Submitted By jmqd1995

Words 888

Pages 4

Words 888

Pages 4

SOLUCIO

Soluci´ provisional Examen Setembre 2009-10 o 1. (a) Trobeu l’equaci´ d’una circumfer`ncia que passi pels punts (0, 2), (2, 0) i (4, 2). o e

(b) Trobeu el valors de k que fan que aquesta equaci´ sigui d’una circumfer`ncia, i en aquest o e cas indiqueu-ne el centre i el radi: x2 − 2kx + y 2 − 4y = −20

´

SOLUCIO

(a) (x − 2)2 + (y − 2)2 = 4.

(b) k > 4 o k < −4; centre (k, 2), radi

√

−16 + k 2 .

2. Digueu a quines funcions corresponen les seg¨ents gr`ﬁques, sabent que una s’obt´ a partir u a e d’una exponencial de la forma Aax i l’altra ´s un polinomi. Cal donar l’expressi´ de cada e o funci´ en la forma f (x) = ... o 3

2

1

-5

-4

-3

-2

-1

0

1

2

3

4

5

-1

-2

-3

´

SOLUCIO

3x

1

2 ∗ 2 i 2 (x − 2)(x − 3)(x + 1).

3. La capacitat de producci´ el`ctrica d’una central va ser l’any 2000 de 1000 unitats, o e

(a) Quant tardar` la producci´ a ser igual a 2000 unitats, si la producci´ augmenta un 3% a o o anual?

(b) Si la producci´ augment´s en 50 unitats anuals, quant tardar` a ser superior a 2000 o e a unitats? Plantegeu i resoleu aquest apartat usant desigualtats.

´

SOLUCIO

(a) 1000(1.03)t = 2000 → t = 23.44

(b) 1000 + 50t > 2000 → t > 20.

1

1

1−x2

4. Donada la funci´ f (x) = o (a) Calculeu l’aproximaci´ quadr`tica en x = 0. o a

(b) Useu aquesta aproximaci´ per a trobar el valor aproximat de o 100

.

99

´

SOLUCIO

(a) 1 + x2

(b) Si fem

5. (a) Calculeu

100

99

=

1

1−x2

x10 +

obtenim x = 0.1 i per tant

1 x2 + 4ex + 1 +

100

99

√ x3 dx

= 1 + 0.12 ≈ 1.01

(b) Calculeu l’`rea tancada entre la funci´ f (x) = −(x − 2)(x + 2) i l’eix de les x. a o

´

SOLUCIO

(a)

x11

11

+

−1 x + 4ex + x +

(b)

−

2

5

√

x5 + C

2

−2

x2 + 4 dx = −[

x3

32

− 4x]2 =

−2

3

3

6. (a)…...

...Buenaflor 10/25/12 Rationale What I would like to learn from this assignment is to be able to analyze someone and give a correct response about them, whether it may be a positive or negative response. While writing this paper, I think it is a good idea to learn to give honest opinions about the subject and also provide a good amount of detailing to help describe whether this teacher did or did not have a good impression on me. It is very important to 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......

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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 Feynmsn....

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...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 is to pay attention, practice a lot outside of class, and do ALL of your homework. If you do that, I am sure your year will be successful. Good......

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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......

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...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 of their distances from two fixed points is a constant. Each fixed point is called a focus (plural: foci) A hyperbola is the set of all points in a plane for which......

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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...

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...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 investigated in this course can apply to your personal and professional life? In the course, I have learned about polynomials, rational expressions, radical equations, and quadratic equations. Quadratic equations seem to have the most real life applications -- in things such as ticket sales, bike repairs, and modeling. Rational expressions are also important, if I know how long it takes me to clean my sons room, and know how long it takes him to clean his own room. I can use rational expressions to determine how long it will take the two of us working together to clean his room. The Math lab site was useful in some ways, since it allowed me to check my answers to the problems immediately. However, especially in math 117, it was too sensitive to formatting of the equations and answers. I sometimes put an answer into the math lab that I knew was right, but it marked it wrong because of the math lab......

