Sample size calculations are needed to determine how many subjects should be enrolled in the clinical study. The statistician starts from a list of assumptions such as the required levels of the type-I and type-II errors, the study design, and the size of the treatment effect with some estimate of its variability. It is not just a calculation, but rather an in-depth team discussion about these assumptions. Especially the assumed treatment effect requires team input. Typically the statistician will perform a whole series of calculations, including what-if scenarios to find out how sensitive the calculations are to the assumptions made.
Sample size calculations are not an exact science. Formulae and computerized systems are used for the calculations, but always there are uncertainties and strong assumptions. It is in these circumstances that the statistician will present more than just sets of numbers, but will trigger the necessary discussions to find out how realistic the assumptions actually are. This is crucial. It unfortunately happens that a clinical study turn out inconclusive simply because of unrealistic assumptions.
The Emtex statistician has over 25 years of experience in sample size discussions.


Regularized Harmonic Surface Deformation
Kozlov, Y. and Martinez Esturo, J. and Seidel, H.-P. and Weinkauf, T.
Harmonic surface deformation is a well-known geometric modeling method that creates plausible deformations in an interactive manner. However, this method is susceptible to artifacts, in particular close to the deformation handles. These artifacts often correlate with strong gradients of the deformation energy.In this work, we propose a novel formulation of harmonic surface deformation, which incorporates a regularization of the deformation energy. To do so, we build on and extend a recently introduced generic linear regularization approach. It can be expressed as a change of norm for the linear optimization problem, i.e., the regularization is baked into the optimization. This minimizes the implementation complexity and has only a small impact on runtime. Our results show that a moderate use of regularization suppresses many deformation artifacts common to the well-known harmonic surface deformation method, without introducing new artifacts.


|ISBN-10 / ISBN-13||0486248232 / 9780486248233|
|Publisher||Dover Books (on 1985)|
|Number Of Pages||672|
|User Ratings||4.3 out of 5 stars (15 votes)|
|This book has been found by 1867 other users. Do you have this book? Trade it in for cash!|
|This textbook is primarily used in: (150 total votes)|
|High school courses||43.33% (65 votes)|
|Associates programs||28.67% (43 votes)|
|Bachelors programs||18% (27 votes)|
|Masters programs||2.67% (4 votes)|
|Doctoral programs||2.67% (4 votes)|
|Vocational programs||4.67% (7 votes)|
Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen.
Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.
In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.
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From the formula, in a 메리트카지노 position to} see the standard deviation is proportional to the square root of the number of rounds performed, while the expected loss is proportional to the number of rounds performed. As the number of rounds will increase, the expected loss will increase at a much faster rate. This is why it's unimaginable for a gambler to win in lengthy term|the long run}. It is the excessive ratio of short-term standard deviation to expected loss that fools gamblers into considering that they'll win. The calculation of the roulette home edge is a trivial exercise; for different video games, this isn't usually the case. Combinatorial analysis and/or laptop simulation is important to complete the duty.


The middle school my daughters attend started a new math program based on their poor performance for the third year on the standardized testing required by NO CHILD LEFT BEHIND, which should really be called EVERY CHILD LOSES BRAIN CELLS and PARENTS DON’T UNDERSTAND WHY THEY LEARNED THE OLD FASHIONED WAY AND CAME OUT FINE.
One of my daughters asked for help on her homework and I soon found out it wasn’t because it was difficult.
There were five problems similar to this one:
1. Chayton buys Northern Spy apples for his mother’s pie. He buys 3.2 pounds at $1.10 a pound. What is his bill?
Okay, 6th grade. I get this. But then:
6. Why does it make sense to use multiplication to solve these problems?
We debated this for a while. Because that’s how you get the answer? Because it works? What deep meaningful answer are they looking for?
I thought that question was hard until I read the next one:
7. When one factor in a multiplication problem is greater then 1, is the product greater or less than the other factor? Explain.
I don’t even know how to answer the question without using the beginning to answer the end. The product is greater than the other factor because it’s multiplied by a factor greater than one? I tried to get her to use one of my other answers:
- Emily’s Butt
- Because this math is making me stupider
- Because my mother says so
And the final straw came with the last question on the page:
8. When one factor is less than 1, is the product greater or less than the other factor? Why?
At this point she accidentally attached her bracelet to her three-hole binder while closing it, told me “lesser than” was not correct English, erased and fixed her numbering errors because she apparently can’t count to 2, and we both felt much stupider for even attempting to do 6th grade math.


Quantum Mechanics and Quantum Computation
Institution: Berkeley (Coursera)
Date: July 20, 2012 - September 18, 2012
Bio: With an eye towards Quantum Computation, this course introduces students to the basics of quantum mechanics and eventually explores quantum theory, quantum gates, and various quantum algorithms; with a strong emphasis on mathematics and solving complex equations.
Accomplishments: I completed this course with a grade of 91%. It was an extremely challenging course both conceptually and mathematically, but a very interesting topic. The course has since moved from Coursera to edX.


