A Theory Of Human Motivation - 1086 Words

A Theory of Human Motivation Maslow (1943) sets out to provide a theory as to why we as individuals become motivated to satisfy our basic needs and seek to fulfill other needs once the previous ones have been satisfied. He developed a concept called the hierarchy of needs, which he uses to interpret the different levels of needs individuals acquire. This theory is of importance as it provides reasoning and structure for the fulfillment of our everyday needs. After describing the five needs, the author talks about the pre-conditions that must be met in order to satisfy basic needs. Further discussion of characteristics pertaining to the theory will lead into the degree of fixity of the hierarchy. Thirteen propositions from a previous article were initially presented. These were meant to set somewhat of a guideline as to what should be accepted and what should not. Some of the more important propositions in my opinion were: conscious desires are not as fundamental as unconscious goals, human needs are arranged in hierarchies of prepotency, and motivation classification is based on goals. I felt like he focused a bit more on these propositions than the others. Following the thesis statement, we learn about the hierarchy of needs, which consists of physiological needs, safety needs, esteem needs, belonging needs, and lastly, self-actualization. Physiological needs consist of the dual-components, homeostasis and hunger. The state of being at homeostasis signifies thatShow MoreRelatedThe Theory Of Human Motivation Essay1091 Words   |  5 Pagesessence, the theory believes human behaviour can be predicted, as each person is driven by a set of needs, which the transactional leadership framework assumes to be money and simple rewards. Two main theories of human motivation have influenced the transactional framework: Abraham Maslow’s hierarchy of needs and Douglas McGregor’s Theory X. Maslow’s hierarchy of needs Psychologist Abraham Maslow first proposed his ideas around human needs in a 1943 paper â€Å"A Theory of Human Motivation†. The paperRead MoreThe Theory Of Human Motivation843 Words   |  4 PagesMotivation is a topic that is highly popular in modern media. Many medias such as television commercials use motivation as a selling point to most company’s. Human motivation is a strong topic used to sell products such as workout and dietary supplements.The concept of human motivation is the thought of how one can be motivated to do a specific task. People are motivated in many different ways, motivation can come from a drive to want to do something with a tenacious ideal. Motivation is not somethingRead MoreThe Theory Of Human Motivation2839 Words   |  12 PagesIntroduction Motivation is a force that causes employees to select and choose certain behaviors from the many alternatives open to them (Lawler, E Suttle 1972 , 281). It has been widely accepted that motivation is one of the primary drivers of behavior in work place. The theory of human motivation describes motivation as the effective and efficient laden anticipations of preferred situations that guide the behavior of humans towards these situations. There are various motivational theorists asRead MoreA Theory Of Human Motivation2110 Words   |  9 Pagesare countless facets and many temperaments we need to take into account. In modern day, progressive circles, groups are comprised of much diversity and an assortments of ideals. In his 1943 paper A Theory of Human Motivation in Psychological Review. [2]. Philosopher Abraham Maslow stated the third human interpersonal essential as the need to belong. (Include one more sentence commenting the need to belong in groups). Groups tend to form around many collectives including cultural, racial, religiousRead MoreThe Theory Of Human Motivation Essay1839 Words   |  8 PagesPensions Transfers †¢ Summative Coursework †¢ Session B60854 †¢ Course Start Date: 22 august 16 †¢ Submission Deadline: Midday 1 November 16 †¢ Candidate C53500. â€Æ' Introduction The theory of human motivation was introduced in 1943 by psychologist Abraham Maslow as the Hierarchy of needs. Basic needs like food and shelter once met give rise to psychological needs, which motivate behaviour. To feel good people, have a bias for instant gratification. The FCA are taking a keen interest in behaviouralRead MoreMaslow s Theory Of Human Motivation1560 Words   |  7 Pagesof what ideology one follows, is â€Å"what motivates humans?