...solutions. If you have a graphing calculator, this method is the quickest. If you don't have a calculator, it can be difficult to graph the equation. Completing the square: This is probably the most difficult method. I find it hardest to remember how to apply this method. Since the quadratic formula was derived from this method, I don't think there is a good reason to use completing the square when you have the formula Factoring: this is probably the easiest method for solving an equation with integer solutions. If you can see how to split up the original equation into its factor pair, this is the quickest and allows you to solve the problem in one step. Week 9 capstone part 1 Has the content in this course allowed you to think of math as a useful tool? If so, how? What concepts...
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...This article is about the study of topics, such as quantity and structure. For other uses, see Mathematics (disambiguation). "Math" redirects here. For other uses, see Math (disambiguation). Euclid (holding calipers), Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.[1] Mathematics is the study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change.[4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.[7][8] Mathematicians seek out patterns[9][10] and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary...
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...Diana Garza 1-16-12 Reflection The ideas Stein presents on problem saving and just math in general are that everyone has a different way of saving their own math problems. For explains when you’re doing a math problem you submit all kinds of different numbers into a data or formula till something works or maybe it’s impossible to come up with a solution. For math in general he talks about how math is so big and its due in large measure to the wide variety of situations how it can sit for a long time without being unexamined. Waiting for someone comes along to find a totally unexpected use for it. Just like has work he couldn’t figure it out and someone else found a use for it and now everyone uses it for their banking account. For myself this made me think about how math isn’t always going to have a solution. To any math problem I come across have to come with a clear mind and ready to understand it carefully. If I don’t understand or having hard time taking a small break will help a lot. The guidelines for problem solving will help me a lot to take it step by step instead of trying to do it all at once. Just like the introduction said the impossible takes forever. The things that surprised me are that I didn’t realize how much math can be used in music and how someone who was trying to find something else came to the discovery that he find toe. What may people were trying to find before...
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...Sample Exam 2 - MATH 321 Problem 1. Change the order of integration and evaluate. (a) (b) 2 0 1 0 1 (x y/2 + y)2 dxdy. + y 3 x) dxdy. 1 0 0 x 0 y 1 (x2 y 1/2 Problem 2. (a) Sketch the region for the integral f (x, y, z) dzdydx. (b) Write the integral with the integration order dxdydz. THE FUNCTION f IS NOT GIVEN, SO THAT NO EVALUATION IS REQUIRED. Problem 3. Evaluate e−x −y dxdy, where B consists of points B (x, y) satisfying x2 + y 2 ≤ 1 and y ≤ 0. − Problem 4. (a) Compute the integral of f along the path → if c − f (x, y, z) = x + y + yz and →(t) = (sin t, cos t, t), 0 ≤ t ≤ 2π. c → − → − → − (b) Find the work done by the force F (x, y) = (x2 − y 2 ) i + 2xy j in moving a particle counterclockwise around the square with corners (0, 0), (a, 0), (a, a), (0, a), a > 0. Problem 5. (a) Compute the integral of z 2 over the surface of the unit sphere. → → − − → − → − − F · d S , where F (x, y, z) = (x, y, −y) and S is → (b) Calculate S the cylindrical surface defined by x2 + y 2 = 1, 0 ≤ z ≤ 1, with normal pointing out of the cylinder. → − Problem 6. Let S be an oriented surface and C a closed curve → − bounding S . Verify the equality → − → − → → − − ( × F ) · dS = F ·ds − → → − if F is a gradient field. S C 2 2 1...
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...say whether I was able to learn how to be a better teacher and what the teacher did that I could possibly use in the future. While analyzing and going through the process of this assignment it is helping realize how to become a better teacher as well. I would also like to get more comfortable and experience on using this template of the paper. Memories Of A Teacher My teacher, Mr. G, used many different instructional techniques and approaches to his lessons. Mr. G had taught me math for three years in a row, so I think that I have a good grasp on his approaches to the lessons that he would teach. He would assign many homework assignments, as well as in-class assignments, which helped me and other students understand and get practice with the lesson that we were learning. I think that with math having a lot of homework is a good thing. In my mind, the only way to learn how to do math is plenty of practice. The more you practice, the easier it will be. Mr. G would also have the students do some math problems on the chalk board or smart board to show the class and go over the corrections with the whole class so that everyone would understand the problem. Playing “racing” games also helped and added fun to the class. With the “racing” games, the students would get into groups and have to take...
