... do is check it. Next, is cramer's rule. Cramer's rule is a 3rd way to solve a system of 2 linear equations by using determinants. The determint is A* D - B * C = AD * BC. The determint of X is E * D - B * F. The determint of Y is A * F - E * C. And to find the answer you divide DET X/ DET, and DET Y/ DETI guess systems of equations would come into play when, well I don't think this system would help with real world stuff ... . Maybe engineers. But thats the only real world way I think these systems would come into play. The method I like the most is cramer's rule cause it's the easiest. ...

• Word Count: 495
• Approx Pages: 2
• Grade Level: High School

... unknowns, or variable, then finding an equation in which it appears. Elimination works nicely when you have coefficients that are integers and three or less system of equations and unknowns, but as the number of equations and unknowns increases, and fractions come into play, Elimination can be cumbersome and the margin for error widen. You will see in contrast to other methods, that when ... n unknowns. Alot of multiplication and division are done mixed in with addition making it more difficult. If the values in the system are not relatively close, the system will be open to errors. Exp...

• Word Count: 653
• Approx Pages: 3
• Grade Level: High School

... , process text, generate and manipulate images and sounds, fly air and space craft, and so on. (Ceruzzi 1)." However, early electronic computers were designed basically to solve equations. The scope of how far computers would reach into our everyday lives was something that was only dreamed about in early science fiction novels. Our textbook defines an operating system as "a program ... also adapted, to a limited extent for scientific applications as early as the 1930s. And some privileged scientists had access to one of the few models of the electrically driven differential analyzer, a...

• Word Count: 2223
• Approx Pages: 9
• Has Bibliography

... his colleagues. He instead believed that there must be a more basic explanation for how the planets moved. He proposed, that instead of many systems of circles, the planets moved in an elliptical fashion. This was Kepler's first law. This allowed for many of the complications caused by the circular system to go away, and involved a much simpler system, which matched relatively well with actual ... things that are not as solidly based, as we would think they might be. Einstein came up with theories, which could be quantifiably proved, and they were. These ideas and equations were part of...

• Word Count: 3486
• Approx Pages: 14
• Has Bibliography

... if the mass is dark, then it's a good guess that there's a black hole there. There are two kinds of systems in which astronomers have found such compact, massive, dark objects: the centers of galaxies (including perhaps our own Milky Way Galaxy), and X-ray-emitting binary systems in our own Galaxy (internet 1). According to a recent review by two prominent astronomists Kormendy and Richstone, eight galaxies ... have supermassive black holes at the center (internet 1). Taken together, these arguments strongly suggest that the cores of these galaxies contain black holes, but these theorie...

• Word Count: 3066
• Approx Pages: 12
• Has Bibliography

... and mathematics. Machines are very good at performing repeated without mistakes while mathematics especially the production of mathematics tables often required a series of repeated steps. Babbage's first attempt at solving this problem was made in 1822 when he made a machine to calculate differential equations called a Difference Engine. Powered by steam and as large as a locomotive the machine could store ... (1890 - 1974) who developed a calculator for solving differential equation in 1931. The machine could solve complex differential equations but it was cumbersome due to its hundred...

• Word Count: 2409
• Approx Pages: 10
• Grade Level: High School

... between machines and mathematics: machines were best at performing tasks repeatedly without mistake, while mathematics often required a repetition of steps. The problem was applying the ability of machines to the needs of mathematics. Babbage's first attempt was in 1822 when he proposed a machine to perform differential equations, called a Difference Engine. It was powered by steam and large as a locomotive. The machine would have ... as Burroughs, Control Data, Honeywell, IBM, Sperry-Rand, and others. They contained all the components we associate with the modern day computer: printers,...

• Word Count: 2243
• Approx Pages: 9
• Grade Level: Undergraduate

... machine were meant to work with each other. He saw that many mathematical problems had to be solved through a "simple repetition of steps" (Computers: History n.p.) Babbage invented his first calculating machine that solved differential equations and dubbed it the "differential machine." All of his work would not have been possible if it hadn"t have been for one woman. Augusta Ada King, Countess ... n.p.). Another invention revolutionized the way we see computers today, only this time the invention was a software program. Operating systems allowed the user to run multiple programs at one...

• Word Count: 1519
• Approx Pages: 6
• Grade Level: High School

... determine software and hardware needs, design or update software using scientific analysis, and mathematical equations. Working conditions are very bearable because work is always indoors but you do have to sit for land periods of time. Hours are up to 40 hours per week but I would have to ... school diploma and at least have a bachelors degree. The time needed to get up to that starts with an internship which is usually part of a four-year degree program. some necessary skills that are needed are able to express ideas clearly when speaking or writing. Identify problems and ... the sign...