† In the year of 1943, Abram Maslow wrote his paper A Theory of Human Motivation. In this paper, Maslow described a theory in which he claimed that all people had basic needs, and these needs were fulfilled in order of their importance to the individual. Each need would need to be met prior to working towards another need, eventually achieving the ultimate goal of self-actualization. This theory is the basis of the humanistic perspective, whichRead MoreMaslow s Theory Of Human Motivation901 Words   |  4 PagesIn our everyday lives, we go through certain needs and behaviors. Abraham Maslow’s article of Theory of Human Motivation begins with the explanation of the Basic Needs of behavior. He goes over how our basic needs are safety , love, self-esteem, and self-actualization. (Physiological needs tend to go along with the other four needs.) When it comes to craving violence, four of the above needs apply to the given behavior. Starting with physiological needs; they are those needs that include survivalRead MoreAbraham Maslow : The Theory Of Human Motivation1356 Words   |  6 PagesAbraham Maslow: The Theory of Human Motivation Abraham Harold Maslow was an American psychologist, born on April 1st 1908 in Brooklyn New York City, N.Y. Maslow is better known for the creating of Maslow’s hierarchy of needs, which I believe to be human motivation. This is considered to be a theory of psychological health predicted on fulfilling human needs in priority, culminating in self-actualization. Maslow being ranked as the 10th most cited psychologist of the 20th century; from a book whichRead MoreMaslow s Theory On Human Motivation1310 Words   |  6 PagesMaslow’s (1943) hierarchy of needs was one of the earliest theories developed on human motivation. With the basic principle that higher-level motives could not become active before the basic needs had been met (Lahey, 2001). Maslow suggested that these basic needs such as food, water and safety needed to be in place and satisfied before motivation to meet higher needs is possible and takes effect. Maslow (1943) organised these human needs into five sets and then arranged those into a pyramid, withRead MoreA Theory Of Human Motivation By Abraham Maslow911 Words   |  4 Pagesthe passage, â€Å"A Theory of Human Motivation,† by Abraham Maslow, and then write an analysis of the film, Homeless to Harvard: The Lizz Murray Story (The Analysis Assignment Instructions). We were told to use Maslow’s theory as an analytical tool and apply what he states in regards to human motivation to the characters in the film (201-205). Mr. Barrera, my English professor, helped with additional amplification and illustration in showing the connection of the film to Maslow’s theory. The study of this

Patterns Within Systems of Linear Equations Free Essays

Jasmine Chai Grade 10 196298501 Patterns within systems of linear equations Systems of linear equations are a collection of linear equations that are related by having one solution, no solution or many solutions. A solution is the point of intersection between the two or more lines that are described by the linear equation. Consider the following equations: x + 2y = 3 and 2x – y = -4. We will write a custom essay sample on Patterns Within Systems of Linear Equations or any similar topic only for you Order Now These equations are an example of a 2Ãâ€"2 system due to the two unknown variables (x and y) it has. In one of the patterns, by multiplying the coefficient of the y variable by 2 then subtract the coefficient of x from it you will be given the constant. As a word equation it can be written like so with the coefficient of x as A and coefficient of y as B and the constant as C, 2B – Ax = C. This can be applied to the first equation (x + 2y = 3) as 2(2) – 1 = 3. To the second equation (2x – y = -4), it is -1(2) – 2 = -4. By using matrices or graphs, we can solve this system. Regarding other systems that also has such as pattern, it should also have the same solution as the two examples displayed. For instance, 3x + 4y = 5 and x -2y = -5, another system, also displays the same pattern as the first set and has a solution of (-1, 2). Essentially, this pattern is indicating an arithmetic progression sequence. Arithmetic progression is described as common difference between sequences of numbers. In a specific sequence, each number accordingly is labelled as an. the subscript n is referring to the term number, for instance the 3rd term is known as a3. The formula, an = a1 + (n – 1) d, can be used to find an, the unknown number in the sequence. The variable d represents the common difference between the numbers in the sequence. In the first equation (x + 2y = 3) given, the common differences between the constants c – B and B – A is 1. Variable A is the coefficient of x and variable b represents the coefficient of y, lastly, c represents the constant. The common difference of the second equation (2x – y = -4) is -3 because each number is decreasing by 3. In order to solve for the values x and y, you could isolate a certain variable in one of the equations and substitute it into the other equation. x + 2y = 3 2x – y = -4 x + 2y = 3 * x = 3 – 2y * 2(3 – 2y) – y = -4 * 6 – 4y – y = -4 * 6 – 5y = -4 * -5y = -10 * y = 2 Now that the value of y is found, you can substitute 2 in as y in any of the equations to solve for x. x + 2y = 3 x + 2(2) = 3 * x + 4 = 3 * x = 3 – 4 * x = -1 Solution: (-1, 2) Even though the solution has already been found, there are many different ways to solve it, such as graphically solving it. By graphing the two linear lines, you can interpolate or extrapolate if necessary to find the point where the two lines intersect. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Graph 1 Graph 1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Just from the equations given, it is not in a format where it can be easily graphed. By changing it into y=mx + b form, the first equation will result as y = – (1/2) x + 3/2 or y = -0. 5x + 1. 5 and the second equation will result as y = 2x + 4. The significance of the solution is that it is equal to the point of intersection as shown on Graph 1. This can then allow the conclusion that the solution of the two linear equations is also the point of intersection when graphed. According to this arithmetic progression sequence, it could be applied to other similar systems. For instance, the examples below demonstrates how alike 2Ãâ€"2 systems to the previous one will display a similarity. Example 1: In the first equation the common difference between (3, 4 and 5) is 1. In the second equation, the common difference is -3. The common differences in these equations are exact to the previous example. 3x + 4y = 5 x – 2y = -5 x – 2y = -5 * x = 2y – 5 (Substitution) 3x + 4y = 5 * 3(2y – 5) + 4y = 5 * 6y – 15 + 4y = 5 * 10y – 15 = 5 * 10y = 20 * y = 2 (Substituting y) x – 2y = -5 * x – 2(2) = -5 * x – 4 = -5 * x = -5 +4 * x = -1 Solution: (-1, 2) Example 2: In the first equation below, it has a common difference of 18 for (2, 20 and 38). For the second equation, in (15, -5 and -25), it has a common difference of -20. In this example, the system is solved graphically. 2x + 20y = 38 15x – 5 y = -25 Solution: (-1, 2) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Graph 2 Graph 2 | | | From the examples given above that are very similar to the first system, we can conclude that there is something common between them, that is the point of intersection or the values of x and y. That would imply that the x and y values and the point of intersection will always be (-1, 2) for all systems that follow arithmetic progression sequences. Due to that similarity, an equation that can be applied to these types of equations can be made. If the first coefficient of the first equation is identified as A and the common difference is c, an equation such as, Ax + (A + c) y = A + 2c, is made. This equation is so, because it is describes an arithmetic sequence, where the coefficients and constant are increasing by one in response to the coefficient before. In the second equation of the system, another equation can be made relatively the same to the first, with exceptions of different variables used. If B is used to represent the first coefficient of the second equation and d is used as the common difference, the equation, Bx + (B + d) y = B + 2d is created. With 2 equations, we have now created a system; to solve the system we can use the elimination method. This method is used to eliminate certain variables in order to find the value of another variable. After doing so, you could substitute in the value for the found variable and solve for the other(s). Ax + (A + c) y = A + 2c Bx + (B + d) y = B + 2d In order to use the elimination method, you must make the coefficient of x or y the same depending on which one you would like to eliminate. In this case, we will start by eliminating x. To proceed to do so, we must first multiply the first equation by B and the second equation by A: ABx + (AB + Bc) y = AB + 2Bc ABx + (AB + Bd) y = AB + 2Bd After we have made the coefficient of x the same for both equations, we can now subtract the equations from one another: ABx + ABy + Bcy = AB + 2Bc ABx + ABy + Bdy = AB + 2Bd * Bcy – Bdy = 2Bc – 2Bd To find the value of y, we must isolate the variable y. Bcy – Bdy = 2Bc – 2Bd * y(Bc – Bd) = 2(Bc – Bd) * y = 2 Now that the value of y is found, to find the value of x is to substitute the value of y, which is 2, into any equation that includes that variable x and y. Bx + (B + d) y = B + 2d * Bx + (B + d) 2 = B + 2d * Bx + 2B + 2d = B + 2d * Bx + 2B – B = 2d – 2d * Bx + B = 0 * Bx = -B * x = -1 To conclude the results of the equations above, it is making thee statement that all 2Ãâ€"2 systems that display an arithmetic progression sequence, which has a common difference between the coefficients and constant, it will have a result, point of intersection, of (-1, 2). To confirm that this is correct, the example systems below will demonstrate this property: Equation 1 (common difference of 8): 2x + 10y = 18 Equation 2 (common difference of 3): x + 4y = 7 Substitution Method x + 4y = 7 * x = 7 – 4y Substitute 2x + 10y = 18 * 2 (7 – 4y) + 10y = 18 * 14 – 8y +10y = 18 * 14 + 2y = 18 2y = 18 – 14 * 2y = 4 * y = 2 Substitute x + 4y = 7 * x + 4(2) = 7 * x + 8 = 7 * x = 7 – 8 * x = -1 Solution: (-1, 2) Once again from the example above, it displays that the solution or the point of intersection is identified as (-1, 2). From previous examples, all have a common difference that is different from the other equation involved in that system. In the fol lowing example, it will experiment whether having the same common difference will make a difference in the result. Equation 1 (common difference of 3): 2x + 5y = 8 Equation 2 (common difference of 