Calculus free essay sample

The discovery of calculus is often attributed to two men, Isaac Newton and Gottfried Leibniz, who independently developed its foundations. Although they both were instrumental in its creation, they thought of the fundamental concepts in very different ways. While Newton considered variables changing with time, Leibniz thought of the variables x and y as ranging over sequences of infinitely close values. He introduced dx and dy as differences between successive values of these sequences. Leibniz knew that dy/dx gives the tangent but he did not use it as a defining property. On the other hand, Newton used quantities x and y, which were finite velocities, to compute the tangent. Of course neither Leibniz nor Newton thought in terms of functions, but both always thought in terms of graphs. For Newton the calculus was geometrical while Leibniz took it towards analysis. It is interesting to note that Leibniz was very conscious of the importance of good notation and put a lot of thought into the symbols he used. We will write a custom essay sample on Calculus or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Newton, on the other hand, wrote more for himself than anyone else. Consequently, he tended to use whatever notation he thought of on that day. This turned out to be important in later developments. Leibnizs notation was better suited to generalizing calculus to multiple variables and in addition it highlighted the operator aspect of the derivative and integral. As a result, much of the notation that is used in Calculus today is due to Leibniz. The development of Calculus can roughly be described along a time line which goes through three periods: Anticipation, Development, and Rigorization. In the Anticipation stage techniques were being used by mathematicians that involved infinite processes to find areas under curves or maximize certain quantities. In the Development stage Newton and Leibniz created the foundations of Calculus and brought all of these techniques together under the umbrella of the derivative and integral. However, their methods were not always logically sound, and it took mathematicians a long time during the Rigorization stage to justify them and put Calculus on a sound mathematical foundation. In their development of the calculus both Newton and Leibniz used infinitesimals, quantities that are infinitely small and yet nonzero. Of course, such infinitesimals do not really exist, but Newton and Leibniz found it convenient to use these quantities in their computations and their derivations of results. Although one could not argue with the success of calculus, this concept of infinitesimals bothered mathematicians. Lord Bishop Berkeley made serious criticisms of the calculus referring to infinitesimals as the ghosts of departed quantities. Berkeleys criticisms were well founded and important in that they focused the attention of mathematicians on a logical clarification of the calculus. It was to be over 100 years, however, before Calculus was to be made rigorous. Ultimately, Cauchy, Weierstrass, and Riemann reformulated Calculus in terms of limits rather than infinitesimals. Thus the need for these infinitely small (and nonexistent) quantities was removed, and replaced by a notion of quantities being close to others. The derivative and the integral were both reformulated in terms of limits. While it may seem like a lot of work to create rigorous justifications of computations that seemed to work fine in the first place, this is an important development. By putting Calculus on a logical footing, mathematicians were better able to understand and extend its results, as well as to come to terms with some of the more subtle aspects of the theory. When we first study Calculus we often learn its concepts in an order that is somewhat backwards to its development. We wish to take advantage of the hundreds of years of thought that have gone into it. As a result, we often begin by learning about limits. Afterward we define the derivative and integral developed by Newton and Leibniz. But unlike Newton and Leibniz we define them in the modern way in terms of limits. Afterward we see how the derivative and integral can be used to solve many of the problems that precipitated the development of Calculus.

