial involved was a cubic function of the third degree. For instance the polynomial y=84-143-92+11x-1 Linear Algebraic Equations A teacher is looking for the best option in purchasing school supplies for a classroom. Company A is offering a discount for every dollar amount spent; Company B is offering a higher discount for every dollar spent above $20. Determine which company will offer a better price based upon the dollar amount the teacher spends on the school. In this scenario, it mostly involves the computation of the purchase of the school inventories at a cheaper price. Inventory generally is the stock of raw materials, work in progress units, finished goods, consumables and spare parts being held in store at a given time period. There are different kinds and groups of inventories that includes; movement inventories which are inventories on transit from one point to another, safety stock or the buffer stock which are the inventories that must always be maintained in the store so as to meet the unexpected demand, cyclical inventory, anticipatory inventory and the decoupling inventory. However, in this scenario we will focus on how to purchase inventory while at the same time using the mathematical knowledge to reduce inventory related costs. Here, the teacher is looking for the best option in purchasing school supplies for a classroom and therefore the best option is the option with reduced costs. The customer also has to ensure that tho ugh the goods are purchased at a cheaper price, they are of the best and desirable quality. The supplier of the goods should also be in a position to supply goods to the customer when they are needed both in the short term period and in the long term period and in time as to the date of the specifications. Therefore the customer has to look deep into these needs before making the decision on where to make their orders. The hypothetical customer, the teacher in this case has to make an informed decision based on questions such as how many units to order at that time, how often should the school supplies be made, how many orders are to be placed in that particular year and this is mainly done to reduce cost. In this scenario therefore we will focus mainly on two cost options that are for Company A which is offering a discount for every dollar spent. This is where a constant rate of discount for every dollar spent. This is where a constant rate of discount is offered irrespective of the number of units purchased and it is commonly known as a single discount. We will assume that the unit price of each product that is to be purchased is $5 and that the discount for every dollar spent is 5 percent (5%). In this scenario, the discount offered is for every dollar that will be spent and no conditions as to the amount and the limit of expenditure. The second option is for Company B which is offering a higher discount for every dollar spent above $20. This therefore guarantees the teacher discount after spending $20 in the purchase of school supplies which will be a much higher discount than that of the purchase of the goods worth $20. In this case the teacher will get a discount similar to that of the single discount up to the expenditure of $20 and later the discount is increased accordingly. We will therefore assume that the unit purchase price is $5 and that every dollar spent to the expenditure of $20 is 5%, with more dollars spent, the discount increases to 7.5%. In our scenario, the demand should be known in advance with certainty and will remain constant within the relevant range. The algebraic equations to represent the cost of each option are: Company A: Offers a discount for every dollar spent Here there are many cost related to the purchase of the school supplies which includes the purchase cost, the ordering cost, the holding cost and in some cases the shortage cost. However we will only focus on the purchase cost and ignore all the other related cost inorder to come up with the required linear equations. Let’s assume further that the teacher purchases x units of the school supplies Unit price = $5 Discount =5% Let the total cost=y Total purchase cost =$5 * (100% -5%) *x Total purchase cost = $5 *0.95 *x = 4.75x Company B: Offers a higher discount of 7.55 for every dollar spent above $20. The teacher here should know that for the first $20 spent, the discount is 5% and above the expenditure of $20, the discount increases to 7.5%. This will probably lure customers desire to purchase more but we will try evaluating the two equations. The equation for company B is therefore as follows Let’s assume that the teacher purchases x units of the school supplies The discount for the first 4 purchases of the school supplies =5% i.e ($20/5) Unit price =$5 Let the total cost=y The discount for the purchase of more than 4 =7.5% Total purchase cost = ($5*4*0.95) + ($5*0.925)(x-4) Total purchase cost = $19+4.625x –$18.5 =$0.5+4.625x The equation of company A is used since the company only offers a single discount for all the purchases that are made by the customer. Therefore the discount will be distributed equally. For Company B, there is a constant in the algebraic equation since in the purchase of the first $20 items, the discount is 5% that is it is constant and since the customer has to purchase more than this to gain the discount of 7.5% then that part of the equation will vary with the extra units purchased. The solution to the equation can be done through several ways such as elimination method, substitution method or the graphical method; the equations are normally written as y= 4.75x y= 0.5+4.625x We are going to solve the equation using the substitution method. Since in the first equation y=4.75x, we will substitute this to the second equation.4.75x= 0.5+4.625x and we therefore solve the equation mathematically. In this equation, the solution is x=4. Where the total costs will be the same. But with the increase in the purchase of the school supplies, the total cost will be higher for the purchase related to Company A than that of the purchase from Company B. Also, with the decrease in the purchase of the school supplies, the cost purchases from Company A are less than that of Company B. The graph of the two scenarios can be represented as follows. Though the cost associated in the two scenarios are close, there is a negligible difference as a result of the discounts. It is therefore correct to conclude that if the teacher is in need of less than four units of purchase, it is advisable to purchase the school supplies from Company A, if the teacher wants to purchase 4 units of item, this can be done from any company and if it is more than 4 company, it is cost effective to purchase from Company B. At the lower levels of purchase, presence of discount appears attractive for the company with a single discount for any unit of purchase made. That is, there is no constant related to the purchase of goods in the algebraic equation.. However beyond a certain level of purchase, taking up a discount results into a net increase in total cost in the company using a single discount method. In the other case for company with an increased discount after purchase of some discount, the purchase of many items become cost effective in this company. Therefore the teacher should ensure that he or she takes up the least quantity required to qualify for the highest discount in order for the total cost to be less than that of company A. Since the principle of discount states that only the least quantity required to qualify for the discount should be purchased.