In the following, you may listen to the beautiful music of ancient Iran (Kurdish music). The name of this great vocal piece is “Hay Gerdûn”.
The Iranian female vocalist is Maryam Shahbazi, a student of a famous Iranian female singer, Afsaneh Rasaei.
The conductor of Sahargahan ensemble is the Iranian Kurdish tanbour player, Heydar Kaki, a student of master tanbour player, Ali Akbar Moradi.
American tourist, Monica, has had fun in Iran, ISNA reported:
Her blog has some interesting posts about Iran:
Neil Epstein and Jay Shapiro continue their study on the content function and the five types of algebras with respect to this function, i.e. content algebra, weak content algebra, semicontent algebra, Gaussian algebra and finally Ohm-Rush algebra. Refer to http://arxiv.org/abs/1405.3000
My PhD Thesis that I wrote under the supervision of Prof. Winfried Bruns was on content algebras (cf. http://www.nasehpour.com/peyman/id129.html) and one of the concepts that I introduced in my thesis was Gaussian algebra. I re-introduced the concept of Gaussian algebra in my recent paper that was about Badawi-Anderson conjecture: http://arxiv.org/abs/1401.0459
The very great master of Persian tar, setar and kamancheh and radif repertoire and a pioneer in Persian music passes away on May, 2nd, 2014 after suffering of cancer for a while.
The news in Persian: http://www.mehrnews.com/detail/News/2283055
Photo resource: http://en.wikipedia.org/wiki/Mohammad-Reza_Lotfi
Danish mathematician and professor of commutative algebra in University of Copenhagen, Professor Hans-Bjørn Foxby, passed away on 09 April 2014. According to the Mathematics Genealogy Project, he was a student of Christian Ulrik Jensen and he supervised PhD thesis of some mathematicians such as Dmitri Apassov, Lars Winther Christensen, Anders Juel Frankild, Esben Bistrup Halvorsen, Henrik Holm, Peter Jørgensen and Siamak Yassemi.
Professor Siamak Yassemi was supervisor of my MSc thesis in 1999 and he invited me to be a local organizer for the workshop on “homological methods in commutative algebra” at IPM in 2002. In this workshop a couple of important pioneers of commutative algebra attended and one of them was the late Professor Hans-Bjørn Foxby who was actually one of the main organizers of this workshop.
I convey my sincerest condolences to his family, friends and commutative algebra community.


Welcome to Math
In this course, you will be introduced to basic algebraic operations and concepts, as well as the structure and use of algebra. Topics include linear inequalities and graphing, exponents, polynomials, and rational expressions. You will study basic algebraic operations and concepts, as well as the structure and use of algebra. This includes solving algebraic equations, factoring algebraic expressions, working with rational expressions, and graphing linear equations. You will apply these skills to solve real-world problems (word problems). Each unit will have its own application problems, depending on the concepts you have been exposed to. This course is also intended to provide you with a strong foundation for intermediate algebra and beyond. It will begin with a review of some math concepts formed in pre-algebra, such as ordering operations and simplifying simple algebraic expressions, to get your feet wet. You will then build on these concepts by learning more about functions, graphing of functions, evaluation of functions, and factorization. You will spend time on the rules of exponents and their applications in distribution of multiplication over addition/subtraction.
If you invest in financial markets, you may want to predict the price of a stock in six months from now on the basis of company performance measures and other economic factors. As a college student, you may be interested in knowing the dependence of the mean starting salary of a college graduate, based on your GPA. These are just some examples that highlight how statistics are used in our modern society. To figure out the desired information for each example, you need data to analyze.
The purpose of this course is to introduce you to the subject of statistics as a science of data. There is data abound in this information age; how to extract useful knowledge and gain a sound understanding in complex data sets has been more of a challenge. In this course, we will focus on the fundamentals of statistics, which may be broadly described as the techniques to collect, clarify, summarize, organize, analyze, and interpret numerical information.
This course will begin with a brief overview of the discipline of statistics and will then quickly focus on descriptive statistics, introducing graphical methods of describing data. You will learn about combinatorial probability and random distributions, the latter of which serves as the foundation for statistical inference. On the side of inference, we will focus on both estimation and hypothesis testing issues. We will also examine the techniques to study the relationship between two or more variables; this is known as regression.
By the end of this course, you should gain a sound understanding about what statistics represent, how to use statistics to organize and display data, and how to draw valid inferences based on data by using appropriate statistical tools.
In geometry, you will explore the objects that make up our universe. Most people never give a second thought to how things are constructed, but there are geometric rules at play. Most people never think twice about a rocket launch, but if that rocket is not launched at an exact angle, it will miss its target. A football field has to be measured out to be a rectangle; if you used another shape, such as a trapezoid, that would give an unfair advantage to one team, because that one team would have more space to work with.
In this course, you will study the relationships between lines and angles. Have you ever looked at a street map? Believe it or not, there is a lot of geometry on a map, as you will see from this course. You will learn to calculate how much space an object covers, which is useful if you ever have to, say, buy some paint. You will learn to determine how much space is inside of a three-dimensional object, which is useful for those times you are trying to fit four suitcases, three kids, two adults, and a dog into the back of your vehicle.


Valid question. Let’s take a look at an example question from the exam:
Second grade teacher is planning a lesson on the addition of whole numbers based on the concept of place value. Which of the following best helps the teacher to assess prior to the lesson?
A. Students ability to write number names in numerals.
B. Students ability to count on a number line.
C. Students ability to compose numbers to make ten
D. Students ability to count by grouping in groups of ten.
Fortunately for us, this exam is multiple choice, giving us a 25% chance of getting the question right. Good for us, haha.
Let’s break down the question. I want to take at least three key words from the question itself. I see “planning”, “addition of whole numbers”, “place value”, and “assess prior”.
Now let’s break down the answers. All start with “Students ability”. “Count” is what stands out to me for B and D, because we are talking about “addition of whole numbers”. “Number line” is only used for real numbers, not exactly whole numbers.
D seems like it would be the best answer, because we are specifically looking to help with place values.
I know this question might take sometime, but you may recall it later on during the test. My best advice is to skip over the questions that might take you more time, and come back to them when you have answered the other questions you know right off the bat.
I truly hope this helps you pass your exam. If you are looking for more questions to practice with from the actual exam, please take a look at our Math Only Insider Study Guide.
Best wishes and good luck!