Salve Deus Rex Judaeorum Essay Example

Salve Deus Rex Judaeorum Essay Example Salve Deus Rex Judaeorum Paper Salve Deus Rex Judaeorum Paper Dues Rexes Judicature: The Words of Liberation for Women When Amelia Lancer wrote Salve Dues Restaurateur in 1 61 1 she intended to use her words as a platform In her fight to liberate women from the unjust treatment, and corrupt representation that the early male-dominated belief system bestowed upon them. It was not only her words that sought out this liberation, but also the structure in which she presented them. Her poem is broken up into distinctive parts that speak of women and the freedom, knowledge and power that was rightfully heirs. The title that she had chosen for her poem is Just one of many decisions Lancer made that gave her work more meaningful Impact on her readers. Latin was spoken and understood mostly by scholars or those who came from rich blood lines, and It Is the first sign of who Lancer wished her audience to consist of. She pleads her case to women of high-class status of which she also commends with her words. The language used to make up her title Is not the only significance wealth It. In the conclusion of her poem she explains why she had chosen this title, she writes if thou sire to be resolved, why I give this title, Salve Dues Restaurateur, know for certain , that it was delivered unto me in sleep many years before I had any intent to write In this manner, And thinking It a significant token that I was appointed to perform this work, I gave the very same words I received In sleep as the fittest title I could devise for this book. Gilbert, Guava 82) That statement handed down to her by God, however true it was, expressed her reasoning and might have also given her protection from opposition of her words that It followed. By appealing to the noble omen of her time, Lancer might have hoped that they would hear her words and that someday they could fight together to be accepted as equal no matter their status or education. The actual meaning of Salve Dues Rexes Judicature is Hail God, ki ng of the Jews, which was a variation of the words that were fixed above Jesus when he was crucified. Gilbert, Guava 82) It Is the actions of the women at the time of Chrisms death that Lancer uses these words to show the value that Jesus gave to women. Since he was born of a woman, nourished of a woman, and gave message of his surjection to a women that all creation should view them the same has their Father. Her argument in the defense of women begins with her re-interpretation of the story of Genesis. We have all heard the story of Adam and Eve and how Eve betrayed both Adam and God out of pure evil, and because of that betrayal both she and Adam were banished from the Garden of Eden. Of course with this Interpretation most would be upset with Eve and her actions. The blame was fully hers and because of 1 OFF ten Dealer Tanat women were Interior to men, Eves octagons In castes upon women as a whole. E Bide Ana Eden In Eves Apology, Lancer brings non-traditional concepts of women and religion into her explanation of Eves role in the Genesis story. She portrays Eve as Gods gift to Adam instead of an evil temptress responsible for the downfall of mankind. In her argument she points out that Eve is not given the same power as Adam, but instead, her role is to make Adam happy and do what he asks of her. From the beginning Eve is not considered Adams equal. She was conceived from a portion of Dams rib and therefore she is seen as lesser being from the start. She is not warned of the danger that eating from the tree of knowledge would cause them. Adam had been cautioned before Eves conception and his failure to inform her of the knowledge that God had given him left her open to temptation. When Lancer writes Eve, had no power to see The after-coming harem of her actions, (Gilbert, Guava 85) proves that she couldnt have known the danger and in fact did so out of love not betrayal. It is the misuse of Dams knowledge that damns all mankind. God had given him knowledge of the tree and when Eve brought her erasure to him to share, instead of educating her; he took the fruit out of greed so that he may gain the forbidden knowledge. Some refuse to see the discrepancy within each of the assigned roles these characters play. It seems that it was far easier to blame the naive Eve for the error, instead of admitting that Adam had made his own educated decision. Nevertheless, Lancer provides a great argument that potentially frees Eve of all guilt and again restores her to the righteous position she should have always held as a good woman with a good heart. Throughout Salve Dues Rexes Judicature Amelia uses many different rhetorical strategies such as persuasion with a touch of flattery when addressing her strong and powerful female audience, and gives the female gender a voice with her prevailing words and concepts. Following her strong argument in the defense of women is the imagery charged Description of Cooke-ham. Within this country-house poem, which is also believed to be the first of its kind, she uses unbelievable symbolism to describe an imaginary paradise for women that is kept alive by women without the need of a mans influence. It is here that she writes her book with the outside influence of the Countess of Cumberland, which seems to