Is Mr Rochester the Man for Jane free essay sample

Mr Rochester is not the man for Jane because he is nearly twice Jane’s age. ‘ Oh yes. But you see there is a considerable difference in age. Mr Rochester is nearly forty; she is but twenty-five. ’ In Jane’s monologue she states ‘ You, a favourite with Mr Rochester? You gifted with the power of pleasing him? You of importance to him in any way? Go! Your folly sicken me. ’ Why would Jane be doubting herself so much if she really loved him. She has never come across such a man and doesn’t not know how to feel around him. Jane is a Governess and Mr Rochester is her boss a figure of authority and there is a clear line in the working environment that should never be crossed. They should not be together. Jane saves him twice once when he slid on some ice when they first met, and then she put out a fire that was in his room. We will write a custom essay sample on Is Mr Rochester the Man for Jane? or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Usually it’s would be the man saving and sweeping the woman off her feet but it’s the other way round here. Mr Rochester makes Jane jealous when he invites his aristocrat friends over and sings a duet with Blanche Ingram Jane’s rival. Mrs Ingram is more of the right sort for Mr Rochester status wise and importance. ‘Blanch, an accomplished lady of rank,’ Jane says in her monologue. ‘Mr Rochester, I thought you were not fond of children? ’ ‘Nor am I’. So if Mr Rochester was ever to take it any further with Jane then they will not have children. Every girl wants the perfect husband or partner, live in a elaborate fairly tale type house and have children the fairy tale ending, he obviously is not the right man for Jane. Mrs Ingram genuinely doesn’t like Jane, when they decide they are going to play charades Mr Rochester says ‘Will you play? ’ Lady Ingram interrupts ‘No, she looks too stupid for any game of the sort. ’ Mr Rochester pretends to marry Lady Ingram in the game to make Jane jealous. Mr Rochester is very devious and disguises himself to be a gypsy in order to try and get to know more about Jane but his plan alters as Jane knows better to talk about her business to someone she just met. He is a person who doesn’t like to fail at anything and holds a arrogant attitude, which is obvious. Another example that shows Mr Rochester isn’t the man for Jane is ‘resume your seat, and answer my questions. ’ He says this when he is interviewing Jane, he is rude and very demanding. ‘You examine me, Miss Eyre, do you think me handsome? ’ Mr Rochester is flattering himself as Jane doesn’t necessarily like him and even if she did deep down she wouldn’t say it she has too much pride, Whereas he is too proud and arrogant. All Mr Rochester wants is company, he has many friends which he can talk to instead of boring Jane. He seems to be displeased by his choice and expects Jane to entertain him. ‘You ought to have replied no such thing. Beauty of little consequence, indeed!. ’ Jane is way out her comfort zone as he tries to make awkward conversation with her. These are all key example of why Mr Rochester is not the right man for Jane. He is no Prince Charming in fact the complete opposite, he is a very arrogant, spiteful, cunning, devious, and pretentious man and doesn’t deserve Jane.

