Math Equations free essay sample

This paper will show two mathematical problems, the first is â€Å"To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationists estimate of the size of the bear population? † (Dugopolski, 2013, pp. 37, probem 56). The second will be to complete problem 10 on page 444 of Elementary and Intermediate Algebra. Here all steps in solving the problem will be explained step by step. The first problem is to estimate the size of the bear population located on the Keweenaw Peninsula conservation. In reading over the â€Å"Bear Population† method #56 on page 437you will notice we are to assume that the ratio of originally tagged bears to the whole population is equal to the ratio of recaptured bears to the size of the sample. The ratio of the originally tagged bears to the whole population is 2100 The ration of the recaptured tagged bears to the sample size is 50x 2100=50x Since x is on the right-hand side of the equation, we need to switch the sides so it is on the left-hand side. We will write a custom essay sample on Math Equations or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page 50x=2100 This is the proportion set up and ready to solve. I will cross multiply setting the extremes equal to the means. 100(50) = 2x Here 100 and 50 are the extreme, while x and 2 are the means. 0002=22 Next we must divide each term in the equation by 2. X=50002 Cancel out the common factor X=2500 The bear population in Keweenaw Peninsula is estimated to be around 2500. For the second problem in this assignment I am asked to solve this equation for y. The first thing I notice is that it is a single fraction (ratio) on both sides of the equal sign so basically it is a proportion which can be solved by cross multiplying the extremes and means. y-1)=-34*((x+3))Multiply both sides of the equation by (x+3) (y-1)=-34*(x+3)Remove the extra parentheses (y-1) = -3(x+3)4Multiply the rational expressions to get 3(x+3)4 y-1= -3(x+3)4Remove the parentheses around the expression y-1 Since -1 does not contain the variable solve for, move it to the right-hand side of the equation by adding 1 to both sides. y=1 *44 3(x+3)4Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 4. = 14 (-1*4) 3(x+3)4Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4. y= 44 3(x+3)4 Multiply 1 by 4 to get 4. y = 4-3(x+3)4 The numerators of expressions that have equal denominators can be combined. In this case, (4)4 and 3(x+3)4 have the same denominator of 4, so the numerators can be combined. y = 4-3 (x+3)4 Remove the parentheses around the expression 4. y = 4-3 x-3 (3)4 Multiply -3 by each term inside the parentheses (x-3). = 4-3 *x-3 (3)4 Multiply -3 by the x inside the parentheses. y = 4-3 x-3 (3)4 Multiply -3 by x to get – 3x. y = 4-3 x-3* 34 Multiply -3 by the 3 inside the parentheses. y = 14 (4-3x-9) Multiply -3 by 3 to get -9. y = 14 (-5 -3x) Subtract 9 from 4 to get -5 y = 14 (-3x -5) Reorder the polynomial -5 -3x alphabetically from left to right, starting with the highest order term. y = 14 (-3x-5)Simplify the right-hand side of the equation. Here I have notice that the solution for y = 14 (-3x-5) but the equation for x is different and x as a rational expression is (y-1)  · 4=-3  · (x+3) which is solved by which is solved by a ration. Simplify the equation for x = 4y3 53 . Another thing I have learned is if you go from x = y to x^2 = y^2 you have introduced the extraneous root. References: Dugopolski, M. (2013). Elementary and Intermediate Algebra, 4th Ed. New York, NY: The McGraw-Hill Companies, Inc. Math Equations free essay sample This paper will show two mathematical problems, the first is â€Å"To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationists estimate of the size of the bear population? † (Dugopolski, 2013, pp. 37, probem 56). The second will be to complete problem 10 on page 444 of Elementary and Intermediate Algebra. Here all steps in solving the problem will be explained step by step. The first problem is to estimate the size of the bear population located on the Keweenaw Peninsula conservation. In reading over the â€Å"Bear Population† method #56 on page 437you will notice we are to assume that the ratio of originally tagged bears to the whole population is equal to the ratio of recaptured bears to the size of the sample. The ratio of the originally tagged bears to the whole population is 2100 The ration of the recaptured tagged bears to the sample size is 50x 2100=50x Since x is on the right-hand side of the equation, we need to switch the sides so it is on the left-hand side. We will write a custom essay sample on Math Equations or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page 50x=2100 This is the proportion set up and ready to solve. I will cross multiply setting the extremes equal to the means. 100(50) = 2x Here 100 and 50 are the extreme, while x and 2 are the means. 0002=22 Next we must divide each term in the equation by 2. X=50002 Cancel out the common factor X=2500 The bear population in Keweenaw Peninsula is estimated to be around 2500. For the second problem in this assignment I am asked to solve this equation for y. The first thing I notice is that it is a single fraction (ratio) on both sides of the equal sign so basically it is a proportion which can be solved by cross multiplying the extremes and means. y-1)=-34*((x+3))Multiply both sides of the equation by (x+3) (y-1)=-34*(x+3)Remove the extra parentheses (y-1) = -3(x+3)4Multiply the rational expressions to get 3(x+3)4 y-1= -3(x+3)4Remove the parentheses around the expression y-1 Since -1 does not contain the variable solve for, move it to the right-hand side of the equation by adding 1 to both sides. y=1 *44 3(x+3)4Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 4. = 14 (-1*4) 3(x+3)4Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4. y= 44 3(x+3)4 Multiply 1 by 4 to get 4. y = 4-3(x+3)4 The numerators of expressions that have equal denominators can be combined. In this case, (4)4 and 3(x+3)4 have the same denominator of 4, so the numerators can be combined. y = 4-3 (x+3)4 Remove the parentheses around the expression 4. y = 4-3 x-3 (3)4 Multiply -3 by each term inside the parentheses (x-3). = 4-3 *x-3 (3)4 Multiply -3 by the x inside the parentheses. y = 4-3 x-3 (3)4 Multiply -3 by x to get – 3x. y = 4-3 x-3* 34 Multiply -3 by the 3 inside the parentheses. y = 14 (4-3x-9) Multiply -3 by 3 to get -9. y = 14 (-5 -3x) Subtract 9 from 4 to get -5 y = 14 (-3x -5) Reorder the polynomial -5 -3x alphabetically from left to right, starting with the highest order term. y = 14 (-3x-5)Simplify the right-hand side of the equation. Here I have notice that the solution for y = 14 (-3x-5) but the equation for x is different and x as a rational expression is (y-1)  · 4=-3  · (x+3) which is solved by which is solved by a ration. Simplify the equation for x = 4y3 53 . Another thing I have learned is if you go from x = y to x^2 = y^2 you have introduced the extraneous root. References: Dugopolski, M. (2013). Elementary and Intermediate Algebra, 4th Ed. New York, NY.