How do you know when to connect the dots on a graph?
If you are trying to decide the slope of a line between the two issues, then connecting them to display a line is smart. If you have Three issues on a graph and you are enthusiastic about the house created via connecting the 3 issues, then it makes sense to connect them.
Why must you now not connect the dots on a graph?
Sometimes we plot points that don’t make a best trend or that haven’t any values in between. This is called discrete information and we don’t connect the dots with a line. They don’t have knowledge in between the issues already given. A continuing graph has a line because there may be knowledge in between the points already given.
What is the dating between the solutions of an equation in two variables and its graph?
The graph of a linear equationAx+By=C A x + B y = C is a line. Every point on the line is a resolution of the equation. Every solution of this equation is a level on this line.
Do you connect the dots in a scatter plot?
Scatter plots are an identical to line graphs in that they begin with mapping quantitative data issues. The difference is that with a scatter plot, the choice is made that the particular person points will have to no longer be connected without delay together with a line but, as a substitute specific a development.
Why are issues attached in a line graph but not in a bar graph?
A line graph differs from a bar graph in that you plot particular person points on the two axes and sign up for neighboring issues up using immediately traces. The continuous line (or strains) implies a trend over time or no less than over some amount that increases sequentially, like distance from a given level.
How do you graph the dating between two variables?
The most beneficial graph for showing the relationship between two quantitative variables is a scatterplot. Many research projects are correlational studies as a result of they investigate the relationships that may exist between variables.


Dr. David W. MacPhee
- Assistant Professor
- Ph.D., Mechanical Engineering, University of California - San Diego and San Diego State University
- M.A.Sc., Mechanical Engineering, University of Ontario Institute of Technology
- B.S. Mathematics and Engineering, Queens University
Dr. David W. MacPhee’s research involves the application of computational methods to solve energy related problems. This includes the design of novel morphing-blade wind turbines and simulation of thermal energy storage processes.
He is also generally interested in optimization, continuum mechanics, fluid-structure interaction and other projects related to wind and solar energy conversion.


News & Updation
VECTOR ANALYSIS OF ELECTROMAGNETIC FIELDS AND WAVES USING, GREEN’S THEOREM FOR POISSON’S AND LAPLACE, S EQUATIONS, STOKE’S THEOREM, MAXWELL EQUATION AND LAURENT’S FORCE LAW.
Engr. Dr. C. I. Obinwa*
Vector analysis, having been acquainted with gradient of scalar fields, divergence of vector fields, curl of vector fields, line integral, surface integral and volume integral of vector fields with applications of Gauss? theorem, here , the work emphasizes on Green?s theoremwith different approach to Gauss divergence theorem, where for instance, if , then integral around a closed path is zero, meaning, the work done is zero and the force field is conservative. Application of Green theorem on Poisson?s equation, where scalar point function vanishes outside a finite region. It also shows that, for Laplace equation where, , which is a scalar point function for every point of the region,is said to be HARMONIC in that region. Maxwell?s equation is fully analysed. Stoke?s theorem and its tangential line integral of vector field over any closed surface over any closed surface S bounded by a curve and which is equivalent to normal surface integral of curl of the vector field over the surface. Also Laurent?s force law analyses force field through concentric circles.[Full Text Article]


Live Classes Starting from 15 May 2023
Welcome to our live workshop on “Calculus Unleashed: Discovering Differential Calculus with OpenAI GPT and GeoGebra“. This workshop is designed to provide an interactive and engaging learning experience to students of all levels, from high school to university.
During this 15-week workshop, we will explore the fundamentals of Differential Calculus, starting from the basics and gradually building up to more advanced topics. We will use a combination of OpenAI’s state-of-the-art language model, GPT, and GeoGebra’s powerful visualization software to provide a hands-on, experimental approach to learning Calculus.
Our experienced instructors will guide you through each lesson, providing detailed explanations, interactive simulations, and engaging learning games to help you master the concepts of Differential Calculus. You will also receive four electronic books on Calculus by Ashraf Iqbal, which include thousands of GeoGebra simulations and learning games.
Whether you are new to Calculus or seeking to deepen your understanding of the subject, this workshop is an opportunity to learn in a supportive, collaborative environment with like-minded individuals.
We offer special discounts for group registrations, and special seats are available for those who cannot afford the full fee. Don’t miss this once-in-a-lifetime opportunity to discover the beauty and power of Differential Calculus with OpenAI GPT and GeoGebra. Register today and unlock your potential!
Important Course Registration Note:
- 20,000 per month only.
- One-time payment of Rs 20,000 will be valid for 1 month only and you have to resubscribe after 1 month.
- Duration 3 months (48-72 hours).
- 2 live workshops per week (2-3 hour each)
- Starting from 1 May 2023
- 20,000 per month for regular student.
- 10,000 per month
- 5,000 per month
- 3,000 per month.
- FREE for FATA and Gilgit Baltistan or Balochistan students.
To avail Scholarships:
For Scholarship issues email: email@example.com
Deep Understanding: The workshop will help students develop a deep understanding of the fundamental concepts of differential calculus, which will lay a strong foundation for their future studies in STEM fields.
Interactive Learning: The workshop is designed to be highly interactive and adaptive, allowing students to engage with the material through a variety of activities and simulations. This type of learning is much more engaging and effective than passive learning methods like reading or watching videos.
Access to Resources: Students who participate in the workshop will have access to a wealth of resources, including electronic books, GeoGebra simulations, and learning games. These resources are designed to reinforce the concepts learned in the workshop and help students master the material.
Competitive Advantage: Students who develop a strong foundation in differential calculus will have a competitive advantage in their academic and professional pursuits. This workshop provides a unique opportunity for students to gain this advantage in a supportive and collaborative environment.
Fun and Unique Experience: Participating in the workshop is not just about learning calculus, it’s also about having fun and exploring new ways of thinking about math. The workshop is a unique experience that students will remember for years to come.
What Will You Learn?
- A deep understanding of differential calculus and its applications in various fields.
- Mastery of using GeoGebra and OpenAI GPT-3.5 to visualize and explore complex mathematical concepts.
- Enhanced problem-solving skills and critical thinking abilities through hands-on experience with real-world examples and exercises.
- Increased confidence in working with complex mathematical concepts and communicating them to others.
- Ability to apply learned concepts to real-world scenarios and create innovative solutions using calculus.
- Exposure to cutting-edge technology and pedagogical techniques to make learning calculus more engaging and accessible.
- Networking opportunities with like-minded individuals in the field of mathematics education.
- Access to free electronic books, GeoGebra simulations, and learning games on calculus.