be the life blood of the estate. Her description of this paradise is one filled with symbols for the love and acceptance that radiates from this place. As she explains how all the land and its creatures gravitate towards the presence of the Countess, it is like you are there witnessing the influence she has on the universe itself. The most dramatic imagery is when it seems that the Countess is leaving and Cooke- ham begins to die all around her departure. Upon her exit from this place she kisses a tree that before had shaded them from the Sun as they shared their knowledge with one another. Lancer quickly kisses the tree after the Countess, so that she may take ten Knowledge Tanat seen Delves ten tree NAS galena Witt n r Nils act AT Slang the tree seems to be a metaphor. Like Eve who took from the tree of knowledge so does Lancer, but she does so not out of evil but instead with hope that she may spread the knowledge and power she had gained from her stay at Cooke-ham. I found great pleasure in reading Amelia Lancers Salve Dues Rexes Judicature. Her argument within Eves Apology actually opened my eyes to the inconsistencies of the actual meaning within the book of Genesis. For as long as I can remember I Just accepted the fact that Eve was the one to blame for their banishment from Eden. I didnt like the fact that anyone you ask thats the first thing they say is if it wasnt for Eve Now having read Lancers interpretation I clearly see the error in this long held belief and I am once again proud to be a descendant of such a noble women. However, by far my favorite portion of these readings was the Description of Cooke- am. In the way that her words flow and the detail that she places on objects and events is awe-inspiring. When the Countess is leaving the tone of sadness in her words makes even the reader feel as if they are losing their pass to this inspiring place. The knowledge and emotion that I gathered from these readings truly kept me wanting more. To think that her words were kept from the public for so long seems as if we were robbed of the Joy that I am sure that anyone who has the pleasure of reading this piece has gained. Amelia Lancer has done what she planned to do, and hat is to inform and inspire yet another reader and that is what makes her a truly gifted writer and woman.

Fieldstone Private Capital Group Essay Example | Topics and Well Written Essays - 3000 words

Fieldstone Private Capital Group - Essay Example ally offers advisory services to the corporation about leveraged buyouts, private capital raises and mergers and acquisitions in infrastructure and energy industries globally. The company takes pride in being an independent employee owned venture and that allows them to offer unbiased, objective and independent ideas that are specifically designed and developed for the purpose of fulfilling the client’s long term needs (FPCG, 2013a). The company caters to a diversified client base. It ranges from small and medium sector enterprises to some of the world’s largest corporations. In addition to private sector companies, Fieldstone also offers advisory services to the government firms especially in the area of infrastructure and energy. Apart from the financial services, Fieldstone is also active in the field of CDO and high yield markets through its Fieldstone Capital Group, which is a division of Fieldstone Services Corp (Forbes, 2009). b) Location of Fieldstone Fieldstone is a company which has been able to generate a sense of trust among the consumers around the world. This is due to the company’s presence in the market for over 2 decades. During this epoch, there are hardly any negative statements came into light which was against the company or that hampered the image of the company (Keillor, 2007). Fieldstone operates in a number of places around the world. The places in which the company has presence are Berlin, Johannesburg, Hyderabad, Kuala Lumpur, London and New York (Bloomberg, 2013). The service offered by the company is almost similar in every country. However in case of South Africa, where the company operate through its Johannesburg office, offer some additional services to the customers. In the context of German market, the company is considered as an... Fieldstone is a company which has been able to generate a sense of trust among the consumers around the world. This is due to the company’s presence in the market for over 2 decades. During this epoch, there are hardly any negative statements came into light which was against the company or that hampered the image of the company. Fieldstone operates in a number of places around the world. The places in which the company has presence are Berlin, Johannesburg, Hyderabad, Kuala Lumpur, London and New York. The service offered by the company is almost similar in every country. However in case of South Africa, where the company operate through its Johannesburg office, offer some additional services to the customers. In the context of German market, the company is considered as an important player in the financial advisory services industry. For example, it has played the role of a financial advisor for a number of vital projects within the country. In the recent past, Fieldstone ac ted as exclusive debt advisor for Mainova AG in structuring, developing and facilitating the execution of the transactions.