Free Essays on Dream

When people think of the â€Å"American Dream† they generally think a middle class, well-off family in a beautiful home with a couple of kids and maybe a dog. Both Lorraine Hansberry’s A Raisin in the Sun and Author Miller’s Death of A Salesman deal with the concept of having a dream and trying to achieve it. In some sense both families have the same dream, a dream to be successful and happy, and the dream to have money. But the families face many different obstacles that they must overcome. Some are physical and some are mental or emotional struggles. Also in both plays, each member of the family has their own personal dream and sometimes struggle to realize that the family is the most important symbol in a home. Throughout both plays we see the struggles and hardships that both families must face in order to attain their dreams. In Lorraine Hansberry’s A Raisin in the Sun, we see a poor black family struggling to keep their family united. The play is almost entirely based on the concept of dreams, whether it is an individual dream or the family dream. At the beginning of the play we see all of the characters individual dreams. Mama strongly believes in the importance of family and tries throughout the play to teach this to her children and grandchildren. Dreams are also more important to her than material wealth, and her dream is to one day own a house. Ruth, Mama’s daughter-in-law, agrees with Mama. She too sees the importance of family and having a new home to unite the family. Mama’s son, Walter has a more selfish dream of opening a liquor store with his friends. He believes that money is the way to happiness and that it will solve all of the family problems. He learns the hard way that money is only a physical element, and not happiness. Walter, for the most part, is not s uccessful with money and most of his actions throughout the play hurt the family. He rarely listens to his mother, wife, and sister... Free Essays on Dream Free Essays on Dream When people think of the â€Å"American Dream† they generally think a middle class, well-off family in a beautiful home with a couple of kids and maybe a dog. Both Lorraine Hansberry’s A Raisin in the Sun and Author Miller’s Death of A Salesman deal with the concept of having a dream and trying to achieve it. In some sense both families have the same dream, a dream to be successful and happy, and the dream to have money. But the families face many different obstacles that they must overcome. Some are physical and some are mental or emotional struggles. Also in both plays, each member of the family has their own personal dream and sometimes struggle to realize that the family is the most important symbol in a home. Throughout both plays we see the struggles and hardships that both families must face in order to attain their dreams. In Lorraine Hansberry’s A Raisin in the Sun, we see a poor black family struggling to keep their family united. The play is almost entirely based on the concept of dreams, whether it is an individual dream or the family dream. At the beginning of the play we see all of the characters individual dreams. Mama strongly believes in the importance of family and tries throughout the play to teach this to her children and grandchildren. Dreams are also more important to her than material wealth, and her dream is to one day own a house. Ruth, Mama’s daughter-in-law, agrees with Mama. She too sees the importance of family and having a new home to unite the family. Mama’s son, Walter has a more selfish dream of opening a liquor store with his friends. He believes that money is the way to happiness and that it will solve all of the family problems. He learns the hard way that money is only a physical element, and not happiness. Walter, for the most part, is not s uccessful with money and most of his actions throughout the play hurt the family. He rarely listens to his mother, wife, and sister...

Your Tequila May Contain Methanol

Your Tequila May Contain Methanol Happy Cinco de Mayo! If your holiday celebration includes tequila, you may be interested to know the American Chemical Society (ACS) has found that some tequila contains methanol, 2-methyl-1-butanol, and 2-phenylethanol. What are these chemicals? In case youre wondering, no, these are not good and desirable chemicals to drink. The alcohol in alcoholic beverages that you drink is ethyl alcohol or ethanol (grain alcohol). Methanol (wood alcohol) and other alcohols are the types that can make you go blind and otherwise cause permanent neurological damage, not to mention give you a nasty hangover. The ACS purposely timed the release of the results to coincide with Cinco de Mayo, to raise awareness of the quality control issue. Tequila made from 100% blue agave tended to have higher levels of undesirable chemicals than other types of tequila (pure agave tequila is usually considered superior). What This Means Does this mean tequila somehow bad? No, actually tequila is one of the best-regulated alcoholic beverages in the world. The results not only point out a potential health hazard for this drink but also indicate other beverages are probably adulterated with contaminants. Its the nature of distillation. The process relies on boiling point differences between liquids, which means good control of temperature is key. Also, the first and last portion of alcohol that is distilled (the heads and the tails) contain other compounds besides ethanol. Not all of these molecules are bad, so a distiller may choose to retain a certain amount. Then, there is a risk of picking up contaminants during the aging process. Its tricky, which is why top-shelf tequila is likely way better than home-grown moonshine, as far as your health goes. Yet, its possible to distill alcohol without unwanted compounds. Why does the problem persist? Its partly a matter of economics, where a distillery determines what level of contamination is acceptable. Increasing purity decreases yield which decreases profit. Its partly a compromise between making a product with premium flavor, color, and scent while keeping toxins to a minimum.