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...STAT2011 Statistical Models sydney.edu.au/science/maths/stat2011 Semester 1, 2014 Computer Exercise Weeks 1 Due by the end of your week 2 session Last compiled: March 11, 2014 Username: mac 1. Below appears the code to generate a single sample of size 4000 from the population {1, 2, 3, 4, 5, 6}. form it into a 1000-by-4 matrix and then find the minimum of each row: > rolls1 table(rolls1) rolls1 1 2 3 4 5 6 703 625 679 662 672 659 2. Next we form this 4000-long vector into a 1000-by-4 matrix: > four.rolls=matrix(rolls1,ncol=4,nrow=1000) 3. Next we find the minimum of each row: > min.roll=apply(four.rolls,1,min) 4. Finally we count how many times the minimum of the 4 rolls was a 1: > sum(min.roll==1) [1] 549 5. (a) First simulate 48,000 rolls: > rolls2=sample(x=c(1,2,3,4,5,6),size=48000,replace=TRUE) > table(rolls2) rolls2 1 2 3 4 5 6 8166 8027 8068 7868 7912 7959 (b) Next we form this into a 2-column matrix (thus with 24,000 rows): > two.rolls=matrix(rolls2,nrow=24000,ncol=2) (c) Here we compute the sum of each (2-roll) row: > sum.rolls=apply(two.rolls,1,sum) > table(sum.rolls) sum.rolls 2 3 4 5 6 7 8 9 10 11 742 1339 2006 2570 3409 4013 3423 2651 1913 1291 1 12 643 Note table() gives us the frequency table for the 24,000 row sums. (d) Next we form the vector of sums into a 24-row matrix (thus with 1,000 columns): > twodozen=matrix(sum.rolls,nrow=24,ncol=1000,byrow=TRUE) (e) To find the 1,000 column minima use > min.pair=apply(twodozen,2,min) (f) Finally compute the...
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...Jasmine Petersen Dr. Abdeljabbar MAT 1111 April 23, 2014 Algebra is one of the most important subjects someone can learn. It is a subject that transfers into daily life. A lot of people do not realize that they are using algebra. Algebra can be anything from calculating the amount of money you’ve spent on your grocery shopping, designing structural plans for a building, and keeping track of the calories you have in your diet. Our professor told us that in every subject, we use math. My major is chemistry and mathematics is used widely in chemistry as well as all other sciences. Mathematical calculations are absolutely necessary to explore important concepts in chemistry. You’ll need to convert things from one unit to another. For example, you need to convert 12 inches to feet. Also, we use simple arithmetic to balance equations. A lot of things I’ve had learned from this course and one of them was that we use Math for everyday life. I’ve also learned many ways how to solve equations such as linear, quadratic, exponential, and logarithmic equations. All the material that we did learn was all easy to learn and understand. I believe that the instructor did a good job explaining on how to solve problems. If my friend was asking me how to determine the differences between the equation of the ellipse and the equation of the hyperbola, I would first give he or she the definition of the two words ellipse and hyperbola. An ellipse is a set of all points in a plane such that the sum...
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...Math is used everyday – adding the cost of the groceries before checkout, totaling up the monthly bills, estimating the distance and time a car ride is to a place a person has not been. The problems worked this week have showed how math works in the real world. This paper will show how two math problems from chapter five real world applications numbers 35 and 37 worked out. Number 35 A person hired a firm to build a CB radio tower. The firm charges $100 for labor for the first 10 feet. After that, the cost of labor for each succeeding 10 feet is $25 more than the preceding 10 feet. That is, the nest 10 feet will cost $125; the next 10 feet will cost $150, etc. How much will it cost to build a 90-foot tower? Solving this problem involves the arithmetic sequence. The arithmetic sequence is a sequence of numbers in which each succeeding term differs from the preceding term by the same amount (Bluman, 2011). n = number of terms altogether n = 9 d = the common differences d = 25 ª1 = first term ª1 = 100 ªn = last term ª2 = ª9 The formula used to solve this problem came from the book page 222. ªn = ª1 + (n -1)d ª9 = 100 + (9-1)25 ª9 = 100 + (8)25 ...