Enhancement of Customer Satisfaction Essay Example | Topics and Well Written Essays - 8750 words

Enhancement of Customer Satisfaction - Essay Example I would like to thank the Kempinski team who allowed us to access the data, especially Katherine de Fountain who always provided us with a lot of valuable information as well as arranging the interviews. Â  This study mainly explores how luxury Hotels make use of guest technology to improve customer satisfaction. The researcher focuses upon which factors that have a relationship between them, in guest technology, employee satisfaction, and customer satisfaction; the critical factors of CRM that achieve the highest service quality; the role of guest technology in increasing customer satisfaction and service quality. Â  In this paper, a combination of qualitative and quantitative research is used, which includes questionnaires and interviews to collect primary data and found out that there were problems of service efficiency, service quality and customer data management, etc. existing in hotel management. The data is analyzed using SPSS software. The result from the data indicates that guest technology can improve service quality and efficiency, as well as manage customer information to improve customer satisfaction, which suggests that guest technology will play an important role in hotel management in the future. This research uses Kempinski Geneva as an example, analyzing the guest technology that Kempinski already had, combined with future trends and customer readiness. Â  The global economic integration makes the sources of customers of the hotel industry more diverse. As market channels are getting broader, the hotel industry is also facing more intense competition, with increasingly fierce and rising customer expectations, which force members of the industry to continually seek for methods to further expand marketing channels, improve service quality, reduce management costs and improve customer satisfaction to enhance the core competitiveness of hotels’. Â  

Disney Land Essay Example | Topics and Well Written Essays - 1250 words

Disney Land - Essay Example This made him purchase another property, 160-acre at a site near Anaheim in 1953 (Trahan, 7). The construction of the park started in 1954, and it was completed and launched later in 1955. Since its launch, the business has experienced immense growth and expansion, starting from local expansion and later venturing to other countries in Europe and Asia. While compared to other theme parks in the world, Disneyland Theme park has been quoted as the most successful of them all, hitting a cumulative 600 million visitors by the year 201 (Seth and Len, 12). Its expansion in other countries has also been successful, with its resort complexes and theme parks recording high growth, profitability and popularity over the years. It is in the light of this consideration that there is a need to evaluate the factors that have made Disneyland such a successful venture, thus making it popular the world over. First, the major factor that contributed to the high-notch start for Disneyland is the nature of its launch in July 17, 1955, where a live guest of 15, 000 people were invited to grace the occasion, and the number swelled to an unexpected 30, 000 guests, on top of the 90 million people who watched via a live television broadcast (Barrier, 240). Just by the mere launch of the business venture, it became popular and attracted the attention of many prospective visitors, since such was a rare spectacle in the minds of many who attended the live unveiling and also those who watched it live. Due to the popularity that Disneyland cultivated that day, it was sure to continue receiving visitors consistently, among those who had watched the launch on live television, but now wanted to see the real Disneyland (Seth and Len, 23). The next day after the launch was not different, with visitors streaming in to view the theme park and thus the business kicked off at a relatively high rate, compared to other new business ventures. The success of the kickoff has greatly contributed to the suc cess of Disneyland as it is experienced today, since it started off as a popular business venture, whose popularity and fame has constantly increased over the decades. The other success factor that has shaped the destiny of Disneyland business venture to present day is the initial pricing strategy (Trahan, 13). Having attracted the attention of many potential visitors, the business venture had to differentiate itself from the other amusement parks through charging relatively high