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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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...ability I would say that is “Making decisions”. According to the “The Case for Quantitative Literacy handout”, “making decisions is the ability to use mathematics, make decisions and solve problems in everyday life”. In my everyday life I have to keep the balance in my check book, pay bills, take care of kids, run my house, cook, clean etc. With cooking I am using math, measuring how much food to make for four people (I still haven’t mastered that one). With bills I am using math, how much each company gets, to how much money I have to spare (which these days is not much). In my everyday life I do use some form of a math. It might not be how I was taught, but I have learned to adapt to my surroundings and do math how I know it be used, the basic ways, none of that fancy stuff. For my weakest ability I would say I fall into “Confidence with Mathematics”. Math has never been one of my favorite subjects to learn. It is like my brain knows I have to learn it, but it puts up a wall and doesn’t allow the information to stay in there. The handout “The Case for Quantitative Literacy” states I should be at ease with applying quantitative methods, and comfortable with quantitative ideas. To be honest this class scares the crap out of me, and I am worried I won’t do well in this class. The handout also says confidence is the opposite of “Math Anxiety”, well I can assure you I have plenty of anxiety right now with this class. I have never been a confident person with math, I guess......

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... | | |Location | | |on-line | | | | | |Times | | |on-line, or in Maier Hall , Math Lab, Peninsula College | | | | | |Start Date | | |Sept. 21, 2015 End Date Dec. 9, 2015 | | | | | |Course Credits ...

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...child |500mg adult, 187mg child | |I or R |adult dose 400mg ibuprofen; 7 year old child |1200mg adult,200mg child | |K or P |adult dose 500mg amoxicillin; 9 year old child |100mg adult, 12.5mg child | |M or N |adult dose 1000mg acetaminophen: 6 year old child |600mg adult, 200mg child | |O or L |adult dose 75mg Tamiflu; 11 year old child |1000mg adult, 600mg child | |Q or J |adult dose 400mg ibuprofen; 8 year old child |500mg adult, 250mg child | |S or H |adult dose 500mg amoxicillin; 4 year old child |300mg adult, 100mg child | |U or F |adult dose 1000mg acetaminophen; 3 year old child |75mg adult, 12.5mg child | |W or D |adult dose 75mg Tamiflu; 5 year old child |1200mg adult, 300mg child | |Y or B |adult dose 400mg ibuprofen; 2 year old child |400mg adult, 50mg child | • Explain what the variables in the formula represent and show all steps in the computations. • Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the......

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...How I use Math in everyday Life DeVry University Math-032 October 9, 2012 How I use Math in Everyday Life Math is everywhere you go. It is at the store when you go groceries shopping, when you go out for dinner, when you’re at work, and even when you’re asleep. We are always using some kind of fraction throughout the day. I deal with numbers just about everywhere I go. Math has always been on my vocabulary since I was young. Coming from a house of five, I deal with math every single day. I have to use math for my bills, the rent, groceries, gas, things that are important in the house. Now that I completed eleven and half years in the united Stated Marine Corps, I deal with a tremendous budget in my house. I know that things are not the same because I don’t have a steady income coming in I have to keep track of our expenses and cut back on a lot of unimportant expenses. No matter what we do whether it’s at work, home, or out in town, numbers will always be a factor. Math will be involved and that’s the good think about life. Most people need a solid understanding for financial success and math is the answer. (Huebsch, 2009) In life, you will always have that percent that only need to learn numbers to a certain point. We engage numbers at a very young age. No one really knows how long numbers have been around for. Most people understand the concept of numbers, equations, and the use of daily concepts. (Melayu, 2009) I could say that Im that percentage in......

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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......

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...(P h i li p p i n e Ele m e n ta ry Le a rn i n g Co m p e te n c i e s ) MATHEMATICS MATHEMATICS DESCRIPTION Mathematics in Grades 1 and 2 includes the study of whole numbers, addition and subtraction, basic facts of multiplication and division, basics of geometry, fractions, metric and local measurements, the use of money and their application to practical problems based on real life activities. Grades 3 and 4 deals with the study of whole numbers, the four fundamental operations, fractions and decimals including money, angles, plane figures, measurement and graphs. In Grades 5 and 6 the child is expected to have mastered the four fundamental operations of whole numbers, performs skills in decimals and fractions, conceptualize the meaning of ratio and proportion, percent, integers, simple probability, polygons, spatial figures, measurement and graphs. Simple concepts in Algebra is also introduced to be articulated in the high school. Besides further development of the basic mathematical skills, the child is expected to solve problems related to business and industrial activities in the community. TIME ALLOTMENT Daily Weekly Grade 1 80 400 Grade 2 80 400 Grade 3 80 400 Grade 4 60 300 Grade 5 60 300 Grade 6 60 300 The 20-minute increase in the daily time allotment is given to ensure that all lessons are finished and there will be more activities that involve grouping practical investigations and problem solving. Pupils learn more if they have hands on or......

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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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