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...A | Course Title & Number | Calculus II: MTH104 | B | Pre/Co-requisite(s) | Pre-requisite: MTH103 (Calculus I) | C | Number of credits | 3 | D | Faculty Name | Dr. Ghada Alobaidi | E | Term/ Year | Fall 2014 | F | Sections | Course | Days | Time | Location | MTH104.02 MTH104.04MTH104.06 | UTR UTRMW | 9:00-9:50 10:00-10:50 8:00-9:15 | PHY 113NAB 007NAB010 | | | | | | G | Instructor Information | Instructor | Office | Telephone | Email | Ghada Alobaidi | NAB 249 | 06 515 2754 | galobaidi@aus.edu | Office Hours: UT: 11:00 – 12:30 , R: 11:00 – 12:00 or by appointment. | H | Course Description from Catalog | Covers techniques of integration, improper integrals, sequences, infinite series, power series, parameterized curves, polar coordinates, integration in polar coordinates and complex numbers. | I | Course Learning Outcomes | Upon completion of the course, students will be able to: * Read, analyze, and apply to problems, written material related to the study of calculus. * Use the appropriate technique(s) – including integration by parts, trigonometric substitutions, partial fractions, etc. to integrate algebraic, logarithmic, exponential, trigonometric, and composite functions. * Evaluate improper integrals and test them for convergence. * Compute arc length and surface area of revolution of graphs and parametric curves. * Graph polar curves and find enclosed area and arc length. * Apply theorems about limits of...
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...you come to geometry, your opinion may vary. This class introduces a lot of new topics, which can be challenging, and take lots of practice outside of school if you do not pay attention or do your math homework. I strongly advise you to do your math homework everyday, not for just a grade, but it also helps you when it comes time for quizzes and tests. She rarely checks homework, but when she does, she will not tell you. It is also a great review for tests and quizzes. Ms.Hull’s tests and quizzes are not the easiest things you will take. The quizzes take new concepts and apply to the quiz. Also, her tests are usually always hard. It is a good idea to practice new concepts and review old ones from previous units, so you can get a good grade on the tests. I also advise you to be organized throughout the year. Organization is the key to success especially in math class. Tool kits are an extremely helpful resource to use. There are going to be a lot of conjectures and theorems that will be new, and it would be hard to just memorize them. My overall geometry year was not exactly the way I hoped it would turn out. It was extremely had, and it moves at a very quick pace, so keeping up was hard for me personally. If I could have done something differently, it would have been practicing math more often. Each concept was hard, and I did not have anytime to review it, because I have a lot of honors classes which require a lot of work too. The key to being successful in this course...
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...|7|SURVEY OF MATHEMATICS FALL 2015 | |8| | |8| | |8| | |8| | | | | | |Instructor | | |Gary F. Melendy | | | | | |Title | | |Instructor ...
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...Math 1P05 Assignment #1 Due: September 26 Questions 3, 4, 6, 7, 11 and 12 require some Maple work. 1. Solve the following inequalities: a) b) c) 2. Appendix D #72 3. Consider the functions and . a) Use a Maple graph to estimate the largest value of at which the graphs intersect. Hand in a graph that clearly shows this intersection. b) Use Maple to help you find all solutions of the equation. 4. Consider the function. a) Find the domain of. b) Find and its domain. What is the range of? c) To check your result in b), plot and the line on the same set of axes. (Hint: To get a nice graph, choose a plotting range for bothand.) Be sure to label each curve. 5. Section 1.6 #62 6. Section 2.1 #4. In d), use Maple to plot the curve and the tangent line. Draw the secant lines by hand on your Maple graph. 7. Section 2.2 #24. Use Maple to plot the function. 8. Section 2.2 #36 9. Section 2.3 #14 10. Section 2.3 #26 11. Section 2.3 #34 12. Section 2.3 #36 Recommended Problems Appendix A all odd-numbered exercises 1-37, 47-55 Appendix B all odd-numbered exercises 21-35 Appendix D all odd-numbered exercises 23-33, 65-71 Section 1.5 #19, 21 Section 1.6 all odd-numbered exercises 15-25, 35-41, 51, 53 Section 2.1 #3, 5, 7 Section 2.2 all odd-numbered exercises 5-9, 15-25, 29-37 Section 2.3 all odd-numbered exercises...