entry fees at the gate, with a gate entry fee of $1 (Barrier, 212). This served to present Disneyland as a high class guest attraction, which served to attract the attention of potential visitors even more. Having built on its popularity during the launch, then, the business had to keep the tempo by presenting itself as a high class and unique attraction, which would entice many people to visit and witness the difference between Disneyland and other amusement parks. Another initial success factor that set D isney for more success is the visitor management strategy that was applied from the initial days of the business opening. The management of Disneyland worked towards controlling the attendance of the visitors to the park, through regulating the number of daily visitors to a maximum of 20,000 (Trahan, 13). While limiting the number of customers to any business might appear to be a poor strategy,

Factors affecting the rate of photosynthesis in leafs

Factors affecting the rate of photosynthesis in leafs Photosynthesis is the process in which light is converted to the chemical energy of sugars. It can be summarized in the following equation : This process occurs in the chloroplast of plant cells which are primarily found in the leaves. Photosynthesis is the building up of sugars using carbon dioxide and water as the raw materials. The energy for the process comes from light and a green pigment called chlorophyll allows the plant to transfer the energy from light to sugar. AIM : To measure the effect of light intensity on the rate of photosynthesis in leaf disc. RESEARCH QUESTION : What is the effect of different light intensity on the rate of photosynthesis of fresh leaf disc when the other factors that can affect the rate of photosynthesis are remained constant? HYPOTHESIS : As the distance of fresh leaf disc from the source of light is increasing (indicate the lower in light intensity),the time taken for the fresh leaf disc to float on the surface of 3% sodium hydrogen carbonate will be increase indicate the decreasing in the rate of photosynthesis when the other factors are remained constant. It is because photosynthesis is a light dependent process. At the low light intensities, this may become the limiting factor. Imagine light as a straight line which you can see with your own eyes. A plant typically has chloroplasts within their cells. So this straight line of light comes from the Sun, a natural source. It hits the surface of a green leaf. Firstly, is all of the light absorbed? No because some of the light is reflected off the surface and some light cannot penetrate the surface because it is the wrong wavelength. Most of the light gets in. Does that mean all of the light hits the chloroplasts? No because they are small, so some light rays will miss the chloroplasts all together. It is only the light which hit the chloroplasts which will be used in photosynthesis. So, for the experiment done with a shorter distance between the light source (bulb) and the fresh leaf disc, the leaf receives more light compared to that of longer distance. So theres a higher chance more li ght will hit the chloroplasts and therefore more oxygen and glucose will be produced by the plant. This means the rate of photosynthesis has been increased. However, chloroplasts are sensitive, so if they keep getting hit by light energy, they will eventually become damaged and then the rate of photosynthesis will decline. VARIBLES : Units Range Independent Variables The distance of pineapple leaf disc from the bottom of light bulb/ light intensity. cm 10-60 Dependent Variables The time taken for the pineapple leaf discs to float on the 3% sodium hydrogen carbonate solution. second 314.4-1250.4 Controlled Variables Unit Uncertainties Possible effect(s) on result 1. The number of leaf disc used for each experiment. To make sure the photosynthesis rate for all test is fair and equal within all test. 2. Diameter of each leaf disc used  ± 0.5 The leaf disc is corked by using cork borer and kept constant so that rate of photosynthesis is fair. 3. Concentration of sodium hydrogen carbonate. M To constant and make sure the rate of photosynthesis is fair and equal, and concentration do not be part of manipulating factor for rate of photosynthesis. 4. Surrounding temperature of experiment.  °C  ± 0.5 To make sure the temperature is not too high and suitable for optimum rate of photosynthesis. MATERIALS : No Materials Quantity Volume / size 1. Pineapple leaves 6 2. Sodium hydrogen carbonates solution (3%) 240 ml 3. Tap water APPARATUS : No. Apparatus Quantity Volume / size 1 Lamp 6 Standard size 2 New 10 ml syringes 6 10  ± 1 ml 3 Stopwatch 6  ± 0.05cm 4 Cork borer/hole punch 6  ± 8 mm 5 Thermometer 6  ± 0.5  °C 6 Forceps 6 Standard size 7 Measuring cylinder 6 50  ± 0.5 ml 8 Beaker 6 100  ± 10 ml 9 Meter ruler 6  ± 0.05 cm 10. Marking pen 1 Standard size 11. Marking tape 1 Standard size METHOD : The setup apparatus was designed as shown above. This experiment is done at room temperature of about 28  °C in the laboratory. Before other procedures are carried out, all the lights in laboratory are switched off to avoid interference which may affect the result. The distance between the bottom of the light bulb and the surface of laboratory table is adjusted to 10.0 cm; with the assumption that the surface of laboratory table represents the location of 10 pineapple leaf discs before the light is switched on. 10 ml of 3% sodium hydrogen carbonate is measured using measuring cylinder. Then, the 10 ml of 3% sodium hydrogen carbonate is poured inside a 100 ml beaker. From inside the beaker containing 10 ml of 3% sodium hydrogen carbonate, 10 ml of 3% sodium hydrogen carbonate is taken out using new 50 ml syringe. Then, 10 of approximately 8 mm pineapple leaf discs is cut out from the pineapple leaf using cork borer/hole punch to give the same diameter for all 5 discs. Now, your thumb or finger is placed over the small hole at the tip of the syringe and its plunger is slowly pulled out. After each disc is cut out, it is immediately transferred into the 50 ml syringe containing 10 ml of 3% sodium hydrogen carbonate solution. After all 10 pineapple leaf discs are transferred into the syringe; the plunger is pushed back inside the syringe. With all the pineapple discs still inside the syringe and your finger or thumb is still at the small hole at the tip of the syringe, the plunger is pushed in and out to compress and expel the air. After that, the content of the syringe was poured into the beaker which contain the rest of 3% sodium hydrogen carbonate solution; minimizing contact with air. The pineapple leaf discs are checked so that they are not on top of each other. Then, the beaker is immediately placed right below the adjusted lamp. The lamp is switched on and the stopwatch is started simultaneously. The time taken for each disc to rise is recorded. Steps 1 to 12 are repeated by varying the light intensity. To vary the light intensity, the distance from the bottom of the bulb to the pineapple leaf disc is varied to 20 cm, 30 cm, 40cm, 50cm and 60 cm. DATA COLLECTION: Distance of the beaker to the light source, d/cm ( ±0.5cm) Time taken for each pineapple leaf discs to float on the surface of 3% sodium hydrogen carbonate for Trial 1, t/s ( ±0.1s) Disc 1 Disc 2 Disc 3 Disc 4 Disc 5 Disc 6 Disc 7 Disc 8 Disc 9 10.0 314.4 346.8 349.8 353.4 354.6 354.6 358.8 360.6 367.2 20.0 473.4 480.6 498.0 512.4 518.4 518.4 526.2 527.4 539.4 30.0 601.2 647.4 648.6 654.6 658.8 674.4 679.2 684.0 690.6 40.0 713.4 718.8 720.6 724.8 725.4 729.6 741.0 741.0 750.0 50.0 849.6 889.8 889.8 901.8 907.2 907.2 907.2 929.4 930.6 60.0 1080.6 1100.4 1135.8 1153.8 1164.6 1181.4 1189.8 1189.8 1206.0 Quantitative Analysis Of Experiment Distance of leaf discs from light source, cm ( ±0.5 cm) Observations 10.0 At the edge of the leaf discs, some bubbles are seen after a few minutes. A lot of bubbles are produced and the leaf discs rise to the surface after a while. 20.0 Some bubbles are released at the edge of the leaf discs after a few minutes. Then, one by one the leaf discs rises to the surface after a few minutes. 30.0 Tiny bubbles are released at the edge of the leaf in a short period of time. After that, the leaf discs from the bottom to the surface. 40.0 The leaf discs rises one by one and float to the surface after quite a long period of time. Bubbles are produced quite slowly at the edge of the leaf discs. 50.0 The production of bubbles is slower and the leaf discs rises to the surface after a long period of time. 60.0 The production of bubbles is very slow and the leaf discs rises to the surface after a very long period of time DATA PROCESSING : The calculation of average time taken for the leaf discs to rise. In order to get the time taken for the leaf disc to rise, an average reading from all ten reading needed to be calculate and the average will be used to calculate the average time taken for the leaf disc to rise. The calculation, are obeying formula as stated below: Based on the formula above, the average time taken for the leaf disc to rise in respective temperature is calculated. The average time taken that has been calculated from above formula is shown below: Temperature of surrounding/ °C Average time taken for the leaf disc to rise in respective temperature. 