3): x + 3y = 6 Graph 3 Graph 3 As you can see on the graph, it shows that the two lines do not intersect at (-1, 2) even though it is a 2Ãâ€"2 system that has a common difference in both equations, meaning that the intersection at (-1, 2) can only be applied to systems that has 2 different common differences. To conclude, all 2Ãâ€"2 systems that follow arithmetic progression sequence with different common difference have a solution of (-1, 2). Furthermore, now that it is known that there is a certain pattern for a specific type of system, if this property is applied to a 3Ãâ€"3 system, with 3 different variables can it still work? Consider the following 3Ãâ€"3 system, (x + 2y + 3z = 4), (5x + 7y + 9z = 11) and (2x + 5y + 8z = 11). In this system, it has similar patterns to the 2Ãâ€"2 systems above due to its arithmetic progression. In the first equation, it has a common difference of 1 and the second equation has a common difference of 2 and lastly, the third equation has a common difference of 3. To solve this system, we can solve it using the method of elimination or matrices. Equation 1 (common difference: 1): x + 2y + 3z = 4 Equation 2 (common difference: 2): 5x + 7y + 9z = 11 Equation 3 (common difference: 3): 2x + 5y + 8z = 11 Elimination Method To eliminate the variable x, we must first start by making the coefficients of x in two equations the same. We can do so by finding the lowest common multiple of the two coefficients and multiplying the whole equation by it. Equation 1: x + 2y + 3z = 4 * 2(x + 2y + 3z = 4) * 2x + 4y + 6z = 8 We can eliminate the variable x now that the coefficients of x in both equations are the same. To eliminate x, we can subtract equation 3 from equation 1. Equation 1 and 3: 2x + 4y + 6z = 8 2x + 5y + 8z = 11 -y -2z = -3 After eliminating x from two equations to form another equation that does not involve x (-y -2z = -3), another equation that does not involve x must be made to further eliminate another variable such as y or z. Equation 1: x + 2y + 3z = 4 * 5(x + 2y + 3z = 4) * 5x + 10y + 15z = 20 We can eliminate the variable x now that the coefficients of x in both equations are the same. To eliminate x, we can subtract equa tion 2 from equation 1. Equation 1 and 2: 5x + 10y + 15z = 20 – 5x + 7y + 9z = 11 3y + 6z = 9 Now that two different equations that do not involve x ((-y -2z = -3) and (3y + 6z = 9)) are created, we can find the common coefficient of y and eliminate it to find the value of the variable z. Let (-y -2z = -3) to be known as equation A and (3y + 6z = 9) will be known as equation B. Equation A: -y -2z = -3 * 3(-y -2z = -3) * -3y -6z = -9 Equation A and B: -3y -6z = -9 + 3y + 6z = 9 0 = 0 As you can see from the result, 0 = 0, this is indicating that the system either has many solutions, meaning a collinear line or no solution, where all the lines do not intersect together at a specific point. Even if you attempt to isolate a different variable it will still have the same result. For instance, using the same equations above, you eliminate the variable y first as displayed below. Equation 1 (common difference: 1): x + 2y + 3z = 4 Equation 2 (common difference: 2): 5x + 7y + 9z = 11 Equation 3 (common difference: 3): 2x + 5y + 8z = 11 Elimination Method Equation 1: x + 2y + 3z = 4 * 7(x + 2y + 3z = 4) * 7x +14y + 21z = 28 Equation 2: 5x + 7y + 9z = 11 * 2(5x + 7y + 9z = 11) * 10x + 14y + 18z = 22 Equation 1 and 2: 7x +14y + 21z = 28 – 10x + 14y + 18z = 22 3x + 3z = 6 Equation 1: x + 2y + 3z = 4 * 5(x + 2y + 3z = 4) * 5x +10y + 15z = 20 Equation 3: 2x + 5y + 8z = 11 * 2(2x + 5y + 8z = 11) * 4x + 10y +16z = 22 Equation 1 and 3: 5x +10y + 15z = 20 – 4x + 10y +16z = 22 x – z = -2 Two equations have been made that has already eliminated the variable y. Let (-3x + 3z = 6) be equation A and let (x – z = -2) be equation B. Doing this, is in attempt to sol ve for variable x. Equation A: -3x + 3z = 6 Equation B: x – z = -2 * 3(x – z = -2) * 3x – 3z = -6 Equation A and B: -3x + 3z = 6 + 3x – 3z = -6 0 = 0 As you can see the result, it is the same even if you try to solve another variable, from that we can confirm that this system has either no solution or infinite solutions, meaning that they are collinear lines. Furthermore, because this is a 3Ãâ€"3 system, meaning that it has three different variables, such as x, y and z, graphing it will also be very different from a graph of a 2Ãâ€"2 system. In a 3Ãâ€"3 system, the graph would be a surface chart, where the variable z allows the graph to become 3D. From this, we can conclude 3Ãâ€"3 systems that follow an arithmetic progression will always have either no solution or infinite solutions. This is saying that all linear equations do not intersect together in one point or they do not intersect. A way to prove this is through finding the determinant. The determinant is a single number that describes the solvability of the system. To find the determinant of all 3Ãâ€"3 systems that possesses arithmetic progression, we can start by creating a formula. Allow the first coefficient of the first equation be A and the second equation’s first