Pockets Of Pool Problem Statement Homework Essay Sample

Picture a pool table with modified pockets positioned solely at the corners. The viewpoint of the table is from above, resembling an aerial perspective, and different components and forms are designated. Envision the ball being struck diagonally at a 45-degree angle from the lower left corner. Furthermore, presume that when the ball collides with one of the table’s edges, it bounces back at a 45-degree angle and persists in its course until reaching one of the four pockets. The dimensions and configuration of the table will consistently affect the trajectory taken by the ball.

The behavior of the ball is affected by the size and shape of the table. If the table is square, the ball will go straight into the corner pocket without bouncing. Our goal is to comprehend how the ball behaves with various table dimensions. To achieve this, we have certain assumptions: both height and width are integers, and the ball is consistently shot at a 45-degree angle from the lower-left corner. We must take into account all rectangular shapes. To explore further, I began creating rectangles of different sizes and observing how the ball bounces in order to reach a pocket.

I obtained a piece of graph paper containing 60 rectangles of various sizes. This allowed me to easily plot the path the ball took to reach a pocket. I will demonstrate this with the following display, which includes both the rectangles and a corresponding table.


Instead of creating 6 patterns, I created 10 for my solution. Here is a clear listing of them: This POW was initially challenging but became much easier once I understood the exact steps to take. Therefore, I believe I should receive at least an A.

Cultural And Religious Beliefs Of David Green: School Ties

 is a football all-star that got accepted into an anti-Semitic prep school, the only problem…. he was a Jew. David Green should not have to expose his cultural and religious beliefs to his fellow students. The first claim that I will use to justify my case is if he had told “the boys” they would have treated him differently. Furthermore, if he told them it would affect his chances of keeping his football scholarship. Lastly, even if Green had told the boys earlier, it would not alter the way he was treated because when “the boys” found out David was indeed a Jew he was still insulted and disrespected.

Based on all these 3 valid arguments I can confidently state that he should not tell the boys that he was Jewish. Green would have been treated differently this is clearly demonstrated on multiple occasions that took place throughout this film. The first point to justify the claim is the scene where they are singing “ The Smokey song” and David’s roommate comments “I jewed him down to 30”. Furthermore, in the shower scene Mcgoo quotes “ I wouldn’t go to Harvard if you paid me with all those Jews”.

Considering these 2 events it is evidently shown that “the boys” strongly dislike Jewish people and if Green had told “the boys” he was a Jew his stay at St. Matts would defiantly change for the worse. By the same token, another example that marvelously validates my point is Sally. In the beginning of the film Sally is very fond of David and seems to have no problem having a physical and emotional relationship with him. However, when Sally finds out that David is a Jew all of that comes to an abrupt stop. Sally had instantly eluded Green and quoted “ You have no idea what you put me through” also “You didn’t tell me the most important thing.

Sally could not be with David for one reason, his religion. Based on this Green should not have to tell his fellow classmates of his religion because had he told he would clearly not have been treated the same. David has been accepted into St. Matt’s for one reason and one reason solely, his ability to football. If Green told everyone that he was a Jew they would not want to cooperate and listen to him in order to be successful in football. This would result in them to lose games and David would lose his scholarship.

This is proven in the Film during the scene where Dylan and David have a conversation and Dylan quotes “ That’s what draws people, not that your quarterback”. By this he is stating that people are attached to Green because he is who is. However, he would not have people liking him if they knew he was a Jew and that would have affected his football play. Green is able to keep a good repetition at St. Matt’s and win countless matches of football by not telling his fellow classmates about his religion. To further expand, the boys did not like Jewish people one bit.

This is justified through several circumstances in the movies, one example is when Dylan quotes “How would you not know, it’s hard to miss a heeb”. Since the boys hate Jewish people if David told them he was a Jew, they would be pissed and reluctant to work with Green. Finally, even if David told “the boys” that he was in fact Jew It would not have changed the way he was treated by them. Green was still being brutally harassed after all his classmates found out that David was a Jew, so by not telling them he was simply delaying the time of being disrespected not changing the course of their actions.

This claim is justified throughout the movie in 2 scenes. In the beginning “the boys” insult Jews by commenting “ He always wants something for nothing and he’s not even Jewish” (in the “Smokey song” scene before they knew he was a Jew) and they insult David and his religion after they find out he is a Jew during the shower scene when Dylan says “ Pat Boone got up and sang there’s a gold mine in the sky, 10,000 people Jews joined the air force”.