10 352.74 20 513.48 30 672.72 40 731.64 50 906.06 60 1165.26 Table 1: Calculation Average time taken for the leaf disc to rise in respective temperature. Since we have calculated the average time taken for the leaf disc to rise in the surface of sodium hydrogen carbonate solution, the next step is to calculate the rate of photosynthesis of the leaf disc. The formula shown below is obeyed: By obeying the formula as shown above, the rate of photosynthesis is calculated and the calculated rate of photosynthesis is shown below: Distance of leaf discs from light source, cm ( ±0.5 cm) Rate of photosynthesis of leaf discs, s-1 10.0 0.002835 20.0 0.001947 30.0 0.001487 40.0 0.001367 50.0 0.001104 60.0 0.000858 From the above calculation, next we need to calculate the standard deviation of the rate of respiration photosynthesis of leaf discs in the different light intensities, and stated as uncertainties if the average time taken itself. The calculation used is using GDC, by following these steps: 1. First press button STAT then press button ENTER 2. Insert the data (in table 2) for 10 °C temperature inside the table then press button ENTER 3. After insert the data press again button STAT then press > to calculate 4. Choose 1-Var Stats then press button ENTER twice 5. ÏÆ'x shows the standard deviation of the time taken for the indicator solution to change colour from purple to greenish for 10  °C temperature. 6. Use all this steps for all the temperature (20 °C, 30 °C, 40  °C, 50  °C, and 60  °C) The data of uncertainties calculated above, is shown below, as calculate: Distance of leaf discs from light source, cm ( ±0.5 cm) Standard deviation 10.0 0.000132 20.0 0.000086 30.0 0.000099 40.0 0.003900 50.0 0.003130 60.0 0.000038 The next calculation involved is calculation of light intensity, which relates the distance of light source from leaf disc, and obeying given formula: And by obeying the formula as stated above, the calculation is as follow: Temperature of surrounding/ °C Working calculation of rate of respiration 10 20 30 40 50 60 Table 2: Calculation of light intensity. DATA PRESENTATION : DISCUSSION : 1. When the light source is 60.0 cm away from the surface of the sodium hydrogen carbonate solution, the average time taken for the leaf discs to rise to the surface of the sodium hydrogen carbonate solution is the longest, which is 1165.26 s. This shows that the rate of photosynthesis of the leaf discs under this light intensity is the lowest, which is 0.00086s-1  ± 0.000038 s-1. When the light is further away from the leaf discs, the chloroplasts can only trap a smaller amount of light to carry out photosynthesis. Thus, when less light is trapped, the rate at which photosynthesis occurs will decrease. 2. When the light source is 50.0 cm away from the surface of the sodium hydrogen carbonate solution, the average time taken for the leaf discs to rise to the surface of the sodium hydrogen carbonate solution decreases, which is 906.06 s. Hence, the rate of photosynthesis increases, which is 0.00110s-1  ± 0.00313s-1. With the light source closer to the sodium hydrogen carbonate solution, the chloroplast manages to work with a greater amount of light. This increase in light intensity increases the rate of photosynthesis. 3. This trend repeats itself when the light source is 40.0 cm away from the surface of the sodium hydrogen carbonate solution. With this increasing light intensity, the chloroplast manages to work with more light and this excites more electrons in the chloroplast and the whole process of photosynthesis occurs at faster rate which is 0.00137s-1  ± 0.00390s-1. 4. When the distance of the light source from the surface of the water is at 30.0 cm and 20.0 cm, the rate of respiration increases with the rate being higher at 20.0 cm away from the surface of the sodium hydrogen carbonate solution. The light intensity is higher at 20.0 cm compared to 30.0 cm away from the sodium hydrogen carbonate solution. The rate of photosynthesis for 20.0cm and 30.0cm is 0.001947s-1  ± 0.000039s-1 and 0.001487s-1  ± 0.000099s-1. Thus, the rate of photosynthesis is higher when the distance of the light source is 20.0 cm away compared to 30.0 cm from the sodium hydrogen carbonate solution surface. 5. When the distance of the light source is 10.0 cm away from the sodium hydrogen carbonate solution, the rate of photosynthesis is at its highest level. At this level of light intensity, the leaf discs optimize the amount of light which it can use to carry out photosynthesis. The rate of photosynthesis at this moment is 0.002834s-1  ± 0.000132s-1. The process of photosynthesis takes the least amount of time to occur under this level of light intensity, thus it has the highest rate of photosynthesis. 