coefficient be B and lastly, the first coefficient of the third equation be C. The common difference of equation one will be c, the common difference of equation two will be d, and the common difference of equation e will be e. This can be described through the following equations: 1. Ax + (A + c) y + (A + 2c) z = (A + 3c) 2. Bx + (B + d) y + (B + 2d) z = (B + 3d) 3. Cx + (C + e) y + (C + 2e) z = (C + 3e) When developing a matrix to find the determinant, you must have a square matrix. In this case, we do not have a square matrix. A square matrix is where the number of rows and columns are equal, for example, it could be a 2Ãâ€"2, 3Ãâ€"3, or 4Ãâ€"4. Looking at the equations, it is a 3Ãâ€"4 matrix; as a result it must be rearranged. Below is the rearranged matrix of the equations above. x A (A + c) (A + 2c) (A + 3c) y B (B + d) (B + 2d) = (B + 3d) z C (C + e) (C + 2e) (C + 3e) To find the determinant, you must find 4 values from the 3Ãâ€"3 matrix that helps find the determinant of A, B and C. In this case, if you were to find the values for A, you would cover the values that are in the same row and column as A, like so, A (A + c) (A + 2c) B (B + d) (B + 2d) C (C + e) (C + 2e) You would be left with four separate values that can be labelled as A, B, C and D. Respectively to the model below: a b c d In order to find the determinant you must find the four values for A, (A + c) and (A +2c). To find the determinant the equation ad – cb is used. The equation in this situation would be like the one below: A[(B + d)(C + 2e) – (C + e)(B + 2d)] – (A + c)[B(C + 2e) – C(B + 2d)] + (A +2c)[B(C + 2e) – C(B + 2d)] Expand * = A(BC – BC + Cd – 2Cd + 2Be – Be + 2de – 2de) – (A + c)(BC – BC + 2Be – 2Cd) + (A + 2c)(BC – BC + 2Be – 2Cd) Simplify 2ABe – 2ABe + 2ACd – 2ACd + 2Ccd – 2Ccd + 2Bce – 2Bce * = 2ABe – 2ABe + 2ACd – 2ACd + 2Ccd – 2Ccd + 2Bce – 2Bce * = 0 As it is visible, above it shows that the determinant found in this type of matrix is zero. If it is zero, it means that there are infinite answers or no answer at all. Using technology, a graphing calculator, once entering a 3Ãâ€"3 matrix that exhibits arithmetic progression, it states that it is an error and states that it is a singular matrix. This may mean that there is no solution. To conclude, there is no solution or infinite solution to 3Ãâ€"3 systems that exhibit the pattern of arithmetic sequencing. This can be proved when the sample 3Ãâ€"3 system is graphed and results as a 3D collinear segment. As well as the results from above when a determinant is found to be zero proves that 3Ãâ€"3 systems that pertains an arithmetic sequence. Arithmetic sequences within systems of linear equations are one pattern of systems. Regarding other patterns, it is questionable if geometric sequences can be applied to systems of linear equations. Consider the following equations, x + 2y = 4 and 5x – y = 1/5. It is clear that the coefficients and constants have a certain relation through multiplication. In the first equation (x + 2y = 4), it has the relation where it has a common ratio of 2 between numbers 1, 2 and 4. For the second equation (5x – y = 1/5), it has a common ratio of -1/5 between 5, -1 and 1/5. The common ratio is determined through the multiplicative succession from the previous number in the order of the numbers. When the equations are rearranged into the form y=mx+b, as y = – ? x + 2 and y = 5x – 1/5, there is a visible pattern. Between the two equations they both possess the pattern of the constant, where constant a is the negative inverse of constant b and vice versa. This would infer that if they are multiplied together, as follows (-1/2 x 2 = -1 and 5 x -1/5 = -1), it will result as -1. With equations that are also similar to these, such as the following, y = 2x – 1/2, y = -2x + 1/2, y = 1/5x – 5 or y = -1/5x +5. Displayed below, is a linear graph that shows linear equations that are very similar to the ones above. Graph 4 Graph 4 From the graph above, you can see that the equations that are the same with exceptions of negatives and positives, they reflect over the axis and displays the same slope. For instance, the linear equations y = 2x -1/2 and y=-2x +1/2 are essentially the same but reflected as it shows in the graph below. Also, all equations have geometric sequencing, which means that they are multiplied by a common ratio. Secondly, the points of intersection between similar lines are always on the x-axis. Graph 5 Graph 5 Point of intersection: (0. 25, 0) Point of intersection: (0. 