The history and evolution of Chinese women' rights Research Paper

The history and evolution of Chinese women' rights - Research Paper Example This created way for the formation of the communist government in the country under the name of the People’s Republic of China (Johnson 121). The new government committed to implementing social changes with the aim of uplifting the status of women in the society. The evolution of women’s rights in China has been a slow, painful but steady process discussed in the essay below. The growth and radical changes leading to the modern liberal Chinese society that embraces the gender equality has been slow and with myriad sacrifices, between 1966 and 1976 for example, the country experienced a massive cultural revolution as feminist movements sought the inclusion of women in the governance of the country. At the time of the formation of the new people’s republic of china, the country’s workforce had only seven percent of the women. The new communist government formulated and implemented new radical changes that with the view of increasing the status of women in th e new society but the male dominated society resisted most of such changes. By 1992, the percentage of the women in the country’s workforce had risen to thirty eight percent. Marriage in the traditional Chinese society was an arrangement between families. Young girls would be married off to men of the family’s choosing thus nurturing the women in order to befit specific requirements of the spouse’s family. Such arrangement denied women the right and privilege to fall in love and determine their lives. They simply married the men their families thought right for them. The male dominated society thought such to be effective ways of developing strong social ties but at the expense of the girl children. The great Cultural Revolution between 1966 and 1976 sought to address the social vice that had threatened the development of effective cultures in the society. Prior to the revolution, the communist government had initiated policies that sought to address the vice. I n 1950, the government formulated the marriage law. The law provided for the revocation of all previous family arrangements thus setting women previously bound by their families free. The law was a result of effective government research on the effects of such marriages and family arrangement on the social development of the society. By revoking all such arrangements, the governments sought to formulate better and more ethical policies and systems of marriage in the country. The men in the Chinese society opposed the legislation but through concerted government efforts and the works of the numerous feminist movements in the country, the law successful laws. In 1980, the government formulated another family law that banned arranged and forced marriages in the country. By banning such marriages, the government set the children especially the female children free from the dominance of their parents who used benefited from such arrangements. The marriage law of 1950 further permitted wo men to instigate divorces in the society. This would provide disadvantaged women in the forced, arranged and even purchased marriages the freedom to break away and foster their own independent lifestyles. Prior to the legislation, the society only permitted a divorce if it befitted the man. Additionally, the society also permitted polygamy thus allowing men to marry as many women as they wanted. In fact, the number of women in a homestead symbolized wealth and influence in the society. While

Entry into Chinese and Indian Retail Markets Essay

Entry into Chinese and Indian Retail Markets - Essay Example International market situations happen to be multi level in their decision focus, with a hierarchy of decisions from country assessment and performance measurement decisions through to more traditional marketing mix allocations and programs.International market situations happen to be multi level in their decision focus, with a hierarchy of decisions from country assessment and performance measurement decisions through to more traditional marketing mix allocations and programs.For the purpose of this study, entry into Chinese and Indian retail markets is to be considered. In general for a superstore/ retail chain like Tesco, Asda, Walmart, Trust-Mart, Reliance etc. the marketing mix comprises;†¢ Product – this includes the quality levels, production costs, the packaging, the range of products and the product differentiation.  Ã¢â‚¬ ¢ Price – this includes appropriate pricing for the target markets, quality considerations depending upon the pricing and an attackin g pricing or a defensive pricing  Ã¢â‚¬ ¢ Place – depending upon the location of a superstore it is also called a convenience store, therefore the location is very important to reach to the targeted segments.  Ã¢â‚¬ ¢ Promotion – we are today living in a media-savvy world. The power of being seen in print or TV or being heard on the radio can make or break a brand. Integrating the promotion publicity campaign with the marketing mix is very crucial.†¢ People – interface between the retail store and the customers are the people manning the counters and providing technical support and after-sales services. Therefore a friendly, uniformed, well informed and well-behaved person at the counter can help in gaining widening the customer base. HR friendly policies help in attracting and retaining good human resources. Processes - how the retail store manages its front office, back office, system support, online services etc. will definitely help it in earning a good reputation amongst the customers. Physicals - this includes the premises, support vehicles, uniforms and the looks of corporate signature. Service - last, but certainly not the least, is the services part. In fact the retailing business has become more of service oriented now a days. Were all the functions and techniques of using a particular gadget/ equipment told to the customer before the purchase, how the customer felt after buying a new TV set, did it malfunction, did he feel any difficulty in switching it on and tuning it - are some of the issues which can only be known if the retail store has a good mechanism of taking feedback from its customers. China: A leading Economy China is the most populous country in the world; with 1.30756 billion people1 by the end of 2005 it has a share of 22% of the world's total. China's entry into the WTO on December 11, 2001 has ensured regular inflows of FDI. With its gross domestic product (GDP) growing at an annual rate of