Nuclear Warfare essays

Nuclear Warfare essays The effects caused by a nuclear power accident, on the scale of the April 26, 1986 Chernobyl accident, must override any inclination to side with advocates for nuclear power. Surely we have all heard the expression Im only human. If we are indeed only human, and consequently prone to error, we could never perfectly manage and contain an energy as potentially destructive as that of nuclear power, without the possibility of a nuclear accident. Furthermore, the wastes generated by nuclear power, when inadvertently released during a nuclear power accident, have been proven to cause malignant diseases and premature death to those who come into contact with them. Additionally, the vegetation threat we rely on for survival is severely affected when radioactive elements are released into the air and water supply during a nuclear accident. Most alarming, however, is the fact that the general public is vastly unaware of its governments use of nuclear waste in the development of nuclear weapon. Most of us can remember the bombing of Iwo Jima and the effects the bomb had on the lives of the millions of Japanese that lived within a twenty mile radius of the city. We can see what happened to the second generation: children born with severe informities such as sixteen fingers and three arms; children born with cancer; and children with mental and physical handicaps. The radiation of a bomb doesnt always cause instant death, but it is a lingering experience. Japanese people, thought to be healthy, got cancer in later life, and had dis-formed children. Consequently, we must not be swayed by advocates urging us to further develop and expand nuclear power. We must, instead, examine the larger picture; the risks associated with this potentially devastating power. The potential for human error causing a nuclear accident can be ascertained by considering the causes and effects o...

