Animal Farm Chapter Summaries - Free Essay Example

In the first chapter of Animal Farm, Major, the prize Middle White boar(page 3) gets his fellow animals to come and listen to what he has to say. Old Major is the most honored among the animals, and his report that he has something to share is met with great suspense. In the following section from chapter one of Animal Farm, Old Major tells the gathered animals: This single farm of ours would support a dozen horses, twenty cows, hundreds of sheepand all of them living in a comfort and a dignity that are now almost beyond our imagining. Why then do we continue in this miserable condition? Because nearly the whole of the produce of our labor is stolen from us by human beings. There, comrades, is the answer to all our problems. It is summed up in a single wordMan. Man is the only real enemy we have. Remove Man from the scene, and the root cause of hunger and overwork is abolished forever.(page 7) Reading this book, one would be safe in deducing that man is the root of the animals problems. This thought would, of course, be wrong. Man is not the root of the animals problems; the lust for power and desire to obstruct ones vision upon others is the root of the problem. This is showed by Napoleon, a large, rather fierce-looking Berkshire boar with a reputation for getting his own way.(page 16) the reader can deduce, is a model of Joseph Stalin, the ruler of the Soviet Union. Stalin was a murderous but intelligent and rigorously manipulative leader who schemed and killed his way to the top of the Communist Party of the Soviet Union (CPSU), where he remained until he died in 1953. Among his many victims (which was in the millions) were fellow revolutionaries he considered his competitors as threats to his determination to rule alone atop the Communist Party. No, as the book typifies, man is not the root of the animals problems. The animals believe that by getting Farmer Jones and his men off the farm, they can create a better, fairer, more humane system of living. In the very beginning, this works really well, though this will not last long. The animals make the Seven Commandments that state all animals are equal, that no animal will kill another animal and no sleeping in beds or drinking alcohol, for example. At first, they all work together in a beautiful little society. The riddance of the humans doesnt end their problems, however, for their problems are in the desire of some animals, mainly Napoleon, to have power over the other animals. He plots and schemes and is willing to use lies and trickery to gain control. He lacks empathy and doesnt care who he hurts to get ahead of the rest of the animals. He uses the means of the revolution for his personal gain and corrupts others to do so. Unfortunately, many of the animals are too trusting and arent knowledgeable enough to know how to go against him. As we see in the book, until the animals can find a way to root out or restrain the evil within themselves, they will simply keep doing the human system of exploiting other for their own gain If man was really the source of the animals problems then it would follow that the riddance of Mr. Jones would bring about a utopia for the farm. But, as we see from the plot, this does not happen. In contrast, after Mr. Jones departure, there is a rapid ignorance for equality and a general decline in the quality of many of the animals lives. As such, it is more precise to propose that the source of the animals problems is Napoleon†most specifically, his desire for total control of he farm. This is shown a little early in the book when he steals the milk and puts it in the pigs food, instead of sharing it equally among the animal. Later, in Chapter Five, Napoleon shows his true intentions when he gets the dogs to sick Snowball and forces him to leave the farm. From that point, it is clear that Napoleon is self-interested and fiercely determined. By the end of the book, Napoleon is just as dictatorial as his former human masters, if not more than them. In short, the root of the problem challenging the animals in Orwells book is not man. The animals are not better off without Mr. Jones watching over their lives. The pigs are even worse than man, given their skills at political schemes and Napoleons dictatorial tendencies.