Mathematics and Information Engineering (MIEG) is a rigorous and selective programme designed to equip students with solid fundamental knowledge in mathematics, information and computer sciences.
The following shows a graphical presentation of the MIEG programme contents and its outcomes:
Graduates from this programme routinely go for postgraduate studies at the top universities or pursue independent research or careers in various sectors.
MIEG is an interdisciplinary programme jointly offered by the Faculty of Science and the Faculty of Engineering, with the Department of Mathematics and the Department of Information Engineering responsible for its management and actual running. The students of this programme will have an exposure to both mathematical rigour (the math classes are shared with Math majors) and engineering intuition in the information and computer sciences.
Some of Our Graduates
PhD in Communication and Computer Sciences at EPFL
LIU Yinyin Jessica (2022)
MSc in EECS at UC Berkeley
WOO Pui Yang Anna (2022)
PhD in CSE at University of Michigan
HEGAZY, Mahmoud (2022)
PhD in Data & Artificial Intelligence at Institut Polytechnique de Paris
Programme Objectives and Outcomes
Our Programme aims to train our students to have a good understanding of fundamental knowledge and objectives. The following achievements are expected:
- The graduates will have had solid mathematical and engineering knowledge for further studies at the graduate school level or for performing independent research work in engineering, industry, or economic sectors.
- The graduates will have the skills to excel in professional positions in organizations that research, design, develop, deploy, or employ information systems/networks/services.
- The graduates will have acquired the ability to continue their personal development through professional studies and life-long learning, and are already acquainted with the benefits of interdisciplinary learning.
Learning outcomes define the graduate capabilities needed to achieve the programme objectives stated. The following lists the 7 learning outcomes of the programme:
Students will have gained an understanding of the fundamentals of mathematics, science, and engineering and be able to apply them to the research, design, analysis, and implementation of engineering systems.
Students will have gained exposure to and understand the impact of other science and engineering areas as well as non-engineering areas such as social, economic, environmental, health and safety issues.
Students will have possessed sound knowledge in mathematical analysis, linear algebra, communications and networking, and software development.
Students will have possessed the ability to appreciate the value of and develop the ability for lifelong learning.
Students will have developed problem-solving skills and the ability to innovate new engineering solutions.
Students will have gained an understanding of the importance of professional, social, and ethical responsibilities in engineering practice.
- Communication Skills:
Students will have developed the skills to communicate effectively both orally and in writing.