25, 0) To solve a general 2Ãâ€"2 system that incorporates this pattern, a formula must be developed. In order to do so, something that should be kept in mind is that it must contain geometric sequencing in regards to the coefficients and constants. An equation such as, Ax + (Ar) y = Ar2 with A representing the coefficients and r representing the common ratio. The second equation of the system could be as follows, Bx + (Bs) y = Bs2 with B as the coefficient and s as the common ratio. As a general formula of these systems, they can be simplified through the method of elimination to find the values of x and y. Ax + (Ar) y = Ar2 Bx + (Bs) y = Bs2 Elimination Method B (Ax + (Ar) y = Ar2) * BAx + BAry = BAr2 A (Bx + (Bs) y = Bs2) * ABx + ABsy = ABs2 Eliminate BAx + BAry = BAr2 – ABx + ABsy = ABs2 BAry – ABsy = BAr2 – ABs2 ABy (r – s) = AB (r2 – s2) * y = (r + s) Finding value of x by inputting y into an equation ABx + ABsy = ABs2 * ABx + ABs(r + s) = ABs2 * ABx = ABs2 – ABs(r +s) * x = s2 – s(r +s) * x = s2 – s2 – rs * x = rs To confirm that the formula is correct, we can apply the equation into the formula and solve for x and y and compare it to the results of graph 4. T he equations that we will be comparing will be y = 5x – 1/5 and y = -1/5x + 5. The point of intersection, (1, 4. 8) of these equations is shown graphically on graph 4 and 6. The common ratio (r) of the first equation is -0. and the common ratio, also known as s in the equation of the second equation is 5. X = – (-0. 2 x 5) = 1 Y = (-0. 2 + 5) = 4. 8 As you can see, above, the equations are correctly matching the point of intersection as shown on the graphs. Due to such as result, it is known that it can now be applied to any equations that display geometric sequencing. Graph 6 Graph 6 Resources: 1. Wolfram MathWorld. Singular Matrix. Retrieved N/A, from http://mathworld. wolfram. com/SingularMatrix. html 2. Math Words. Noninvertible Matrix. Retrieved March 24, 2011 from, http://www. mathwords. com/s/singular_matrix. htm How to cite Patterns Within Systems of Linear Equations, Essay examples

Social Relation Business Relationship

Question: Describe about the Social Relation for Business Relationship. Answer: Issue The question of law to be determined in this case is; whether there is Derrick and Carmel had the intention to be legally bound and whether consideration was given and if it met the standards set by law. Rule The general rule that is applicable in social relation is that there exists a rebuttable presumption that there is no intention to be legally bound by any agreement made.[1] Conversely, an objective test to determine the intention of parties in a social relationship has been adopted by a majority of judicial decision which appears to eschew the application of the rebuttable presumptions as was observed in Ermogenous v Greek Orthodox Community of SA Inc.[2] On the matter of consideration, it is the general rule that consideration must be provided for a contract to be valid and enforceable. The consideration can either be the performance of an act or profit, benefit or interest that may be incurred in a promised transaction. [3]Some scholars appear to relate intention and consideration, and they argue that consideration determines the intention of the parties. The nerve of the reasoning of the preceding argument is that if consideration is present, then the parties intended to be legally bound. It should, however, be borne in mind that intention is an independent desideratum for a contract formation. In Woodward v Johnston [4] the claimant agreed to help the husband repair a dredge by cleaning the rust. The claimant dutifully performed this task during the weekend. The court held that such a relationship did not demonstrate that the parties had the intention to be legally bound because the claimant could not rebut the presumption that there was in intention to be bound. The presumption will, however, be rebutted in circumstances where a commercial agreement exists between a domestic relationship transaction. Moreover, the court in Todd v Nicol[5] While applying, the rebuttable presumptions ruled that they are rebutted if attention is paid to the nature of the relationship at the time of making the agreement and the extent to which the parties went to perform the promise. It is apparent from the test applied in Tods case that if the agreement goes beyond what would reasonably be inferred as a social agreement, the presumption will be rebutted. The judicial ink that has been spilled in recent cases in Australia is a manifest that the rebuttable presumption test has fallen into disfavor and the Objective test has taken root. It is of interest to note that the objective test has been applied in a case where the court held that the court should take into account the conduct of the parties and the wording displayed by the agreement and determine if on a balance of probability an intention to be legally bound will be inferred. The courts have applied the objective test in several instances to escape the use of the rebuttable presumption test. As has been noted in the Curie case consideration may be either a profit or interest following a promise. In this case, there was an agreed consideration of $20000. It has been held that the consideration must be given by the promisor to the promise and a promise cannot be enforced if a consideration has not been given.