Gingko Biloba and Hypericum Peforatum Uses

Gingko Biloba and Hypericum Peforatum Uses 1.0 Gingko biloba Ginkgo biloba is an herb extracted from the leaves of the tree. It has been traditionally used for improvement of blood flow (vasodilation), protection of cells from oxidative damage (antioxidation) and enhancement of memory and concentration. The herb is known to induce CYP450 enzymes such as CYP2C9, CYP2C19 and CYP2B, changing the metabolism of several drugs.2 Hence, concomitant intake of some drugs with Ginkgo may give rise to herb-drug interactions which can cause serious adverse effect. 1.1 Antiepileptic drugs A recent pharmacogenetic study with 18 volunteers revealed significant inductive effect of CYP2C19 by Ginkgo. Omeprazole which has CYP2C9 activity was used as a substrate. The results demonstrated that Ginkgo decreased the AUC of omeprazole by a significant amount. Besides, the plasma concentrations of omeprazole and its metabolite were reduced by almost 30% when compared to controls. From the results obtained, it might be deduced that Ginkgo reduces serum concentrations of antiepileptic drugs which are substrates of CYP2C19 like phenytoin, phenobarbital and diazepam.3 Ginkgo might also induce CYP2B activity. According to study by Kubota et al 2004, Ginkgo was shown to reduce the hypnotic potency of phenobarbital (50 mg/kg) in rats. The maximum plasma concentration and AUC of phenobarbital were reduced by 40% and 20%, respectively. These might be due to induction of CYP2B activity by Ginkgo since phenobarbital is a substrate for CYP2B in rats, leading to the possible herb-drug interaction.3 Study also shows that Ginkgo contains a potent neurotoxin, which is a vitamin B6 derivative. It is also known as Ginkgotoxin or 4-O-methopridoxine.2, 3 The neurotoxin is said to be responsible for the seizure activity. It is a competitive antagonist of pyridoxil phosphate which is a coenzyme of the glutamate decarboxylase. Inhibition of this coenzyme inhibits the GABA synthesis. This interaction might hence diminish the effect of antiepileptic drugs. 1.2 Anticoagulants medication One of the concerns associated with Ginkgo is the increase risk of bleeding. Several cases have been reported when taking Ginkgo and anticoagulant drugs like aspirin and warfarin simultaneously. The proposed mechanism of bleeding caused by Ginkgo is via the action of ginkgolide B. According to Smith et al. 1996, Ginkgolide B is a component of Ginkgo which acts as a platelet-activating factor (PAF) antagonist. It is reported to displace PAF from its receptor- binding site, thus inhibiting PAF and results in reduced platelet aggregation and eventually bleeding. Nevertheless, some clinical studies have shown that Ginkgo does not decrease PAF-mediated platelet aggregation as well as prothrombin times.4 Warfarin is metabolised by CYP2C9 enzymes. An in vitro study by Gaudineau et al. 2004 stated that Ginkgo inhibits CYP450 enzymes, mainly CYP2C9. Hence, it is possible that this inhibition might lead to increase in warfarin levels and subsequently greater anticoagulant action. However, there are some contradicting studies which reported that Ginkgo induces rather than inhibits hepatic CYP, including (S)-warfarin hydroxylase. It is also reported that bilobalide found in terpene trilactone fraction of Ginkgo is responsible for the induction. This will thus reduce the efficacy of anticoagulants rather than enhancing the anticoagulant action.4 It remains unclear whether Ginkgolide B increase bleeding and whether Ginkgo potentiates or decreases the anticoagulant effect of warfarin in vivo. Nevertheless, it is recommended that for patients on warfarin or other anticoagulants therapy to not take ginkgo-containing products due to a possible risk of serious bleeding. 