6. The number of leaf discs used in this experiment is kept constant for all the levels of light intensity. This is to make sure the competition for light remains the same for all levels of sodium hydrogen carbonate solution. Besides that, the level of sodium hydrogen carbonate solution in the beaker remains the same for all levels of light intensity so that all the leaf discs rise to the water surface by the same distance so that it will enable the calculations to be standardized. The temperature of the surroundings are kept constant for all levels of light intensity so that it does not cause any form of deviation in the sense that it will have an effect on the rate of photosynthesis. LIMITATION : 1. Not all the leaf discs are in good condition or fresh, causing difference in results of the experiment. 2. The number of leaf discs used is not sufficient to measure the rate of respiration. The result obtained is not so reliable and the experiment took a long period to complete. 3. There are other light sources that may affect the result of the experiment and cause it to be inaccurate. SUGGESTION : 1. Only fresh leaf discs that are in good condition should be used. 2. The number of leaf discs used should be increased so that more results can be obtained and the average taken will give a more accurate measurement of the rate or photosynthesis. 3. Conduct the experiment in a dark room which has a minimum source of light so that it wouldnt affect the experiment. CONCLUSION : As a conclusion, when the light intensity increases, the time taken for the leaf discs to rise will be shorter, the rate of photosynthesis of the leaf discs will increase. This is because an increase in light intensity will cause more light to be absorbed by the chlorophyll in the leaf discs and thus, increasing the rate of photosynthesis. However as the light intensity continues to increase, it will have no more effect on the rate of photosynthesis, this is because other factors will become the factors limiting photosynthesis. The hypothesis is accepted.

Hero Status for Chief Joseph :: American History Essays

Hero Status for Chief Joseph A modest and humble monument was raised to this giant Indian. A seven and a half foot white marble shaft sets atop a barren hill where a lone, half dead elm tree stands, 14 miles north of the Grand Coulee Dam, in a small Indian Village on the Colville Indian Reservation. The acre or so of ground is delineated by wire fence. Weeds have overgrown mounds where graves are left unidentified and only apparent by small mounds of rock. The elm stands, gnarled, over his grave. White chipped rock fill a rectangle edged with one by four wood planking, smaller in length than this man stood in all of this grown years. To his honor had been placed a coin purse, cigarettes, a dog tag, dried flowers in mason jars, an arrowhead, keys, notes under rocks, a dream catcher hanging on the tree, where I placed a Nez Perce bead necklace. My heart was sad by the desolation of this mans grave. My heart was sadder, knowing that his last days were spent begging James McLaughlin, Indian Inspector, to let him to return to his beloved home in the Wallowa Valley. Æ’Â ±For Joseph it was a kind of pilgrimage to his ancestral home. When he gazed once more upon the grave of his father...the tears brimmed over in the old chiefÆ’Â ­s eyes.Æ’Â ° McLaughlin issued an adverse report to the government, never allowing the chief and his people to return to Oregon. Æ’Â ±Joseph, silent and brooding for weeks sat stoically for entire days at a time without moving or speaking. Sitting before his fire on September 21, 1904, he fell forward on his face.Æ’Â ° He died of a broken heart. This Indian colossus, this gentle Napoleon-Gandhi that led his people in a feat that will likely be handed down as a legend, accomplished miracles and mysteries that make him misunderstood by the white people and the Nez Perce. Tom and I arrived in Nespelem at about 4:15 in the afternoon after a near four hour drive. 185 miles from Moscow and 100 miles northeast of Spokane. No signs. No historic landmarks. You just have to know that if you are looking for the grave of Æ’Â ±The Red NapoleonÆ’Â ° you must stop and ask at the gas station. Professor Swagerty, history professor at the University of Idaho, had given these directions when he responded to my email about location of the grave site.