History of elizabeth Arden (Make-Up company) Research Paper

History of elizabeth Arden (Make-Up company) - Research Paper Example The Spa was opened on Fifth Avenue, and it has formed the basis of the existing world cosmetics giant, which has been involved in acquiring many other brands and products from various producers, to boost its line of products. The proprietor of the company was a women’s advocate who was very active in advocating for the rights of women, through searching for all ways to empower women, at an age when the rights of women was a disturbing subject that many avoided to confront with. As a way of empowering and showing the solidarity of women, she advocated for beauty and fragrance of women through the use of make-ups, which then gave her the motivation to establish the make-up salon, the Red Door salon, which she could use for advocacy campaign, where alongside other 15,000 women who were suffragettes, she matched past her salon wearing red lipstick, as a show for women’s solidarity2. Initially started as the Red Door salon, the company obtained its present name from the coin age of a name from a previous partnership that Florence Graham had with Elizabeth Hubbard, which dissolved in 1909, and then added the name Arden from her favorite poem, Enoch Arden, to come up with the current name of the company3. She embarked on a journey of growing the business, both as a motivation for other women to get into independent productive ventures, and also to prove to those who were opposed to giving women their rights. Florence Nightingale Graham increased her business management skills through travelling to France in 1912 to learn the techniques of running a beauty salon, while also learning the kind of products that were used in such salons. There, she learnt the beauty and face massage skills, as well as learning how to prepare various powders for use in the massage process. When she returned back home later in that year, she had all the requisite skills of diversifying her business from just offering beauty services and products, to the inclusion of massage serv ices. By 1914, the expansion strategy for the business was well shaped, with the business starting to formulate, manufacture and sell its own beauty and cosmetics products. Thus, the Red Door salon grew and expanded immensely, and by 1915, she embarked on making her business international, through opening other salons in different parts of the world, where the first the Elizabeth Arden salon was opened in France in 19224. By 1930, the Red Door salons had been established in the major fashion capitals of the world, and thus the company, as a brand, had become as popular as the Coca-Cola Company. Until her death in 1962, Elizabeth Arden, Inc. had been recognized the world over as a giant in the cosmetics industry, and she had won several honors for her contribution to the 21st century entrepreneurship. However, the company was highly affected by the great depression occurring in the period 1938, although the brands of the company were still popular, thus it continued to make reasonabl e sales that enabled it to survive the economic crisis, while earning low profits. The Elizabeth Arden, Inc. during the World War II Elizabeth Arden, Inc. was especially active during the World War II period, with a special focus on facilitating women who were joining the fighting forces. This way, the Elizabeth Arden, Inc. engaged in the production of various brands meant for the women soldiers, which included lipsticks that were required to match the uniform of

Analysis Assignment Example | Topics and Well Written Essays - 500 words - 4

Analysis - Assignment Example The problem of labor mobility training can best be solved when program designer embraces training from the learners’ point of view. Moreover, such training can be handled in different timelines depending on the institution and the department in, which training is to be conducted (Swain et al. 2014). Based on the continued development from previous units, labor mobility students are organizational employees sourced across different managerial departments ranging from supervisors to midlevel managers (Swain et al. 2014). Such a class of person is best suited for the above training programs because they are mostly responsible for the productivity of the organization. Despite the fact that no pedagogical consideration may be required for such trainees, the management must ensure proper knowledge are in place. Besides, labor-mobility training program should be aided using decision management system(DSS) as part of the managerial learning process. Training designs would only commence when the decision has been made prior to the analysis process and must end with the models that are perceived critical for the training needs. With consideration to the learning objectives, trainers must come up with valid concepts that clarify what is contained within the training program. Moreover, trainers must determine how comprehensive is the training curriculum and how it should be moderated. In addition, appropriate training material must be allocated must be unveiled depending on the learning procedure (Saks & Belcourt, 2006). Evaluation is considered to be the last stage of the ADDIE model. The procedure gives the trainers opportunity to trace back to the initial training process where they get to understand if any improvement has taken place. As part of the labor mobility training process, organizations incur a lot of expenses for the training process with the expectation of improving productivity. As such, the training department must come up with result oriented