• Word Count: 863
• Approx Pages: 3
• Grade Level: Undergraduate

... the relationship between rectangular hyperbola and the logarithm. He also defined a curve, a "logarithmic" curve, but we call it the exponential curve, the equation is y=ka^x. Huygens also calculated the base of e to 17 decimal places, but e still remains undiscovered. e was finally discovered in 1683 when Jacob Bernoulli was doing a study on compound interest. He looked at the problem, examined continuous compound ... calculated e to 346 places. Although not exactly discovered in the 1600's, e made its mark throughout history. e is very helpful in daily life of banking. e can be used to ...

• Word Count: 711
• Approx Pages: 3
• Has Bibliography
• Grade Level: High School

... named Charles Babbage, who was a professor at Cambride, England. He's considered the father of all computers because of his two inventions. His first invention was the Difference Endine. Concieved in 1812, it solved polynomial equations. After working on this invention for 10 years, he finally lost interest in it because ... it has the following: An input device, output device, control unit, processor, and storage. Many years have gone by since then, and the evolution of computers has changed dramatically giving us now what we have, PC's (Personal Computers). This brings me to the comp...

• Word Count: 1291
• Approx Pages: 5
• Grade Level: High School

... Manual" Dartmouth College. pp. 95-8. Macroscale and Microscale Organic Experiments, 4th ed. By K.L. Williamson. pp. 606-8 Theory: The product of the reaction is an aromatic compound which exhibits the thermodynamic and kinetic stability expected for the delocalized pi electron systems. Like other aromatic compounds ferrocene will undergo substitution reactions in preference to addition reactions. The aromicity ... of ferrocene is formed when the 6 outer shell electrons of the ferrous ion combine with the 12 pi electrons of the two cyclopentadiene anion. This combination satisfies Huckel...

• Word Count: 793
• Approx Pages: 3
• Grade Level: High School

... best laid out on a white board with great attention given to understanding the concepts behind forces observed in nature. At the heart of these ideas are equations that must be written out and derived to be completely understood. While this could be done online, greater comprehension will come from seeing ... make them easier to understand, however, when an idea is non-complex to begin with, it just adds to the process. With the drawbacks of inoperation we can postulate what would happen to a class that relied heavily on computers and was suddenly hit with a damaging virus. Such an ... ...

• Word Count: 800
• Approx Pages: 3
• Grade Level: High School

... contention. After searching for a suitable definition, one from Encarta was found. The definition is as follows: "Mathematics, a way of describing relationships between numbers and other measurable quantities. Mathematics can express simple equations as well as interactions among the smallest particles and the farthest objects in the known universe. Mathematics allows scientists to communicate ideas using ... universally accepted terminology. It is truly the language of science." This definition is partially correct. It is true, that mathematics provides a mean to express relationships ...

• Word Count: 642
• Approx Pages: 3
• Grade Level: Undergraduate

... of twists and turns that lead to the answer of a problem that we have all sought in the past. Although the subject creates pain and suffering in all of us, it is considered a core knowledge that we all need to know. We live in a world that is plagued with numbers and systems of equations, from simple prices of ... the apples we buy, to the velocity of cars that we see everyday. It helps us better understand everything we see and feel in life. For many, ... their own pace with their own ideas and curiosity, many mathematicians still argue today about who should deserve the most credit fo...

• Word Count: 719
• Approx Pages: 3
• Grade Level: High School

Meadows or Malls? Portfolio Solving Systems of Equations Systems with two variables: 1. Take a pair of equations and eliminate the same variable from each equation. 2. Do this by multiplying either equation through by a negative number so that when the coefficients are added together, they will cancel each other out. 3. Solve the sum of the equations by dividing answer by remaining coefficient to get ... the value for the remaining variable. 4. Substitute the value into one of the original equations. 5. Solve equation by subtracting constant from both sides and dividing by coefficient for rem...

• Word Count: 853
• Approx Pages: 3
• Grade Level: High School

... to the Matrix and the Matrix Reloaded like equations, axioms, tessellations, and many other ideas on a more toned down level. The Matrix is just one very large set of equations generated by the computers as derived from their own regulated set of equations. Thus one is then suppose to be able ... to get all the other problems from this main set of equations, which serves as the operation system, also known as ... the matrix. This main set of equations is the axioms, which cannot be changed or broken. Any derivation can be changed or broken if the equation systems are changed. The movie...