This means that they would have ridiculed him regardless, if David told them right away or if they eventually found out. By the same fashion, the argument is also proven in the scene where David and his roommate are having a conversation. His roommate quotes “Why didn’t you tell me in the first place? However, what difference would it make? The roommate was the one who discriminated Jews by saying “I jewed him down to 30” He clearly dislikes Jews as well so it would not make a difference if he told him earlier.

Furthermore, David did not tell “the boys” that he was Jewish because he knew they would eventually find out and that is why he quoted “I thought I was dreaming”. Considering this Green did not tell them in order to fit in and be treated fairly for the short period of time until they found out. I strongly believe that the David Green should not expose his cultural and religious beliefs to his fellow students. David just wanted to fit in and was well aware if he told everyone he was Jewish that would not become a reality.

Green most defiantly would not have been treated the same, it could of inflicted with his scholarship (the only reason he was there) and it wouldn’t necessarily be a resolution in terms of him getting harassed. In conclusion, if I were in David Green shoes I would probably have done the same thing, Green didn’t do anything wrong he just did what he had to do in order to get his education. “You used me for football… I’ll use you to get into Harvard”

Quantitative Analysis Of A Soluble Sulfate

uantitative Analysis of a Soluble Sulfate Steven English Lab Instructor: Dr. Campo Date: Tuesday, February 5th 2013 Pre-Lab Questions A. Adding the acid to the sodium sulfate solution results in an increase in the solubility of any free anions present in the sample. This will happen because the present anions will bind with the hydrogen cations present in the acid. B. The sodium sulfate is boiled because experiments have shown that barium sulfate is 50 times more soluble at 100°C than at room temperature.

At the higher temperature, the Ba2+ and the SO42- are more likely to find each other and to form bonds and precipitate more slowly. If this happens too rapidly, then there is a high chance that impurities will be trapped in the precipitated crystals. C. The sodium sulfate solution is kept hot for an hour in order to allow enough time for the entirety of the sulfate present in the solution to precipitate. D.

Digestion refers to the formation of the barium sulfate crystals that can then be filtered out of the solution E. The crucible must remain uncovered both to ensure that there is good oxygen flow into the crucible ensuring that the burning off of the filter paper can be achieved, and also to allow the escape of the smoke and fumes that result from it. The oxygen flow also prevents the sulfur in the sample from being reduced. Objective

This experiment has three main objectives: Determining the amount of a substance, sulfate (SO42-), in a sample of sodium sulfate (Na2SO4) with soluble impurities Learn about the process of selective precipitation by seeing how barium sulfate (BaSO4) forms while other soluble materials remain in a solution To learn how to use gravimetric analysis to calculate the present sodium sulfate’s mass by measuring the mass of the precipitated barium sulfate

Materials and Methods Chemicals/Solutions: Sodium sulfate (Na2SO4) Distilled water (H2O) 0. 25M Barium chloride solution (BaCl2) Silver nitrate (AgNO3) Equations for chemical reactions: Na2SO4 (aq) + BaCl2 (aq) —–> BaSO4 (s) + NaCl (aq) Equipment: 400 mL beaker Analytical balance Dropper Bunsen burner Buret Watch glass Cotton Two crucibles with covers Blue wax pencil Ringstand with triangle and wire gauze Funnel Experimental Procedure: A.

A 400 mL beaker was cleaned and dried Approximately 0. 5 grams of unknown sulfate solution was weighed and unknown selection’s letter was written in the lab book Sample was added to beaker and weighed, and amount transferred into beaker was noted 50 mL of distilled water was added to beaker 1 mL concentrated HCl was added after sample dissolved 150 mL more distilled water was added and solution was heated to just boiling B. Buret with 50 mL of 0. 5 M barium chloride solution was set up Heat was turned down to low as sodium sulfate began to boil 20 mL barium chloride solution was added drop by drop from buret to sodium sulfate solution with constant stirring and gentle heat Bunsen burner was turned off to allow precipitated barium sulfate to settle A few drops of barium chloride was added to test for complete precipitation 5 mL barium chloride drop by drop was added until precipitation was complete Beaker was covered with a watch glass once the precipitation was complete and insulated by wrapping with cotton Solution was set aside for one hour