Both the Adventure Essay Example for Free

Both the Adventure Essay Both the Adventure of the Speckled Band and Lamb to the Slaughter share some characteristics of murder mysteries. Which story is the most typical one? Which story is most successful in creating suspense? Attracting readers of all ages for hundreds of years, it is evident through these two stories that the murder mystery genre has evolved from a more stereotypical whodunit structure, however still continuing to enthral its reader by creating a sense of the unexpected, and engaging them in anxiety through the effective use of language and characters. The Speckled Band and Lamb to the Slaughter share characteristics of murder mysteries and demonstrate the significant difference, which has changed the typical structure through the years. The Speckled Band written in the Victorian times (1882) by Sir Arthur Conan Doyle during the reign of Queen Victoria, features one of the finest ever adventures of the legendary detective Sherlock Holmes whereas on the other hand Lamb to the Slaughter demonstrates a less predictable or typical whodunit structure written in the 1950s by Roald Dahl. Those essential elements of a murder mystery are witnessed in both stories including the detectives, villains, motives, atmosphere, and the narration allowing the reader a more direct participation. The Speckled Band looks at how a tragic death has left Helen Stoner, who lives in Stoke Moran with her stepfather, extremely frightened. Helens sister Julia died in mysterious circumstances just prior to her marriage, and Julia had spoken to Helen about a low whistling sound she had heard in the night just before she died, and she said something to Helen about a Speckled Band she had seen. Helen goes to visit Sherlock Holmes and she reveals that an agreement was made, whereby all her mothers money would go to Dr Roylott (her stepfather), with a provision that a certain annual sum should be allowed for each of us in the event of our marriage. After investigation, Holmes later finds out that each sister would get i 250, which at the time was a great deal of money. The reader sees a clear motive for the murder of Julia Stoner, as she was about to inherit a huge sum of money, which her stepfather would have to give. The reader is lead to believe that because Dr Roylott would have to give a large sum of money to both the girls this may be his motive for murdering Helen prior to her marriage. Helen also therefore appears to be in danger building the suspense from early in the plot. The story then goes on to look at the typical detective manner of Sherlock Holmes, who uncovers the truth behind the unexpected death of Julia Stoner, always accompanied by his friend Dr Watson from whom the adventure is seen through, allowing the reader an immediate involvement in the mystery and a force to believe Dr Watson. Holmes and Watson work on various clues with the help of Helen to find out that it was a snake let out by Dr Roylott that killed Julia. Sir Conan Doyle wrote detective fiction in the Speckled Band for a reader who would appreciate the traditional structure, adapting from a more serious, realistic Victorian lifestyle where the doctors were of a higher society. The story gives the reader a hint or motive for murder in the very beginning whereas on the other hand Lamb to the Slaughter, holds back a lot of information and tricks the reader, giving a more unexpected approach and a less typical one such as the Speckled Band. The audience had a different liking and therefore The Speckled Band was more popular compared to a more varied approach, which is popular with the modern audience. The Speckled Band is written looking at the Victorian lifestyle therefore looking at the traditional views. This reflects the storys structure as it is set in an old mansion in mysterious surroundings, which was a traditional setting. Sir Conan Doyles story revolves around the character of the detective, Sherlock Holmes, which is a preferred technique of mystery novelists, probably because it leaves a place for sequel. The story, though centred on Holmes, is told as seen through the eyes of his companion, Dr Watson, providing a good example of writing in the first person. The Speckled Band was published in a magazine called the Strand magazine, which gave short chapters every week, therefore always leaving the reader in suspense, guessing until the next chapter was published. There are many things that tell us that this story was written in the late 19th century, for example Helen Stoner arrived by dog-cart. Miss Stoner is dressed in all black and wearing a veil, possibly suggesting that she is in mourning which was common at the time when someone close to you died. In the Victorian times middle class women were very dependent on their husband and were therefore without very much independence. We know this because Holmes says when young ladies wander about the metropolis at this hour of the morning, and knock sleepy people up out of their beds, I presume that it is something very pressing which they have to communicate, suggesting that the woman wouldnt come at this time for no reason. It also suggests that for this reason he is interested in why this woman is here therefore first calling Dr Watson to meet her too. In contrast, Lamb to the Slaughter is probably set in a house in an American suburb. The story gives the first image of a devoted housewife who has an understandable love for her house. Everything is done, as if to perfection as Dahl presents her surroundings as clean, comfortable and peaceful. The room was warm and clean, the curtains drawn, the two table lamps alight-hers and the one by the empty chair opposite. This suggests that she has made sure everything is prepared for her husbands arrival as she has even lit the table lamp beside the empty chair. The story is seen from Marys perspective however it is written in a third person narration (omniscient narrator); this allows the reader to picture the story from her perspective and gets a greater depth into her character. This is not very typical of the murder mystery genre as usually the story is seen through the detective, victim or from another perspective but it is not common to be from the murderers view. Dahl has used a very untypical narration, which works very well to see a character in depth. This also makes the reader sympathise for Mary, as the narrator seems to do. Secondly Dahl describes Mary as a pregnant woman with soft, loveable features and a skin that has a wonderful translucent quality. This makes the reader now care for Mary and makes her a perfect victim being weak and a woman. It appears that Mary waits patiently every day for her husband to arrive from work and is overjoyed at his arrival.