2.0 Hypericum Peforatum (St. John’s Wort) St. Johns Wort preparations may interact with medicines either by increasing the rate of their metabolism or increasing levels of neurotransmitters. 2.1 Drugs metabolized by CYP-450 St. John’s Wort interferes with metabolism of drugs by inducing some CYP450 enzymes in the liver and gut. For instance, the main enzyme affected is CYP3A4, as well as 1A2 and 2C9. This results in decrease in blood levels and efficacy of some drug metabolised by CYP450 enzyme. The principle behind the induction might be due to presence of hyperforin, which is a component of St. John’s Wort. A study by Moore et al. has shown that hyperforin activates a CYP3A4 regulator transcription. This activation thus induces CYP3A4 expression in human liver cells, thus increase the metabolic rate of drugs and subsequently decrease in therapeutic level. It can be deduced that St. John’s Wort inhibits CYP3A4 acutely and induces this enzyme upon repeated administration based on a systematic review.5 An example of this herb-drug interaction is St. John’s Wort and antiretroviral drugs such as protease inhibitors (PI) and nonnucleoside reverse transcriptase inhibitors (NNRTI). St. John’s Wort has been shown to decrease plasma concentrations of the drugs by CYP3A4 induction. The effects may also be due to induction of P-glycoprotein. For instance, there was a significant reduction in concentrations of indinavir when taken concurrently with St. John’s Wort in an open-label study.5 This will lead to loss of viral control or development of virus resistance. 2.2 Antidepressants medication St. Johns Wort also increases the neurotransmitter levels in the brain particularly serotonin through additive effect on selective serotonin reuptake inhibitor (SSRI) antidepressants such as fluoxetine and paroxetine. These interactions may lead to mental state changes, sweating, increased blood pressure and motor effects due to increase in serotonin level. Studies have demonstrated that St Johns Wort inhibits the synaptosomal uptake of certain neurotransmitters. It inhibits the uptake of 5-HT, noradrenaline, dopamine, glutamate and GABA. This action is not related to specific binding of the St. John’s Wort to the different transporter molecules, but associated with mechanisms related to Na+ conductive pathways.6 It is found that chronic administration of St. John’s Wort downregulates ÃŽ ²1-adrenoceptors and upregulates postsynaptic 5-HT1A receptors. Nevertheless, the study shows St. John Wort’s upregulates 5-HT2 receptors unlike other antidepressants.6 References xxxx Kupiec T, Raj V. Fatal Seizures Due to Potential Herb-Drug Interactions with Ginkgo Biloba. Journal of Analytical Toxicology 2005 Oct; 29:755-58 Landmark CJ, Patsalos PN. Interactions between antiepileptic drugs and herbal medicines. Bol. Latinoam. Caribe Plant. Med. Aromaticas 2008; 7(2):109-18 Takia Y, Yokotania K, Yamadab S, Shinozukac K, Kubotad Y, Watanabed Y, Umegakia K. Ginkgo biloba extract attenuates warfarin-mediated anticoagulation through induction of hepatic cytochrome P450 enzymes by bilobalide in mice. Phytomedicine 2012 Jan 15; 19(2):177-82 Hammerness P, Basch E, Ulbricht C, Barrette EP, Foppa I, Basch S, Bent S, Boon H, Ernst E. St. John’s Wort: A Systematic Review of Adverse Effects and Drug Interactions for the Consultation Psychiatrist. Psychosomatics 2003 July- Aug; 44(4):271-82 Carloa GD, Borrellia F, Izzoa AA, Ernst E. Is St Johns wort a ‘Prozac-like’ herbal antidepressant? Trends in Pharmacological Sciences 2001Nov 1; 22(11):559