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...find the national average cost of food for an individual, as well as for a family of 4 for a given month. http://www.cnpp.usda.gov/sites/default/files/usda_food_plans_cost_of_food/CostofFoodJan2012.pdf 5. Find a website for your local city government. http://www.usa.gov/Agencies/Local.shtml 6. Find the website for your favorite sports team (state what that team is as well by the link). http://blackhawks.nhl.com/ (Chicago Blackhawks) 7. Many of us do not realize how often we use math in our daily lives. Many of us believe that math is learned in classes, and often forgotten, as we do not practice it in the real world. Truth is, we actually use math every day, all of the time. Math is used everywhere, in each of our lives. Math does not always need to be thought of as rocket science. Math is such a large part of our lives, we do not even notice we are computing problems in our lives! For example, if one were interested in baking, one must understand that math is involved. One may ask, “How is math involved with cooking?” Fractions are needed to bake an item. A real world problem for baking could be as such: Heena is baking a cake that requires two and one-half cups of flour. Heena poured four and one-sixth cups of flour into a bowl. How much flour should Heena take out of the bowl? In this scenario of a real world problem, we have fractions, and subtraction of fractions, since Heena has added four and one-sixth cups of flour, rather than the needed...
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... h(x)= 7-x/3 First we need to compute (f-h)(4) (f*h)(4)=f(4)-h(4), each function can be done separately f(4)=2(4)+5 f(4)=8+5 f(4)=13 H h(4)=(7-4)/3 same process as above h(4)=3/3=h(4)=1 (f-h)(4)=13-1 (f-h)(4)=12 this is the solution after substituting and subtracting The next part we need to replace the x in the f function with the g (f*g)(x)=f(g(x)) (f*g)(x)=f(x2-3) (f*g)(x)=2x2-1 is the result Now we need to do the h function (h*g)(x)=h(g(x)) (h*g)(x)=h(x2-3) (h*g)(x)=7-(x2-3) (h*g)(x)=10-x2 end result The inverse function-- f-1(x)=x-5h-1(x)=-(3-7) By doing problems this way it can save a person and a business a lot of time. A lot of people think they don't need math everyday throughout their life, but in all reality people use math almost everyday in life. The more you know the better off your life will...
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...Math was always the class that could never quite keep my attention in school. I was a daydreamer and a poor student and applying myself to it was pretty much out of the question. When I would pay some attention I would still forget the steps it had taken me to find the solution. So, when the next time came around I was lost. This probably came about because as a kid I wasn’t real fond of structure. I was more into abstract thought and didn’t think that life required much more than that at the time. I was not interested in things I had to write down and figure out step by step on a piece of paper. I figured I could be Tom Sawyer until about the age of seventy two. My thoughts didn’t need a rhyme or reason and didn’t need laws to keep them within any certain limits. The furthest I ever made it in school was Algebra II and I barely passed that. The reason wasn’t that I couldn’t understand math. It was more that I didn’t apply myself to the concepts of it, or the practice and study it took to get there. I was always more interested in other concepts. Concepts that were gathered by free thinkers, philosophers, idealists. Now I knew that a lot of those figures I read about tried their hand in the sciences, physics, and mathematics in their day, but I was more interested in their philosophical views on everyday life. It was not until I started reading on the subject of quantum physics and standard physics that I became interested in math. The fact that the laws of standard physics...
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