[6] It must also be demonstrated that consideration has an economic value and is not ambiguous in nature. In Dunlop Pneumatic Tyre Co Ltd v Selfridge Co Ltd[7] the court held that consideration must be the price that is paid fro the promise that has been made in the agreement. As such the promise should be valuable of benefit. In the case above Dunlop sold tires to a person on an agreed basis that they will not be sold at a certain undercut price. However, subsequent buyers of the tyres sold them at a lower price and the court held that there was no agreement between them and Dunlop and that there was no valuable consideration that had been given to enable the agreeme nt to be enforced. It is imperative to note that consideration must not necessarily be adequate. As a matter of course consideration must only be sufficient. In Chappell v Nestle[8] Lord Somervell argued that a sufficient consideration is based on the free will of the contracting parties to determine the final value of it. A more persuasive position was arrived at in Thomas v Thomas[9] where the court stated that a consideration of 1 pound as annual rent was sufficient and disregarded the argument that consideration must be adequate. Application Derrick and Carmel are cousins and therefore there relationship can be regarded as a domestic relationship. The fact that the relationship is a domestic one triggers the application of the rebuttable presumption test is strictly applied then the result will be that there was no intention to be legally bound. It can thus be argued that although Derrick and Carmel are great friends and cousins, the nature of their engagement is purely business related as it refers to a commercial service. It can be conceded that an intention to be legally bound existed in the agreement. The fact that agreement between Derrick and Carmel was of a business nature and a consideration of $20000 was given it can be stated that the consideration had an economic value and was very clear from the commencement of the transaction. It can be observed that Derrick and Carmel agreed on the final price after a counter offer which shows that the consideration was determined based on the free will of the parties who n egotiated. Conclusion In light of the above arguments and application of the law it can be concluded that the two parties had the intention to be legally bound by the agreement. However, as some scholars have noted the court determines the intention of both parties but on the real aspect the parties may have had a different intention when entering into the agreement. It could be argued that the court cannot determine what was in the minds of the parties realistically. This put other parties of the agreement at the peril of facing a miscarriage of justice. With regards to consideration, the amount that had been paid by Carmel is sufficient consideration and therefore he can enforce the promise in a court of law raising the above arguments. It is, however, advised that the rebuttable presumptions should not be entirely extinguished because it is most socially agreements that the parties will not likely end up in court incase of any failure to meet the obligations stated in the agreement. The onerous task sh ould be placed on the claimant asserting that there is an intention to be legally bound to rebut the presumptions that an intention to be bound existed in the social or domestic agreement. 1 (b). Issue The issue to be determined in this case whether there was an agreement between the parties for the contract to be enforceable and whether Carmelo is in a proper legal position to compel Derrick to give him the premium travel option. Rule The general rule is that for an agreement to be established there must be a consensus ad idem which is a meeting of the minds between parties entering into contract. The meeting of the minds will be evinced by an offer and a valid acceptance is communicated to the pother party to the agreement. The agreement can be said to have been settled once the other party is in acceptance to final terms that have been proposed and not during a counter offer. An offer has been defined in Australian Woollen Mills Pty Ltd v The Commonwealth[10] as a statement of expression of willingness to enter into a contractual agreement. It, however, begs the critical question on who made the offer in this case. Carmelo made an inquiry over the phone and asked Derrick if he can be booked fro the NBA final tour. Derrick replied with an offer which he communicated to Carmel. However, Carmel replied with an offer of a new price of 20000 pounds. It has been held in Hyde v Wrench[11] that when new terms are made by a party to a contract to an offer they cannot be deemed as an acceptance but rather a counter offer. Further, in the case where an offer and a counter-offer is made the situation is legally regarded as a battle of the forms I which case the last offer that is made and accepted wins the battle. It can thus be agreed that a valid offer in this case was made by Carmel. Acceptance must be communicated to the offeror in an effective manner.[12] It is of particular significance to note that the acceptance that was made by Derrick was communicated through email. The rules relating to acceptance by email state that an acceptance will be made when the email has been received.