A liter â¦ This page features online conversion from liter to gallon.These units belong to different measurement systems. Switch units Please provide values below to convert gallon (US) [gal (US)] to liter [L, l], or vice versa. There are about 3.785 liters in a U.S. gallon. History/origin: The term gallon most closely originates from "galon" in Old Northern French and developed as a system for measuring wine and beer in England, resulting in measures such as the wine gallon, ale gallon, and imperial gallon. The conversion factor from gallons to liters is 3.7854118, which means that 1 gallon is equal to 3.7854118 liters: 1 gal = 3.7854118 L. To convert 1 gallons into liters we have to multiply 1 by the conversion factor in order to get the volume amount from gallons to liters. Further differentiating the US and the imperial gallon, a US gill is divided into four fluid ounces, while an imperial gallon is divided into five. This tool converts gallons per minute to liters per hour (gal/m to lt/h) and vice versa. Gallons and liters are two common units of volume. However, the United States still uses miles per gallon. Before you can convert to liters, you need to know which gallon measure you are using. The Imperial gallon or UK gallon is equal to approximately 277.42 cubic inches. Gallon to liter calculator is available online for free, at BYJUâS. The US gallon is defined as 231 cubic inches (3.785 liters). 50 gallon to litre = 189.27059 litre ›› However, the American gallon and the British gallon are not the same! U.S. liquid gallon is defined as 231 cubic inches and is equal to 3.785411784 litres or about 0.13368 cubic feet. The gallons to liters website is generously sponsored by the stat holidays directory. Its exact value is defined as 4.54609 liters. 5 gallon to litre = 18.92706 litre. The liter is the metric volume unit, while the gallon is the English unit. 25 gallon to litre = 94.6353 litre. To convert mpg to liters per 100 kilometers (L/100 km), divide 235.214583 by the miles per gallon (mpg) value. The different spelling of the word liter or litre originates from the spelling differences between British and American English. The Gallon to Liter / Gallon to Litre Calculator was written as a simple calculator to enable people to easily convert from gallons to liters. The US fluid gallon is defined as 231 cubic inches (3.785411784 liters), the US dry gallon is defined as 1â8 US bushel (4.4048838 liters) and the imperial gallon is defined as 4.54609 liters. Using the gallons to liter converter is as easy as entering in the number of gallons into the field and then clicking on the calculate button! The decimals value is the … One US gallon is equal to roughly 3.79 liters, or 231 cubic inches. Gal to L quick and simple conversion. Gallon to liter is a US gallons to liters volume converter. It converts units from gallons in liters vice versa with a metric conversion. Quarts are then divided into two pints and pints are divided into two cups. The gallon (gal) is a unit of measuring for measuring liquid capacity. A gallon per minute (us gallon, gal/m) is unit of volume flow rate equal to a gallon flow per minute. Liter ↔ Gallon (us) Conversion in Batch. 1 US gallon = 0.83267384 Imp gallon = 3.78541178 Liters, 1 Imperial gallon = 1.20095042 US gallon = 4.54609188 Liters, 1 Liter = 0.264172052 US gallon = 0.219969157 Imp gallon, Gallons (two different kinds) and liters (with two different spellings) exist so this website can convert themand to cause confusion among people ;-). Most of the world measures fuel economy in liters per 100 kilometers. In British English (used in most Commonweath Countries) it is spelled litre while in American English the word is spelled liter. Note: You can increase or decrease the accuracy of this answer by selecting the number of significant figures required from the options above the result. 1 gallon per minute(US) = 3.785411784 liters per minute. The imperial gallon is 4.54 liters and common in the â¦ This is a very easy to use gallon to liter converter.First of all just type the gallon (gal) value in the text field of the conversion form to start converting gal to L, then select the decimals value and finally hit convert button if auto calculation didn't work.Liter value will be converted automatically as you type.. gallon to liter, 10 liters of milk = 22.72 l b 20 lb of milk = 8.80 liters. 1 US gallon = 0.83267384 Imp gallon = 3.78541178 Liters. It is used in both US customary and British imperial systems of measurements. One imperial gallon is approximately 1.2 US gallons. One Imperial gallon is equal to 4.54609 liters, and it can be divided into four quarts, or into 8 pints.. Hence 1 L = 0.001 cubic m. 1 gallon (gal) = 3.785411784 litres (L) = 231 cubic inches = 4 qt = 128 fl oz. Liters. A cup is comprised of two gills, making one gallon equal four quarts, eight pints, sixteen cups, or thirty-two gills. There are three different sizes of gallons used today. There are about 3.785 liters in a U.S. gallon. The gallon used in the United States is equal to exactly 231 cubic inches or 3.785411784 liters. US Gallons (Liquid) to Liters formula. US Gallon to Liter Conversion Example Task: Convert 75 US gallons to liters (show work) Formula: US gal x 3.785411784 = L Calculations: 75 US gal x 3.785411784 = 283.9058838 L Result: 75 US gal is equal to 283.9058838 L To convert between … Liter: Gallon (us): Note: Fill in one box to get results in the other box by clicking "Calculate" button. 15 liters of milk = 34.08 lb 30 lb of milk = 13.20 liters. Conversion Gallon per minute(US) to Liter per second. The US gallon is defined as 231 cubic inches (3.785 liters). 30 gallon to litre = 113.56235 litre. 1 gallon per minute(US) = 227.12470704 liters per hour. 1 gal (US) = 3.785411784 L, l1 L, l = 0.2641720524 gal (US), Example: convert 15 gal (US) to L, l:15 gal (US) = 15 × 3.785411784 L, l = 56.78117676 L, l. A US fluid ounce is therefore 1/128 of a US gallon while an imperial fluid ounce is 1/160 of an imperial gallon. The US gallon is used in the United States and is equal to exactly 231 cubic inches or 3.785411784 liters. The gallon used in the United States is equal to exactly 231 cubic inches or 3.785411784 liters. We are proud to announce that the Gallons to Liters online conversions website now receives over 100 200 300 450 visitors daily! It converts units from gallons in liters vice versa with a metric conversion. A liter, or litre, is a unit of volume in the metric system.A liter is defined as the volume of a cube that is 10 centimeters on a side. One gallon contains 3.785411784 liters. Conversion base : 1 gallon = 3.785411784 l. Conversion base : 1 l = 0.26417205235815 gallon. Gallons are also widely used in fuel economy expression in the US, as well as some of its territories. This site provides a gallons to liters and liters to gallons conversion calculator and information about these measures of volume. Over time, these have been standardized, but there are still three common options. Common Converters. And the definition of the liter was changed to its previous and current definition due to the discovery that the prototype of the kilogram was slightly larger. 3.785411784 l ~= 3 l 785 ml 2/5 ml. An Imperial gallon is a unit of measurement for volume, mainly for gases or liquid substances. This tool converts gallons per minute to liters per minute (gal/m to lt/m) and vice versa. Liters, US and Imperial Gallons Conversion Table. Please select a more specific option. In contrast, the imperial gallon, which is used in the United Kingdom, Canada, and some Caribbean nations, is defined as 4.54609 liters. 10 gallon to litre = 37.85412 litre. History/origin: There was a point from 1901 to 1964 when a liter was defined as the volume of one kilogram of pure water under the conditions of maximum density at atmospheric pressure. Hence 1 L = 0.001 cubic m. A liter, or litre, is a unit of volume in the metric system.A liter is defined as the volume of a cube that is 10 centimeters on a side. The liter is the metric volume unit, while the gallon is the English unit. It is used in the countries practicing the Imperial system like the UK and its former colonies, some territories of Canada, etc. In contrast, the imperial gallon, which is used in the United Kingdom, Canada, and some Caribbean nations, is defined as 4.54609 liters. Definition: A liter (symbol: L) is a unit of volume that is accepted for use with the International System of Units (SI) but is technically not an SI unit. A liter is defined as one cubic decimetre (1 L = 1 cubic dm). Most other countries use "liters" - the metric unit of measure for volume. To convert a gallon to a liter you have to multiply the gallon value by 3.785411784. The conversion factors for the three standard gallon measurements are as follows: 1 U.K. gallon = 4.5461 liters; 1 U.S. liquid gallon = 3.7854 liters; 1 U.S. dry gallon = 4.4049 liters Gallon to liter is a US gallons to liters volume converter. 