C. A filter paper cone was prepared as shown in lab manual and wetted it with distilled water Remaining supernatant liquid was decanted through filter paper Test outlined in step 5 of secton B was preformed to test for complete precipitation D. 1. Precipitate remains in beaker were washed out with a small amount of distilled water 2. Crystals were added to those already in the funnel and washed 8-10 times with hot water, allowing excess water to drain 3. Silver nitrate was used to test for presence of chloride and washed repeatedly until no ion was present in wash water

E. 1. Sample was set aside for one week F. 1. A crucible with cover was obtained, and were both cleaned and dried 2. Crucible was marked with blue wax pen to differentiate it from the rest 3. Crucible was then placed on a triangle placed on a ringstand and heated over blue central cone of bunsen burner flame until it glowed red for 10 minutes 4. Was left to cool in desiccator for approximately 20 minutes 5. Weighed on analytical balance 6. Process was repeated to ensure constant mass within ± 0. 003 grams was reached Experimental Procedure (cont. G. 1. Filter paper was placed in an uncovered crucible above a small flame on a triangle 2. Crucible was heated gently to dry paper then heat was increased to burn the filter paper off, with the crucible tipped to allow good mixing with oxygen 3. Crucible was covered whenever paper ignited 4. Crucible was cooled for approximately 20 minutes, then reheated for 5 minutes 5. Weighed and checked for constant mass 6. Data from another student testing the same unknown compound was obtained to provide an average between the two data sets 7.

Following calculations were completed: Calculation: (Mass of BaSO4) x (MW SO42- ? MW BaSO4) = Mass of SO42- (Mass of SO42-) ? (Mass of original sample) x 100 = Percentage of SO42- in sample Discussion In this lab, unknown sample E was calculated to have a SO42- composition of 61. 71% (0. 3266 grams in a . 05292 grams sample) and 62. 39% (0. 3121 grams out of a 0. 5002 sample), respectfully, which averages to a 62. 05% composition. The actual SO42- percentage of sample E was 53. 03%, which meant the experiment had a 17. 01 percent error. *] Based on the samples actual composition, the mass of the SO42- that should have calculated was 0. 2806 grams for the first sample and 0. 2653 grams for the second. Assuming there was no loss of sulfur, oxygen or SO42- during the experiment and the material weighed at the end contained all the SO42- present in the beginning sample, both experimental samples had about 0. 046 grams of excess foreign mass which resulted in our high percent error. Figuring out exactly what accounted for that extra mass is a bit difficult to pinpoint with any certainty.

Due to time constraints and a somewhat flawed procedure, there were many opportunities for error to be introduced. Chief among them was the fact that the sample was not allowed to digest for the entire hour outlined in the procedure manual. Both samples were digested for only 40 minutes in order to have enough time for the filtering process. By not allowing the digestion period to occur for the prescribed amount of time, then it is possible that impurities might be trapped in the forming crystals which could explain some of the excess mass observed at the end.

The filtering process also had some problems, in that the filter paper configuration did not allow for quick enough filtering to be fully accomplished before we had to leave the lab. When filtering the first sample use two different filter papers were used and ultimately the one with most of the precipitated solid in it had to be stored while there was still a bit of liquid present. This meant that the precipitated material was not able to be rinsed and it is possible that there was some foreign material in the remaining unfiltered supernatant liquid. This foreign material might not ave evaporated with the remaining water and could have been left in the filter paper with the precipitated solid, also contributing to the excess mass measured. These two errors, along with possible incomplete burning off of the fliter paper, were probably the source of the majority of the error observed. Other observed possible sources of error included, contamination of the hydrochloric acid that would have resulted in any foreign ions not being dissolved completely. The possibility of the samples being possibly exposed to air during the week between lab sessions, meaning outside contaminates could have settled on the stored filter paper.

And the beaker being placed on the counter during the digestion process that could have caused a dip in the temperature of the solution and disrupted complete digestion. As a result of this experiment, a better understanding of the process of gravimetric determination was gained as well as a clear understanding of the precipitation and digestion processes. By observing the Na2SO4 precipitating into BaSO4, it also became clear to see that in order to qualitatively measure the amount of one compound in an original sample it is possible for it to be measured easily, even after it has been disassociated.

For future iterations of this experiment, it would probably be helpful to have enough time to allow the solution to digest for the full hour, either by having samples of the Na2SO4 and BaCl2 pre-measured or for having a longer lab period. Also, if there were better filter papers, perhaps also prepared before hand, the process could be made a lot smoother. ——————————— [ * ]. Calculations attached on separate page

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