[13] This differs from the traditional position that has been taken by the postal rule that acceptance is deemed to have been made once the letter has been posted. It therefore follows that the acceptance was made when it was received by Derrick. Additionally, the general legal position is that the agreement is made the place where the acceptance has been received. The acceptance made must be clear and devoid any ambiguity. Essentially it must be one that will not trigger issues to do with interpretation in court. According Brambles Holdings v Bathurst City Council[14] the acceptance may also be implied. This means that acceptance may also be implied from the conduct of the parties w here they carry pout themselves in a manner that shows that they have accepted the terms and they are actually performing the contractual obligations already. It is also a rule of acceptance in contract law that acceptance must be made in relation to the offer that was made. In R v Clarke,[15] the plaintiff had stated in an interview that he was going to give information concerning the murder of two police officers to clear his name because he was under investigation. There was a reward that was to be given to any person who gave such evidence that will lead to the arrest of the real murderers. The plaintiff information led to the conviction the true murders. When he wanted to enforce the reward it was affirmed in court that the acceptance made to give the information was not in relation to the offer but to clear his name from any criminal suspicion. The acceptance that was made in the case of Derrick and Carmel was truly in response to the offer that had been made and therefore the acceptance can be said to be valid. Application Having demonstrated that there was a valid agreement which met the legal requirements of offer and acceptance it can be conceded that Carmelo can claim from the premium service that had been agreed on in the contract. In this case, Carmelo has a right to enforce the agreement as had been agreed. The fact that Derrick is offering a service that is poor implies that he is in breach of the contract that had been agreed between the two parties. In this case, it is advised to Derrick that may apply for damages where he will be awarded damages by the court fro the loss of the money without a service. In this case, he will be compensated an equal amount that he had paid to Derrick. Additionally, he may also be awarded punitive damages which are intended to punish the defendant fro breaching the contract. Apart from the punishment factor in the remedy, it is also intended to deter him from breaching another agreement in future. The court may award unliquidated damages for non-economic loss f actors such as pain and suffering if it is shown that Derrick suffered emotional distress and trauma from the loss of that great opportunity to tour the NBA finals. However, according to the Civil Liability Act 2002 a limit has been placed on the amount of money that can be awarded as damages for non-economic loss Lastly, Carmel may apply from the order of specific performance in court to compel Derrick to perform that which was his obligation in the agreement. This order will only be granted in circumstances where it is shown that damages will not adequately compensate the plaintiff. Conclusion It can be concluded that the requirement of an agreement has been established from the facts of the case in point because it has been demonstrated above that the requirement of offer and acceptance have been as required by law. In addition, the fact that that the parties, in this case, exercised their freedom of contract and engaged in offer and counter offer is sufficient evidence that the final price and terms agreed satisfied the requirement of an agreement. Having noted that there is a valid agreement it can also be concluded that Derrick can insist ion being given the premium accommodation and tour option because that was what he had bargained for. This promise can be legally enforced because all the essential elements required to form a valid and enforceable contract have been met. Most importantly it has been demonstrated that the parties had the intention to be legally bound by the terms that they had agreed on. Suffice to say; the failure to honor the promise in the agreed t erms by Derrick will attract a liability in breach of contract. References Australian Woollen Mills Pty Ltd v The Commonwealth (1954) 92 CLR 424 Brambles Holdings v Bathurst City Council (2001) 53 NSWLR 153 Brogden v Metropolitan Railway Company (1877) L.R. 2 App. Cas. 666 Coward v Motor Insurers Bureau [1962] 1 Lloyd's Rep 1 Chappel v Nestle [1960] AC 87 Coulls v Bagots Executor and Trustee Co Ltd (1967) 199 CLR 460 Currie v Misa (1875) LR 10 Ex 153 Dunlop Pneumatic Tyre Co Ltd v Selfridge Co Ltd [1915] UKHL 1 Entores Ltd v Miles Far East Corporation [1955] EWCA Civ 3 Ermogenous v Greek Orthodox Community of SA Inc [2002] HCA 8 Hyde v Wrench (1840) 49 ER 132 Jones v Vernon's Pools Ltd. [1938] 2 All ER 626 R v Clarke (1927) 40 CLR 227 Thomas v Thomas 1842 2 QB 851 Todd v Nicol [1957] S.A.S.R. 72