1 Imperial gallon = 1.20095042 US gallon = 4.54609188 Liters. Vous êtes en train de convertir des unités de volume de gallon (u.s. liquid) en litre 1 gallon = 3.785411784 l 1 Ounces Per Gallon to common density units; 1 oz/gal = 6.236023291 kilograms per cubic meter (kg/m3) 1 oz/gal = 0.6236023291 centigrams per cubic centimeter (cg/cm3) 1 oz/gal = 623602.3291 centigrams per cubic meter (cg/m3) 1 oz/gal = 0.0006236023291 centigrams per cubic millimeter (cg/mm3) 1 oz/gal = 623.6023291 centigrams per liter … However, due to the mass-volume relationship of water being based on a number of factors that can be cumbersome to control (temperature, pressure, purity, isotopic uniformity), as well as the discovery that the prototype of the kilogram was slightly too large (making the liter equal to 1.000028 dm3 rather than 1 dm3), the definition of the liter was reverted to its previous, and current definition. The imperial gallon is used even more sparingly than the US gallon, with most countries around the world using liters when referencing fuel. Comic Book Collections, 2 Gallon Oil Can, 1 Gallon Oil Can, Sand, Man from U.N.C.L.E. Data should be separated in coma (,), space ( ), tab, or in separated lines. The website started as a hobby site in 2008 - since then it has grown to be a popular one destination for people looking to convert gallons and liters. How to convert miles per gallon (mpg) to liters per 100 kilometers? The British imperial gallon is now defined as exactly 4.54609 litres (277.4194 cubic inches). Is there anything you were looking for but couldn't find? 40 gallon to litre = 151.41647 litre. For example, to convert 24 miles per gallon to liters per 100 kilometers, divide 235.214583 by 24, that makes 24 mpg is 9.8 liters per 100 km. The Imperial gallon or UK gallon is used in the United Kingdom and is equal to approximately 277.42 cubic inches. The user must fill one of … Gallons : The gallon (abbreviation "gal"), is a unit of volume which refers to the United States liquid gallon. The Gallon to Liter / Gallon to Litre Calculator provides the option to select the country as United States of American, United Kingdom and Australia. Converting gallons to liters is easy with the online Gallons to Liters Calculator. Your feedback is always welcome. Then multiply the amount of Miles/gallon(US) you want to convert to Km/liter, use the chart below to guide you. 1 / 8 gallon) and … UnitConverter.net UnitConverter.net V1.2. The US gallon is defined as 231 cubic inches (3.785 liters). 1 Liter = 0.264172052 US gallon = 0.219969157 Imp gallon Son symbole est « gal ». How Many liters in a gallon? The gallon is a good example. 1 Imperial Gallon (UK) = 4.54609188 litres 1 mile = 1.609344 kilometres What is an Imperial Gallon? Conversion Gallon per minute(US) to Liter per hour. Use it to convert gallons and liters for your fish tank, swimming pool, car fuel consumption, water usage and more. This calculator will help you convert from the U.S. system to the global one. There are four quarts in a gallon, the imperial pint is defined as 0.568 261 25 litres (i.e. Definition: A gallon is a unit of volume specifically regarding liquid capacity in both the US customary and imperial systems of measurement. Formule de conversion pour passer d'un gallon en litres : 1 gallon = 3,78541178 litres 1 gallon per minute(US) = 0.0630901964 liters per second. Thank you for your visit and please let us know how we could make this website even better. A liter) is defined as one cubic decimetre (1 L = 1 cubic dm). Note: For a pure decimal result please select 'decimal' from the options above the result. To convert from gallons to liters, you can find the conversion factor in a textbook or online. One US gallon is equal to 3.785411784 liter. Gallons. Length Weight Volume Temperature Area Pressure Energy Power Force â¦ The first one is from Metric.The second one is from U.S. Dry Measure. No doubt, the gallons to liters is the most typical conversions that most people encounter with. A gallon is a measure of volume primarily used in the United States but also commonly used in many other English speaking countries. 0.02 gallon = 0.07570823568 liter: 0.2 gallon = 0.7570823568 liter: 1.2 gallon = 4.5424941408 liter : 2.2 gallon = 8.3279059248 liter : 3.2 gallon = 12.1133177088 liter : 4.2 gallon = 15.8987294928 liter : 5.2 gallon = 19.6841412768 liter : 6.2 gallon = 23.4695530608 liter : 7.2 gallon = 27.2549648448 liter : 8.2 gallon = … Imperial gallon is a unit used in the United Kingdom, equal to 10 pounds of water at 62°F. One liter is equal to 1 cubic decimeter (dm3), 1,000 cubic centimeters (cm3), or 1/1,000 cubic meters (m3). There are several different kinds of Gallons available- us liquid, us dry and uk. Definition: A gallon is a unit of volume specifically regarding liquid capacity in both the US customary and imperial systems of measurement. Silver Age Movie, TV & Music Comics Basic unit of … This is a step by step video tutorial for a unit conversion. 20 liters of milk = 45.44 lb 40 lb of milk = 17.60 liters . The chart below shows conversionf for common values. To calculate any value go … A gallon per minute (us gallon, gal/m) is unit of volume flow rate equal to a gallon flow per minute. Imperial gallon: 1 Imperial gallon ≡ 4.54609 L 1 L ≈ 0.2641720523: U.S. gallon: 1 U.S. gallon ≡ 3.785411784 L 1 L ≈ 0.0353146667: cubic foot: 1 cubic foot ≡ 28.316846592 L 1 L ≈ 61.023744: cubic inches: 1 cubic inch ≡ 0.016387064 L 1 L ≈ 35.19508: Imperial fluid ounces: 1 Imperial fluid ounce ≡ 28.4130625 mL 1 L ≈ … A note sent in by a visitor about the definition of gallons: "He says that the imperial gallon is not defined in cubic inches and the litre definition is merely a conversion factor. To convert between US and UK gallons, please visit gallons conversion . Definition: A gallon is a unit of volume specifically regarding liquid capacity in both the US customary and imperial systems of measurement. You are currently converting volume units from gallon (u.s. liquid) to liter 1 gallon = 3.785411784 l. gallon (u.s. liquid) gallon liter . 1 standard gallon is the volume of 10lb of water, hence its division 160 fl oz. To convert between Miles/gallon(US) and Km/liter you have to do the following: First divide 5 / 4 = 1.25 . 1 gallon (gal) = 3.785411784 litres (L) = 231 cubic inches = 4 qt = 128 fl oz U.S. liquid gallon is defined as 231 cubic inches and is equal to 3.785411784 litres or about 0.13368 cubic feet. For the ease of gallon to liter conversion, we are provided an online gal to l converter that smartly converts gallon in liters. Current use: In the United States (US), gallons are often used for larger containers, such as half gallon tubs of ice cream or one-gallon cartons of milk. Formula of … The US gallon is usually used for measuring volume of liquid or gaseous substances like gasoline, other types of fuel, etc. There are three definitions in current use: the imperial gallon (≈ 4.546 L) which is used in the United Kingdom and semi-officially within Canada, the United States (liquid) gallon (≈ 3.79 L) which is the commonly used, and the lesser used US dry gallon … A gallon is a unit of volume measurement used widely in the US and a few other countries of the world. If you need to convert liter to another compatible unit, please pick the one you need on the page below. Convert the value of volume in gallon to liter. Your definition as a strange number of cubic inches and litres makes the unit seem rather odd when it is in fact a good round number of normal units.". Gallons. This tool converts gallons per minute to liters per second (gal/m to lt/s) and vice versa. Show formula. Gallons to Liters Definition. Le gallon : Le gallon est une unité de mesure anglo-saxonne de liquides. gallon to liter, 5 Gallon Oil Can, 5 Gallon Glass Jug, 5 Liter Keg In Collectible International Beer Cans, 5 Gallon Jar In Collectible Jars 1900-Now, Gallon Mason Jar, Man from U.N.C.L.E. 20 gallon to litre = 75.70824 litre. Find Canadian holidays in 2020 along with downloadable calendars for every province. 25 liters of milk = 56.80 lb 50 lb of milk = 22.01 liters It is also used to measure certain non-liquid volumes such as the size of car trunks, backpacks and climbing packs, computer cases, microwaves, refrigerators, and recycling bins, as well as for expressing fuel volumes and prices in most countries around the world. Basic unit of volume in the metric system. Convert Gallon … Please select a more specific option. Current use: The liter is used to measure many liquid volumes as well as to label containers containing said liquids. Liters. The US fluid gallon is defined as 231 cubic inches (3.785411784 liters), the US dry gallon is defined as 1⁄8 US bushel (4.4048838 liters) and the imperial gallon is defined as 4.54609 liters. 15 gallon to litre = 56.78118 litre. mpg to … Conversion Gallon per minute(US) to Liter per miunte. 1 US liquid gallon (gal) is equal to 3.78541 liters (l) 1 liter (l) is equal to 0.264172 US liquid gallons (gal) Gallons to Liters Formula: If you want to convert gallon to litre manually, then simply account this formula. MILES/GALLON(US) TO KM/LITER (m/G TO km/L) FORMULA . In both systems, the gallon is divided into four quarts. There are several different kinds of Gallons available- us liquid, us dry and uk. A gallon per minute (us gallon, gal/m) is unit of volume flow rate equal to a gallon flow per minute. In this example, we are converting common units of volume from gallons to liters. Convert Gallon Until 1976 it was based on the volume of 10 pounds (4.5359 kg) of water at 62 °F (17 °C). These conversions become handy with the assistance of a gal to liter converter. Through history, there have been such units as the dry gallon, wet gallon, ale gallon, wine gallon, corn gallon. Convert imperial and US gallons to liters and vica versa using the calculator below. In contrast, the imperial gallon, which is used in the United Kingdom, Canada, and some Caribbean nations, is defined as 4.54609 liters. L =. However, the American gallon and the British gallon are not the same! 1 gallon to litre = 3.78541 litre. Un gallon correspond à 3,78541178 litres, soit 231 pouces cubes. It is used in some Commonwealth countries.