Compare Passage A, which is a transcript in which a women working in a :: English Literature

Compare Passage A, which is a transcript in which a women working in a pub, talks about the different managers she has worked under, and passage B, which is an extract from, Odour of Chrysanthemums, a short story by D H Lawrence. Upon reading both passages I can clearly view numerous comparisons and differences. Initially, the subject, (meaning of the text) is extremely different in both extracts. Passage A is a transcript in which a women working in a pub, talks about the different managers she has worked under. Whereas passage B, is an extract from, "Odour of Chrysanthemums", a short story by D H Lawrence, set in the midlands. The passage describes how Elizabeth Bates seeks help from her neighbors one evening, when her husband fails to return home after work. The purpose of the two passages are also extremely diverse, passage A is a transcript, and basically she is informing a group of people or a fellow colleague about her previous managers in comparison to the manager she works under now. For instance she informs the other by telling her how she can get away with things while under her temporary manager, 'were all walking around with four lighted cigarettes in our hand and having a drink off everyone that gives us one. The second passage is there to entertain a particular group of people interested in D H Lawrence's writing. The use of descriptive writing engages the audience brains, in-order for them to carry on reading, 'He stood perplexed'. The audience in passage A is very informal, I believe that she is having a general chat with a fellow worker, because the level of speech is quite informal, 'that's the main thing like isn't it you know', I feel that it is interpersonal, the speaker and listener are in close proximity. While extract B, in my opinion will have an endless audience, because it can be seen over thousands of miles and thousands of years. I believe that the audience will benefit a particular age group, quite elderly people, who understand the particular dialect used. The genre itself is very different as well; principally passage A is a simple review of past and present mangers in which the worker has come across. Whereas on the other hand passage B is a suspenseful story, basically a thriller. You can identify this because of the language used throughout the text. "I don't like leaving the children in bed, and nobody in the house," she said. From this you notice that something eventful has occurred in which has permitted her to leave her children at home by them selves.