History of the Nature Conservancy

History of the Nature Conservancy The Nature Conservancy joins forces with governments, non-profit organizations, local stakeholders, indigenous communities, corporate partners, and international organizations to find solutions to conservation challenges. Their conservation tactics include the protection of private lands, the creation of conservation-minded public policies, and the funding of conservation projects around the world. Among The Nature Conservancys more innovative conservation approaches is the debt-for-nature swaps. Such transactions ensure biodiversity conservation in exchange for debt owed by a developing country. Such debt-for-nature programs have been successful in many countries including Panama, Peru, and Guatemala. History The Nature Conservancy was formed in 1951 by a group of scientists who wanted to take direct action to save threatened natural areas around the world. In 1955, The Nature Conservancy acquired its first parcel of land, a 60-acre tract along the Mianus River Gorge which lies on the border of New York and Connecticut. That same year, the organization established the Land Preservation Fund, a conservation tool that is still used today by The Nature Conservancy to help provide funding for worldwide conservation efforts. In 1961, The Nature Conservancy formed a partnership with the Bureau of Land Management that was aimed at protecting old-growth forests in California. A gift from the Ford Foundation in 1965 made it possible for The Nature Conservancy to bring on its first full-time president. From that point on, The Nature Conservancy was in full swing. During the 1970s and 1980s, The Nature Conservancy setup key programs such as the Natural Heritage Network and the International Conservation Program. The Natural Heritage Network collects information about species distributions and natural communities throughout the United States. The International Conservation Program identifies key natural regions and conservation groups in Latin America. The Conservancy completed their first debt-for-nature swap to fund conservation work in Braulio Carillo National Park in 1988. During that same year, the Conservancy joined forces with the US Department of Defense to help manage 25 million acres of military land. In 1990, The Nature Conservancy launched a large-scale project called the Last Great Places Alliance, an effort aimed at saving entire ecosystems by protecting core reserves and establishing buffer zones around them. In 2001, The Nature Conservancy celebrated its 50th year anniversary. Also in 2001, they acquired Zumwalt Prairie Preserve, a protected area on the edge of Hells Canyon in Oregon. In 2001 through 2005, they purchased land in Colorado that would later form the Great Sand Dunes National Park and the Baca National Wildlife Refuge, as well as expand the Rio Grande National Forest. Most recently, the Conservancy organized the protection of 161,000 acres of forest in the Adirondacks of New York. They also recently negotiated a debt-for-nature swap to protect the tropical forest in Costa Rica.