Math Portfolio Ib Circles

MATHS PORTFORLIO SL TYPE I CIRCLES ? In this portfolio I am investigating the positions of points in intersecting circles. (These are shown on the following page. The following diagram shows a circle C1 with centre O and radius r, and any point P. The circle C2 has centre P and radius OP. Let A be one of the points of intersection of C1 and C2. Circle C3 has the centre A, and radius r. The point P? is the intersection of C3 with (OP). This is shown in the diagram below. As shown on the assignment sheet, r=OA. We therefore need to find the values of OP? hen r=OA=1 for the following of the values of OP: OP=2, OP=3 and OP=4. We first of all extract the triangle OPA from the above diagram and since we have the values for all the three sides we can finds the angle AOP which will later on help to get the value of length OP?. The circle C2 and triangle OPA are shown below with all side of OPA indicated. OP=AP since they are the radii of the same circle, C2. Having all the three sides, we ca n now calubulate the angle AOP using the cosine rule. Angle AOP is calculated below: Cos AOP=(2^(2 _ ) 2^(2 _ ) 1^2)/(-2? 2? 1) Cos AOP=0. 25 ? AOP =COS-10. 5 =75. 52248781 ?75. 5? Since we now having the triangle AOP, we can extract the triangle AOP? from the diagram shown on the previous page which in return will help us to find OP? using the sine rule. The triangle AOP? is shown below: O P For accuracy the value of angle AOP will be used as cos-10. 25 instead of 75. 5?. Since triangle AOP? is an isosceles triangle, AOP=AP? O=cos-10. 25. Therefore OAP? = (180-(2? cos-10. 25)). The calculation of the value of OP? is shown below: (OP? )/(sinOAP? )=(AP? )/(sinAOP? ) (OP? )/sin? (180-(2 cos? ^(-1) 0. 25) ) =1/sin? (? cos? ^(-1) 0. 5) op? = 1/sin? (0. 25) ? (180-(2 cos? ^(-1) 0. 25) ) op? =1/2 When OP=3, the triangle OPA and the calculation of OP? are as follows: Cos AOP = (3^2-3^2-1^2)/(-2? 3? 1) Cos AOP = 1/6 ? AOP = cos-1 1/6 =84. 4? From the triangle AOP? we can now calculate the l ength of OP? using the sine rule as before. The triangle AOP? and the calculator of OP? is shown below: A 16 OP' AP? O=AOP? =cos-11/6 OAP? = (180-(2 cos? ^(-1) 1/6) (OP? )/(sinOAP ? )= (AP? )/(sinAOP? ) (OP? )/sin? (180-(2 cos? ^(-1) 1/6) ) =1/sin? (? cos? ^(-1) 1/6) op? = 1/sin? (1/6) ? (180-(2 cos? (-1) 1/6) ) = 1/3 When OP=4; Cos AOP =(4^2-4^2-1^2)/(-2? 4? 1) Cos AOP = 1/8 ? AOP =cos-1 1/8 =82. 4? Using the sine rule; (OP? )/(sinOAP ? )= (AP? )/(sinAOP? ) (OP? )/sin? (180-(2 cos? ^(-1) 1/8) ) =1/sin? (? cos? ^(-1) 1/8) op? = 1/(sin? (? cos? ^(-1 ) 1/8))? (180-(2 cos? ^(-1) 1/8) ) = 1/4 When OP=2, OP? = 1/2;when OP=3 , OP? = 1/3 and when OP=4, OP? = 1/4 . This indicates that the value of OP? is dependent on the value of OP. In fact it is inversely proportional to the value of OP.To arrive at the value of OP? , 1 is divided by the value of OP. Therefore generally, the value of OP' can be written as: OP=r/OP Moreover, from the values of OP? calculated above, it is observed that the value of OP? is twice Cos AOP. The general statement therefore can be written as: OP? = 2 Cos? Let OP=2. Find OP? when r=2, r=3 and r=4. Describe what you notice and write a general statement to represent this. Comment on whether or not this statement is consistent with your earlier statement. First of all we need to calculate the value of OP? when OP=2 and r=2. The triangle AOP now looks like as follows:A 22 1. 5P' Since all the sides are of the same length, then AOP=APO=OAP=60Â ° (according to the angle sum of the triangle). The triangle AOP? is shown below from which OP? is found. A 22 O2P' AO=AP? from the diagram given on the lab sheet, therefore AOP=APO=60Â °. The remaining angle OAP= (180-(2? 60)) = 60Â °. This then means that triangle AOP? is an equilateral triangle – all its sides are the same. ?AO=AP? =OP? =2 We now need to calculate the value of OP? when OP=2 and r=3. Below is the triangle AOP and the calculation of angle AOP. 22 3 Cos AOP = (2^2-2^2-3^2)/(-2? 2? 3) Cos AOP = 3/4 AOP = cos-1 3/4 = 41. 4Â ° Having calculated the value of angle AOP, we can now calculate the value of OP? from AOP? using the sine rule as shown below: A 33 O P? Angle OAP? = 180-(2 Cos? ^(-1) 3/4) (OP? )/(sinOAP ? )= (AP? )/(sinAOP? ) (OP? )/sin? (180-(2 cos? ^(-1) 3/4) ) =1/sin? (? cos? ^(-1) 3/4) op? = 1/sin? (? cos? ^(-1) 3/4) ? (180-(2 cos? ^(-1) 1/8) ) =9/2=4. 5 The value of OP? is now calculated when OP=2 and r=4 using the same method as above. 22 O4P 44 P? Cos AOP = (2^2-2^2-4^2)/(-2? 2? 4) Cos AOP = 1 ? AOP = cos-1 1= 0AOP? =AP? O=0 ?OAP? =180-(2? 0) = 180Â ° OP? 2= OA2+ AP? 2-2? OA? AP? Cos OAP? = 42+42-2? 4? 4 Cos 180Â ° = 64 OP? = v64 = 8 Below is the table for the vales of r, OP and OP' when OP is kept constant. ROPOP' 222 324. 5 428 When OP=2, OP? =2; when OP=3, OP? = ( 9)/2 and when OP=4, OP? =8. From these results it can be seen that the length OP? increases with the increasing length OP and the general statement for the variation in the values of OP? is as follows: OP? = r^2/OP. This general statement is not fully consistent with the first one because r/OP is not always equal to r^2/OP.When the above values are substituted into the first general statement, wrong values of OP? are obtained but the latter general statement holds for both data. However both the general statements hold true when r=1 since 12=1, which indicates that for this value of r, r^2/n=r/n. Use technology to investigate other values of r and OP. Find the general statement of OP?. I used GeoGebra to draw the intersecting circles with the values of r and OP stated and the values of OP? were automatically calculated. When r=1and OP=2 OP=0. 5