Environmental Health Essay

Overcrowding: Overcrowding in houses can arise from several causes, and the physical and psychological effects on people living in overcrowded conditions can be quite severe. Overcrowding poses serious direct and indirect health risks to all segments of the population, particularly the elderly, young children, and the disabled. Overcrowding results in insufficient ventilation in homes, causing or exacerbating respiratory illness. Susceptibility to disease, the severity of diseases, the spreading of illness, and the mortality due to disease all increase as a result of social and physical overcrowding. Overcrowding physically and emotionally overburdens mothers and other caregivers, increasing health risks of dependents. Lack of space and overcrowding directly impacts on the physical development and psychological wellbeing of disabled residents. Children living in overcrowded and unfit conditions are more likely to experience respiratory problems such as coughing and asthmatic and wheezing. For many children this means losing sleep, restricted physical activity, and missing school. Effects of overcrowding include meningitis, tuberculosis, heart disease, stomach cancer, respiratory disease. Children in overcrowded housing are up to 10 times more likely to contract meningitis than children in general. Meningitis can be life threatening. Long-term effects of the disease include deafness, blindness and behavioural problems. Children in unfit and overcrowded homes miss school more frequently due to illnesses and infections. Overcrowding is linked to delayed cognitive development, and homelessness to delayed development in communication skills. Urbanization: Movement of people from rural to urban areas with population growth equating to urban migration. It is a double edged sword as on one hand it provides people with varied opportunities and scope for economic development and on the other hand it exposes community to new threats. Unplanned urban growth is associated with environmental degradation meaning that population demands that go beyond the environmental service capacity, such as drinking water, sanitation, and waste disposal and treatment. Rapid growth of urban centres has led to substandard housing on marginal land and overcrowding. Outbreaks of diseases transmitted through respiratory and faeco-oral route due to population density. It exacerbates health risks related to insufficient and poor water supply and poor sanitation systems. Lack of privacy leading to depression, anxiety, stress etc. Due to the numbers of motorized vehicles and industries in the cities of the developing world Problems of noise and air pollution arise. Air pollution can affect our health in many ways with both short-term and long-term effects. Short-term air pollution can aggravate medical conditions like asthma and emphysema. Long-term health effects can include chronic respiratory disease, lung cancer, heart disease, and even damage to other vital organs. Water pollution: Water pollution can come from a number of different sources. If the pollution comes from a single source, such as an oil spill, it is called point-source pollution. If the pollution comes from many sources, it is called nonpoint-source pollution. Most types of pollution affect the immediate area surrounding the source. Sometimes the pollution may affect the environment hundreds of miles away from the source, such as nuclear waste, this is called trans boundary pollution. Industrial and agricultural work involves the use of many different chemicals that can run-off into water and pollute it. Metals and solvents from industrial work can pollute rivers and lakes. These are poisonous to many forms of aquatic life and may slow their development, make them infertile or even result in death. Pesticides are used in farming to control weeds, insects and fungi. Run-offs of these pesticides can cause water pollution and poison aquatic life. Subsequently, birds, humans and other animals may be poisoned if they eat infected fish. Petroleum is another form of chemical pollutant that usually contaminates water through oil spills when a ship ruptures. Oil spills usually have only a localized effect on wildlife but can spread for miles. The oil cancause the death of many fish and stick to the feathers of seabirds causing them to lose the ability to fly. Industry is a huge source of water pollution, it produces pollutants that are extremely harmful to people and the environment. Many industrial facilities use freshwater to carry away waste from the plant and into rivers, lakes and oceans. †¢Pollutants from industrial sources include: ? Asbestos – This pollutant is a serious health hazard and carcinogenic. Asbestos fibres can be inhaled and cause illnesses such as asbestosis, mesothelioma, lung cancer, intestinal cancer and liver cancer. ?Lead – This is a metallic element and can cause health and environmental problems. It is a non-biodegradable substance so is hard to clean up once the environment is contaminated. Lead is harmful to the health of many animals, including humans, as it can inhibit the action of bodily enzymes. ?Mercury – This is a metallic element and can cause health and environmental problems. It is a non-biodegradable substance so is hard to clean up once the environment is contaminated. Mercury is also harmful to animal health as it can cause illness through mercury poisoning. ?Nitrates – The increased use of fertilisers means that nitrates are more often being washed from the soil and into rivers and lakes. This can cause eutrophication, which can be very problematic to marine environments. ?Phosphates – The increased use of fertilisers means that phosphates are more often being washed from the soil and into rivers and lakes. This can cause eutrophication, which can be very problematic to marine environments. ?Sulphur – This is a non-metallic substance that is harmful for marine life. ?Oils – Oil does not dissolve in water, instead it forms a thick layer on the water surface. This can stop marine plants receiving enough light for photosynthesis. It is also harmful for fish and marine birds. ?Petrochemicals – This is formed from gas or petrol and can be toxic to marine life. Carbon footprint: Man-made climate change, or global warming, is caused by the release of certain types of gas into the atmosphere. The dominant man-made greenhouse gas is carbon dioxide (CO2), which is emitted whenever we burn fossil fuels in homes, factories or power stations. But other greenhouse gases are also important. Methane (CH4), for example, which is emitted mainly by agriculture and landfill sites, is 25 times more potent per kilogram than CO2. Even more potent but emitted in smaller quantities are nitrous oxide (N2O), which is about 300 times more potent than carbon dioxide and released mainly from industrial processes and farming, and refrigerant gases, which are typically several thousand times more potent than CO2. In the UK, the total impact on the climate breaks down like this: carbon dioxide (86%), methane (7%), nitrous oxide (6%) and refrigerant gases (1%). Given that a single item or activity can cause multiple different greenhouse gases to be emitted, each in different quantities, a carbon footprint if written out in full could get pretty confusing. To avoid this, the convention is to express a carbon footprint in terms of carbon dioxide equivalent or CO2e. This means the total climate change impact of all the greenhouse gases caused by an item or activity rolled into one and expressed in terms of the amount of carbon dioxide that would have the same impact. Loss of biodiversity: Human activities are responsible for most of the loss in biodiversity throughout the world. With an increasing population, we are consuming more and more natural resources.. We do this by driving more, using more energy in our homes, and buying many more products than we need. Biodiversity is important since it provides us with raw materials that we use to make products such as clothes, shoes and paper. And although we use many natural products and materials in our daily lives, we also use many human-made chemicals–cleaners, fertilizers, bug spray, pesticides, and many others. Even though we use them to help us, they have many side effects. Toxins and pollution are very harmful to biodiversity. The chemicals that we use end up in our waterways. Plants and animals are killed by oil spills. Wildlife gets caught in plastic trash.