Hospital Robot Essay Example | Topics and Well Written Essays - 1000 words

Hospital Robot - Essay Example Robots refer to mechanical agents controlled by computer programs and used in completing tasks. They vary in sizes and used for specific purposes. Used with artificial intelligence the machines can perfume precise functions repeatedly without tiring. In healthcare, several hospitals and health facilities in the United States have begun using robots to aid complicated surgeries (Barker 33). The machines run on specific computer programs and follow instructions as fed to them through the computer. Additionally, they operate alongside humans during the operations thus improving the quality of services. Robots have improved the quality of surgical operations and their continued use in the industry will definitely improve the quality of life by improving effectiveness in hospitals as discussed in the essay below.Robots are cost effectiveUnlike humans, a robot is a capital and an asset bought once by a health facility and can perform several functions throughout the clock. Being machines, robots have minimal requirements provided they are in good condition and accurately programmed. They, therefore, function with minimal supervision thus making the practice less labor intensive.Doctors often tire after detailed operations; this makes the operations precarious as they begin making such mistakes as forgetting some of the equipment in the patients they operate. Additionally, they serve more for their services a feature that makes health services very costly thus unaffordable by many (Ichbiah 11).

E-loyalty and Customer relationship management Essay

E-loyalty and Customer relationship management - Essay Example Some sole proprietors use online programs in targeting nationwide and global customers by using accurate information regarding the business and the use consumer programs such as credit card reward programs as a strategy in keeping their loyal customers satisfied. It is common that these reward systems are tailored according to the needs and expectations of the customers. Business-to-business (B2B) or e-biz is an effective tool in the exchange of products, services, and information between business and consumers. Over the years, B2B has proven to be very effective in closing business transactions between the business owner and the customers. According to a study that was published back in early 2000, the profitability of using B2B has exceeded the ‘e-tailing’ by 10 to 1% and is expected to have an annual growth of 41% over the next few years. (Jones, 2001) Customer Relationship Management (CRM) is a ‘software’ that helps a business organization in managing its customers better. (Walsh, 2007) CRM software enables the sales people and service representatives to have a quick access over the information related to the customers. This allows the sales force of the company to immediately provide the customers with a more customized service according to the customers’ needs regarding the products and services the business is offering. (Williams, 2006) According to Kumar and Reinartz (2006), CRM is defined as a strategic process of selecting the customers a firm can most profitably serve. It is also capable of shaping the interactions between a company and these customers with the goal of optimising the current and future value of the customers for the company. (Kumar and Reinartz 2006, 6) Based on the definition, CRM is a process of enterprise-wide that has the potential to affect decisions related to marketing communications, pricing, customisation of products and services, resource allocation across different customers

Foreign Corrupt Practices Act Essay Example | Topics and Well Written Essays - 1250 words

Foreign Corrupt Practices Act - Essay Example While the Act was initially seen as being bad for US business abroad, the long-term effects have been for the benefit of US companies both domestically and internationally. The Foreign Corrupt Practices Act (FCPA) of 1977 was implemented to further restrain the practices of American business in the areas of using undue influence in international business. According to the Congressional Research Service the FCPA was, "...enacted principally to prevent corporate bribery of foreign officials" (Seitzinger). Before the Act was passed, there were cases of corporations using secret funds to influence and bribe foreign officials. The government contended that these illegal payments, "...affected adversely American foreign policy, damaged abroad the image of American democracy, and impaired public confidence in the financial integrity of American corporations" (Seitzinger). The FCPA also reasserted the ideals of fair trade and anti-trust policies by curtailing the unfair practices that might place a corporation in an unfairly advantageous position over a competitor through a corrupt practice. While these business practices had been outlawed by the array of prev ious legislative acts, the FCPA codified and focused the illegal activity under one act. The FCPA of 1977, and the amendments of 1988 and 1998, specifically prohibits the bribery of any foreign official and making false or misleading entries into a company's financial records. Prior to the FCPA, companies would use slush funds to make payments to foreign officials to gain a business advantage. Often these payments would be incorrectly described in their accounting practices (Johnson). In addition the FCPA also expanded the definition of 'foreign official' to include not only highly placed government officials but also private persons who may have a function similar to a government employee. This could include contractors working on government contracts or doing business with a foreign government. The FCPA further outlawed the practice of influencing regulatory policies and the obtaining of permits or licenses through fraud and bribery. The FCPA also further defined and prohibited the practice of "willful blindness" where a company pays money and does not make an inquiry that any reasonable person would make as to the use of said money (Johnson). The FCPA does not differentiate between a bribe that succeeds and an offer that fails or is declined. The Act defines corruption as the intent to unfairly influence. There are two sections that define the enforcement of the FCPA. There is the criminal provision that is enforced by the US Department of Justice and the civil portion that is enforced by the Securities and Exchange Commission (SEC) ("Foreign Corrupt Practices"). The SEC also has responsibility to monitor and enforce the accounting standards set forth in the Act. The criminal fines for violation can be quite extensive. The corporation can be fined up to $2 million, while individual violators can face fines of up to $100,000 and be sentenced to 5 years in prison (Shaheen and Geren, 3). Shaheen and Geren further note that the corporation is banned from reimbursing the fines and penalties levied against an individual violation. The fines that can be levied by the SEC for