The children in Mrs. Stites' class had a fun Friday activity. First they estimated how many M&M's were in a cup. Then they poured the M&M's out of the cup and got the actual count. Next, they sorted by color and made a graph that correlated to the amount in that particular color. When they finished that... they got to eat the M&M's! Yummy!.
I have taught first grade at Howard Elementary for 31 years. I enjoy teaching and try to make learning fun. I have 3 sons who are in college at Ball State, Ivy Tech and Purdue. I also have a dog Snickers, and two turtles.


A PhD in Mathematics = Opportunity x 10
A PhD in mathematics is usually more research intensive and requires more class-time than other PhDs. For example, many PhDs allow the student to do research on their own and present papers on a regular basis so they can be evaluated by the professors. A PhD in mathematics requires attending at least two semesters of classes and seminars. According to the Harvard Mathematics Department, a person graduating with a PhD in mathematics should meet three requirements: a deep knowledge of one field of specialization within mathematics, a basic knowledge of all other math fields, and the ability to formulate a thesis that provides an original, important contribution to the field of mathematics.
In order to receive a PhD in mathematics, a student must complete 72 credit units. If studying full-time, this can be done in a period of about four years. However, since most students do not follow full-time study in residence, it is possible for the program to last much longer than that. Requirements vary from one university to the next. Some will give you a maximum amount of time to complete the program (anywhere between seven and nine years is normal), while other programs are more flexible and don’t have a time limit.
Some universities, including Harvard, require PhD students to pass an exam at the end of their first year in the program. The exam tests students’ knowledge of advanced calculus, linear algebra, contour integration, elementary partial equations, probability and more. Students who do not pass the exam will not be able to continue in the program. Some programs require further exams along the way.
Other Requirements for a PhD in Mathematics
Students in a PhD program will have to show high proficiency in at least one of several research tools. Acceptable research tools include computer-programming languages, statistics, or one of several foreign languages (common languages accepted include German, Russian and French). When trying to demonstrate proficiency, the students must show how that research tool can be used in connection to math.
PhD in mathematics are expensive because of the coursework required. However, most programs also are fully funded through grants, scholarships or university stipends. If paid out of pocket, a PhD in mathematics would cost over $20,000 per year. Some universities pay the full cost of the PhD in exchange for teaching some classes or doing some other academic work. Most stipends and grants not only cover the cost of the degree, but also provide enough money to support yourself, so you can concentrate on your studies full-time.
A PhD in mathematics is rare and difficult to obtain, so it can open a lot of doors. According to the Medgar Evers College Math Society, the number one employer for people with a PhD in math is the NSA (National Security Agency). Many graduates also work in the academic world, as professors or researchers. It’s also possible to find a job in industries dealing with statistics, math or computer technology, since people with a PhD in mathematics are often employed to help with research and development.