• Word Count: 337
• Approx Pages: 1
• Grade Level: High School

... numbers to a whole new perspective. In his mathematical dissertation Algebra, he showed that the roots of negative numbers can be utilized. To solve for certain types of equations such as the square root of -7, a new number needed to be invented. This new number would be called i. Furthermore, the square of i is -1. These early mathematicians realized that multiplying positive and negative numbers by i would create a ... be shown as a real number multiplied by i. Real numbers are all positive numbers, negative numbers, and zero. Except for zero, the square of any imaginary number is a n...

• Word Count: 1237
• Approx Pages: 5
• Has Bibliography
• Grade Level: High School

... , for example, the Golden Section or Golden Ratio = ~1.6180, a shape valued in art and architecture because of its pleasing proportions, and has long been observed occurring in natural systems such as the population of Rabbits, shown later on, spiral arrangement of petals, and branches on certain types of flowers and plants. To better understand the link between the Fibonacci numbers and Golden Section, represented by ... weather. It was a great discovery (and shock!) to scientists in the 1970's when they realized that even very simple equations can generate extremely complicated behavio...

• Word Count: 3003
• Approx Pages: 12
• Grade Level: High School

... after the ones in the human brain. Success was minimal at best because of the lack of computer technology needed to calculate such large equations. AI is achieved using a number of different methods. The more popular implementations comprise neural networks, chaos engineering, fuzzy logic, knowledge based systems, and expert systems. Using any one of the aforementioned design structures requires a specialized computer system. For example, Anderson Consulting applies ... a knowledge based system to commercial loan officers using multimedia (Hedburg 121). Their system requires a fast IBM ...

• Word Count: 2810
• Approx Pages: 11
• Has Bibliography
• Grade Level: High School

... Za) (Equation 7) Same is true for component c, L₀V₂ = (Zc - Yc₂) (Xc₀ -Zc) (Equation 8) Figure 2. A diagram showing the graphical addition rule. These two equations relate the composition of the resultant mixture to the compositions and masses of the original two mixtures. By equating Equations 7 and 8 and then manipulating the equation, the equation {(Xc₀ - Zc)/(Xa₀ - Za)} = {(Zc - Yc₂)/(Za - Ya₂)} which proved that α = β The ... (hΣ - hΣ₁). The inverse lever arm rule that can be applied will be the ratio of V₂/Σ = (h₀ - hΣ₁)/(h₀ - H₂). Solvent-free ba...

• Word Count: 1675
• Approx Pages: 7
• Has Bibliography
• Grade Level: High School

... to perform a different function and make it easier. Eventually IBM made a computer that could perform various tasks such as: figure out equations, store data, and draw graphics. From there the computer industry exploded. Now computers have changed many aspects of life. Computers have had a major effect upon business. One area deals with the advertising industry. It has completely re-arranged the ... can come in handy and be a great benefit when the test rolls around. Multimedia programs give people the chance to have a whole set of encyclopedias, almanacs, maps, dictionaries, and other i...

• Word Count: 995
• Approx Pages: 4
• Grade Level: High School

... ) • Peroxyacetyl nitrate (PAN) • Nitric acid (HNO ) • Partially oxidised hydrocarbons Primary and Secondary pollutants produced by motor vehicles Fuels contain compounds of nitrogen (NOx) these are oxidised when the fuel is burnt and make fuel NOx or thermal NOx when burnt under very high temperatures: N + O + heat ... dioxide and oxygen: O + NO O + NO 3 In natural conditions this reaches a steady state so that the rate of production of ozone is equal to the rate of destruction of ozone. However this is disrupted when hydrocarbons are added. The hydrocarbons are broken down into ...

• Word Count: 1852
• Approx Pages: 7
• Grade Level: High School

... UP139Y-28 includes gamma ray (GRBH), caliper (CABH), bulk density (RBFC), sonic (DTBH), neutron (SSCN), and a deep resistivity log (RDDI). The original oil/water contact was also provided. Equations from Asquith (1982), were used to produce logs that are corrected for the presence of shale. The water saturation curve (SW) concluded that the 1985 oil/water contact had indeed moved upwards ... . Equations will be drawn out and explained. To calculate for shale correction, the volume of shale must be determined using the following equation (Asquith, 1982): Where IGR is a gamma ray index calc...

• Word Count: 1572
• Approx Pages: 6
• Grade Level: High School

... was: Carbon dioxide (CO2) + Water + light energy à sugar (glucose) + oxygen And this one for respiration: Sugar (glucose) + oxygen à CO2 + water + energy Each of these equations is the reverse of the other, and are fundamentally correct in indicating the interdependence of the two life processes. Photosynthesis and respiration are two very complex and they could only be considered reversible in the broadest ecological sense ... and only the green and yellow are transmitted. The absorbed red and blue light are the most important in photosynthesis. There are other pigments other tha...

• Word Count: 2171
• Approx Pages: 9