Experiment of Hookes Law

Experiment of Hookes Law Investigating Hooke’s Law Aim This experiment is aimed to investigate the relationship between the mass that is being slotted at the end of spring and the time taken for the spring to make a 20 complete oscillations. Hypothesis As the mass of the end of the spring increases, the time period for the spring to complete 20 oscillation will also increase. This is because in newton’s second law which is F = ma, if the acceleration is being derived with the presence of time in its formula, it will be F = m(v-u)/t. Which proves that, mass is directly proportional to time. As the mass increases, the time will also increase. Variables Independent variable: Mass that is being slotted at the end of the spring (kg) Dependent variable: Time period taken by the spring to make 20 complete oscillations (s) Controlled variable: i) Spring constant ii) Gravitational acceleration iii) Length of spring iv) Amount of spring oscillations v) Air resistance vi) Amplitude of oscillations Controlling the variables Mass that is being slotted at the end of the spring: The mass that is being slotted at the end of the spring is manipulated from 0.1kg, 0.2kg, 0.3kg, 0.4kg and 0.5kg. Time period taken by the spring to make 20 complete oscillations: With the aid of digital stopwatch, the time period is taken when the spring had completed in making 20 oscillations. This procedure is repeated 3 times and an average reading is taken. Spring constant: The spring constant is kept constant so that the results are relative to each other. It will be controlled by using the same spring throughout the whole experiment. Gravitational acceleration: The gravitational acceleration is kept constant by conducting the experiment in the same place until the end. Amount of spring oscillations: The amount of oscillations is controlled to 20 so that the results are more accurate. The exact results will be divided by 20 afterwards. Air resistance: Due to the place that the experiment is being conducted in a room, the fan and the air conditioner are switched off to reduce the air resistance. The experiment is conducted in the same place until the end to fix the air resistance. Amplitude of oscillations: The amplitude will be controlled each time the mass is increased by using the same length in extending the spring to make is oscillate. For each trial, the spring is extended 5cm downwards. This procedure will be aided by a meter ruler. Materials list Retort stand Clamp and stand Meter ruler Mass holder Slotted mass Digital stopwatch Spring Diagram Method Set up the apparatus as shown in the diagram, with one end of the spring attached to the horizontal support on the clamp stand. Attach the slotted mass of 0.1kg at the end of the spring. Put the meter ruler next to spring and measure the extension. Pull the slotted mass holder down to 5cm and then release it. Let it oscillates for 20 times. Take the time taken for the spring to oscillate completely for 20 times using digital stopwatch. Repeat step 4 to 6 two more times. Record the data each time and take an average reading. Repeat step 2 to 7 by using different slotted mass, from 0.2kg, 0.3kg, 0.4kg, and 0.5kg. Results Data presentation A graph to show the relationship between the mass that is being slotted at the end of the spring, M, and the time taken for one oscillation, T. Data analysis The relationship between mass that is being slotted at the end of the spring and the time taken for spring to oscillate one cycle appears to be non-linear. The data therefore will be processed in order to find a relationship between this two variables either it is directly proportional or not. The graph is parabolic. Hence the T can be manipulated to become T2 so that the graph can be plotted with a variable of mass against T2. Data processing Table 2 – Mass that is being slotted at the end of spring, M, and squared of time taken for one oscillation, T2 Presentation and analysis of the processed data A graph shows the relationship between the mass that is being slotted at the end of the spring, M, and the squared of time taken for one oscillation,T2. Analysis of the graph Gradient of best fit line = 0.50/0.32 = 1.56 kgs-2 Gradient of steepest line = 0.50/0.30 = 1.67 kgs-2 Gradient of shallowest line = 0.42/0.34 = 1.24 kgs-2 For the second graph, it was proved that mass that is being slotted at the end of spring is direclty proportional to the squared of time period. Mathematically, m ÃŽ ± T2 After the investigation and the experiment that had been done, it was found that the formula relating the mass that is being slotted at the end of spring and time period of an oscillating spring is : We know that ; T = 2Ï€/Æœ Where Æœ = k(constant) in this investigation. Therefore, T = 2Ï€ T2 = Which is of the form, y = mx + c (equation of straight line) From the investigation, y is m, m is 4Ï€2/k and x is T2. The gradient of the line is therefore equal to 4Ï€2/k , we can now find the spring constant: Therefore, k on the best fit line ; 1.56 = 1/ = 1/1.56 k = 61.59 Nm-1 The range of uncertainty in this value can be calculated using both the maximum and the minimum lines on the graph. Maximum gradient ; 1.67 = 1/ = 1/1.67 k = 65.93 Nm-1 Minimum gradient ; 1.24 = 1/ = 1/1.24 k = 48.96 Nm-1 Therefore the spring constant, k is in the range of 48.96 Nm-1 to 65.59 Nm-1. Conclusion The aim of this experiment is to investigate the relationship between the mass that is being slotted at the end of spring and time period of oscillation. As the hypothesis being made earlier that mass would be directly proportional to time period of oscillation, it is clearly was wrong as the graph of mass against time period is obviously non-linear. The second graph of mass against squared of time period is however turned out to be linear and therefore it can be concluded that mass is directly proportional to the squared of time period. After the investigation, this conclusion is supported as the equation for time period of an oscillating spring is T = 2Ï€ T2 = So, T2 ÃŽ ± m The gradient of straight line was then used to calculate the spring constant, k, for the spring used in this experiment. This is because the gradient is equal to 1/ The value can be compared to the theoretical value by using Hooke’s so as to verify the result whether it is plausible or not. When the spring is acted a force of 1N, the extension was seen to be 1.6cm. The spring constant can be determine by using the formula of Hooke’s law; F = kx k = 1/0.016 k = 62.5 Nm-1 Calculating percentage deviation: x 100% = 1.5% The actual value and the theoretical value is not that far and only 1.5% in the percentage deviation. In conclusion, it can be said that this experiment is successful and the results are accurate. Evaluation The method and apparatus used worked well throughout the whole experiment. The results obtained are differ from the actual results. This is because they are maybe some mistakes were made during taking the reading or making the experiment works. There are some improvements that were made when collecting the data that were not stated in the original plan. Parallax error occurs when reading the ruler which the recorder’s eye level is not perfectly perpendicular to the ruler. The slotted mass were considered to be the same. Just one of the slotted mass was weighted and for one slotted mass the mass is 0.1kg. Without hesitation, the other slotted mass were all considered to be 0.1kg in mass too. This may have produced a systematic error, depending on how accurate the masses were and consistency of their inaccuracy. When lighter slotted mass were used, the oscillations was so fast. Random errors can occur. Suggested that, the spring should be let to oscillation more so that the results will be more precise. Suggested improvements The investigation could has been more accurate and precise if the following modifications were to be taken: Make sure that the eye is perpendicular to the ruler when taking the reading when doing the extension of spring. This will avoid parallax error. Use another ruler to point at the ruler when taking the reading. This will aid to read the meter ruler easier and more precise. This will avoid parallax error. To make the time taken more accurate, use ultra-sonic motion detector that is placed below the oscillating spring. The ultra-sonic motion detector will collect data more precisely because it does not involve the human interaction which is affected by human reaction. Take more reading and take the average as the lesser the reading are taken, it will create more random errors.