Essay about functions assignment

Functions Assignment Question 1. A function assigns a unique output value to every input value. This definition implies that a vertical line cannot intersect a function in more than one place (Stewart). The set of input values is known as the domain of a function. The set of output values is known as the range of a function. An example of a linear function is, f left (x right ) = 4x+3 where 4 and 3 are the slope and vertical intercept of the straight line f(x). The domain of this linear function is all values x can take on, namely, all real numbers. The range is also all real numbers. A parabola is a good example of a quadratic function, f left (x right ) = {x} ^ {2} The vertex of the parabola coincides with the origin of a Cartesian coordinate system. The domain of this function is all real numbers and its range is all positive real numbers, f(x)≠¥0. An example of a third degree polynomial is, f left (x right ) = {x} ^ {3} +3 {x} ^ {2} +2x+1 The domain and range of this polynomial are all positive real numbers. The exponential function is defined as, f left (x right ) = {e} ^ {x} The domain of the exponential function is all real numbers and its range corresponds to all positive real numbers. The natural logarithm is a good example of a logarithmic function and is defined as, f left (x right ) = ln {x} The domain of the natural logarithm is all positive real numbers, x0. The range is all real numbers. The trigonometric functions are good examples of periodic functions. For instance, the sine function, f left (x right ) = sin {x} It repeats every 2Ï€ radians. The domain of the sine function is all real numbers. The range is -1 ≠¤ f(x) ≠¤ 1. Question 2. The electrical activity of the human heart can be monitored by means of an Electrocardiogram (ECG). An example of ECG signal is shown in Figure 1. The signal was retrieved from National Instruments website (â€Å"National Instruments: Test, Measurement, and Embedded Systems†). The electrical heartbeats are represented by the voltage amplitude (dependent variable) over time (independent variable). The figure shows that heartbeats exhibit nearly periodic behavior. Strong beats repeat approximately every 1.6 seconds. Figure 1. Example of hearts electrical activity. Question 3. The displacement of a piston in an internal combustion engine is represented by a periodic function, f left (t right ) = A sin {ωt} where ω is referred to as the angular frequency and has units of radians per second (rad/s). The independent variable is time t (s). A stands for the amplitude and describes the magnitude of the maximum displacement of the piston. The amplitude is a constant value. One cycle takes place when the crack (a linkage connecting the engine shaft and piston) turns through 2Ï€ radians. In other words, the sine function repeats itself when ωT=2Ï€, where T is the period, so this time is defined as, T= {2Ï€} over {ω} The frequency is the inverse of the period and it is measured in s-1 or hertz (hz) f= {1} over {T} For example, a period of 10s means a frequency of 1 every 10 seconds. The average value of function f(x) over an interval [a,b,] is defined as, F = {1} over {b-a} int from {a} to {b} {f(x)dx} The above expression can be used to calculate the average displacement over one cycle of the piston [0,T], F = {1} over {T} int from {0} to {T} {A sin {{2Ï€t} over {T}} dt=} {1} over {T} {left [- {T} over {2Ï€} cos {{2Ï€t} over {T}} right ]} rsub {0} rsup {T} =- {1} over {2Ï€} left [cos {2Ï€} cos {0} right ] =0 Question 4. The inverse of a function ( f -1) takes on a value from the range of f and assigns a single value from its domain. The inverse of a function exist only if a horizontal line does not intersect the function f in more than one place. This is not satisfied for the case of periodic functions like the sinusoidal displacement of a piston, y=f left (t right ) = A sin {ωt} The domain of sin ωt has to be restricted in order to define the inverse function. It can be worked out as follows, {sin} ^ {-1} {left ({y} over {A} right ) =ωt} {{f} ^ {-1} (y) = t = {1} over {ω} sin} ^ {-1} {left ({y} over {A} right )} The inverse function holds as long as, {Ï€} over {2} ≠¤ {y} over {A} ≠¤ {Ï€} over {2} In a given cycle of the piston, the inverse function provides the time for which the piston is displaced y length units. Question 5. Part 1. The Richter scale is a scientific tool to measure the intensity of an earthquake (â€Å"Khan Academy | Khan Academy†). The following facts summarize the main features of the Richter scale: The Richter scale measures the earthquake magnitude. The intensity or amplitude of the ground motion is collected at the measuring stations. The maximum ground motion detected at a measuring station can be plotted against the distance to the epicenter. The Moment Magnitude Scale (MMS) was calibrated to the Richter scale. MMS is related to the energy released by earthquakes. Unfortunately, strong and weak earthquakes do not fit on the same plot if a linear scale is used. The Richter scale employs a logarithmic scale in order to present the data on the same chart. The Richter scale can be used to compare the magnitude of two earthquakes. For instance, the 5.8 earthquake that took place on the east coast of US in 2011and the 9.0 earthquake off the coast of Japan in the same year. Both magnitudes are reported on a logarithmic scale so the difference between these two earthquakes is not 3.2 but 103.2 (3.2 powers of 10). It means the earthquake in Japan was about 1600 times stronger than the east coast earthquake. Part 2. Table 1 summarizes the facts about the earthquakes chosen to draw a comparison. Date Location of epicenter Richter magnitude scale (M) 25 September 2013 Southwestern Pakistan 7.7 27 February 2010 Central Chile (near city of Concepcià ³n) 8.8 Table 1. Earthquake information. Part 3. Quantitative comparison of the two earthquakes. The equation for Richter magnitude can be written as, M = {log} rsub {10} {A} where A is the amplitude in millimeters directly measured from a seismograph. The equation may also include a distance correction factor originally used by Richter. It is omitted for the sake of clarity. The Richter magnitude of Pakistans 2013 earthquake can be related to its amplitude by, 7.7 = {log} rsub {10} {{A} rsub {Pakistan}} The equation above can be written as an exponential equation, that is, the amplitude read in the seismograph, {A} rsub {Pakista n} = {10} ^ {7.7} Similarly, the magnitude of Chiles 2010 earthquake can be mathematically written as, 8.8 = {log} rsub {10} {{A} rsub {Chile}} It can also be recast as an exponential equation, {A} rsub {Chile} = {10} ^ {8.8} The ratio of exponential expressions can be used to compare the intensities of earthquakes, {{A} rsub {Chile}} over {{A} rsub {Pakistan}} = {{10} ^ {8.8}} over {{10} ^ {7.7}} =12.6 It can be concluded that Chiles earthquake was 12.6 times as intense as the recently ground motion in Pakistan. Task 1. The exponential function ex can be written as an infinite Taylor series about x=0. The Taylor series is, {e} ^ {x} =1+x+ {{x} ^ {2}} over {2!} + {{x} ^ {3}} over {3!} + {{x} ^ {4}} over {4!} +†¦ {{x} ^ {n}} over {n!} +†¦ It can be used to approximate the value of e1 up to n= 10. The results are shown in Table 2. The approximation value for e1 up to 10 decimal places is obtained when n = 15, e = 2.7182818285 n Approximation for e 1 1 2 2 3 2.5 4 2.666666667 5 2.708333333 6 2.7166666667 7 2.7180555556 8 2.7182539683 9 2.7182787698 10 2.7182815256 Table 2. Approximation value for e. Works Cited â€Å"Khan Academy | Khan Academy.† N. p., n.d. Web. 4 Dec. 2013. â€Å"National Instruments: Test, Measurement, and Embedded Systems.† N. p., n.d. Web. 3 Dec. 2013. Stewart, J. Calculus. Brooks/Cole, 2009.