Relationship Between Macbeth and Lady Macbeth Essay

Almost every relationship has those critical arguments or confrontations and requires communication as well as collaboration to overcome its challenges. This is the case between Macbeth and Lady Macbeth where two different personalities and characteristics begin to clash against one another and push each other to their limits. As the play progresses, Lady Macbeth’s motives and desires are revealed and as a result, her aspirations get the best of her and starts to influence her husband Macbeth to take the path of potentially being king which ultimately involves elements of death, fraud, and exploitation. Throughout act one of â€Å"Macbeth†, Macbeth and Lady Macbeth share a controlling yet cooperative relationship. Lady Macbeth plays a very significant role in influencing Macbeth to choose the path towards higher royalty. Her own ambitions of being queen alongside her husband motivated her to plot a wicked act to overthrow or maybe even kill the king. Lady Macbeth first realizes the possibility of being queen in act 1, scene 5, lines 14-15 in which she states, â€Å" Glamis thou art, and Cawdor; and shalt be what thou art promised. When she hears of the news, she immediately begins plotting to gain her husbands desire to be king but while doing so, she questions Macbeth as well as his abilities and personality. Lady Macbeth’s first instinct is to act with cruelty rather than loyalty, revealing her dark nature which go to beyond measures to obtain her desires. Also, starting from line 15 of Act 1, Scene 5, Lady Macbeth states, â€Å"Yet do I fear thy nature; it is too full o’th’milk of human kindness to catch the nearest way†; in other words, Macbeth is a good-hearted man. She knows her husband too well to believe that he would be willing to do any wicked act such as murder especially against the king. As a result, she resolves to convince her husband to do whatever is required to seize the crown. She also believes that by putting her femininity aside, she can possibly do any of the darkest and most wicked acts to possibly seize the crown. Lady Macbeth plays the dominant character throughout the opening scenes, in which she asserts her ambition for her and her husband to gain hierarchic status. Her best bet is to try to influence Macbeth is by questioning his anhood. Through parts of act 1, scene 7, Macbeth gives her his reasons why he shouldn’t kill the king: karma, being the king’s host, being loyal as his subject, the king being humble leader, and compliments given to him by the king made him look favorable in the eyes of the people. It is fair to say that Macbeth does have ambition, but at this point in the play, his conscience is str onger than ambition giving him less motivation to kill the king. As a result, Lady Macbeth repeatedly questions his manhood in the hope that he will defend himself by carrying out the murders. It seems to me that Macbeth has a mental struggle with his masculinity, because Lady Macbeth deprives him of it when he is at his lowest moments and then try to win him over by giving him compliments and expletive comments for example in act 1, scene 7, lines 49-59 in which Lady Macbeth states, â€Å"When you durst do it, then you were a man; and to be more than what your were, you would be so much more the men†¦.. Does unmake you. I have given suck, and know how tender ‘tis to love the babe that milks me. I would, while it was smiling in my face, have plucked my nipple from his boneless gums and dashed the brains out, had I so sworn as you have done this. † Basically, she dares him to commit the murder, using words that taunt rather than persuade in which it frightened and shocked Macbeth so much that he, as a result gives in to her orders. At this point we see Lady Macbeth as a persistent and strong women, while we see Macbeth as her indecisive and cowardly husband in which Lady Macbeth’s uses her strong characteristics to undermine Macbeth’s in order for him to cooperate with her ideas. Under her spell, all of Macbeth’s objections seem to evaporate and he is left only with a weak â€Å"If we should fail? † which is in line 58 of act 1, scene 7. Macbeth is not a good man at this point in the play, but he is not yet an evil one; he is tempted, and he tries to resist temptation. Macbeth’s resistance, however, is not effective enough to stand up to his wife’s ability to manipulate him. We finally get a sense that Macbeth is willing to do what his wife asks of him. She acts as a catalyst for Macbeth to commit treason by disregarding his rational, moral arguments and challenging his manhood.. As a result, Macbeth and Lady Macbeth cooperate and plot to get the servants drunk, and during that time Macbeth and Lady Macbeth would kill King Duncan and frame the drunken guards. In line 79-80 of act 1 scene 7, Macbeth states, â€Å"I am settled, and bend up each corporal agent to this terrible feat. † Since Macbeth succumbs to Lady Macbeth’s wishes, Shakespeare re-confirms just how close the relationship between Macbeth and Lady Macbeth is and that she has the power and he listens to whatever she has to say whether if it’s for his own good or not. Macbeth and Lady Macbeth share a very complex relationship between each other. Lady Macbeth is a complicated woman in the beginning of the play; she was strong and courageous, yet deceitful and problematic. Lady Macbeth endangered Macbeth’s life because had it not been for her influence and motivation, Macbeth would not have been so thirsty for the crown as well the overthrowing of those who currently held it. Lady Macbeth is Macbeth’s soulmate as well as other half, and in doing so she controlled him and his brain, convincing him to do the most wicked acts. If it wasn’t for her, who knows what fate would have brought to Macbeth and his legacy.