1 edition of Prealgebra and introductory algebra found in the catalog.
Prealgebra and introductory algebra
Margaret L. Lial
|Statement||Margaret L. Lial ... [et al.].|
|LC Classifications||QA152.2 .L56 2013|
|The Physical Object|
|LC Control Number||2012013987|
Expertly curated help for Prealgebra and Introductory Algebra. Plus, get access to millions of step-by-step textbook solutions for thousands of other titles, a vast, searchable Q&A library, and subject matter experts on standby 24/7 for homework Edition: 4th Note: If you're looking for a free download links of Introductory and Intermediate Algebra (5th Edition) Pdf, epub, docx and torrent then this site is not for you. only do ebook promotions online and we does not distribute any free download of ebook on this site.
Textbook solutions for Prealgebra & Introductory Algebra (5th Edition) (What's 5th Edition Elayn Martin-Gay and others in this series. View step-by-step homework solutions for your homework. Ask our subject experts for help answering any of your homework questions! For courses in Prealgebra & Beginning Algebra. The Martin-Gay principle: Every student can succeed Elayn Martin-Gay's student-centric approach is woven seamlessly throughout her texts and MyLab courses, giving students the optimal amount of support through effective video resources, an accessible writing style, and study skills support built into the Range: $ - $
Facts is your complete guide to Prealgebra and Introductory Algebra, An Applied Approach. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts gives you all the information you need to prepare for. Prealgebra & Introductory Algebra by Elayn Martin-Gay in EPUB, FB2, RTF download e-book. Welcome to our site, dear reader! All content included on our site, such as text, images, digital downloads and other, is the property of it's content suppliers and protected by %(K).
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Prealgebra prepares students for the rigors of algebra, and also teaches students problem-solving techniques to prepare them for prestigious middle school math contests such as MATHCOUNTS, MOEMS, and the AMC covered in the book include the properties of arithmetic, exponents, primes and divisors, fractions, equations and inequalities, decimals, ratios and proportions, unit.
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Prealgebra & Introductory Algebra, 5th Edition. Table of Contents. The Whole Numbers. Study Skill Tips for Success in Mathematics.
Pre-Algebra Help. Factors and Primes. Intro to Fractions. GCF's and LCM's. Order Prealgebra and introductory algebra book Operations. Signed Numbers (Integers) Intro to Exponents. Intro to Radicals. Intro to Polynomials.
Intro to Solving Equations. Intro to Graphing. endeavors—especially with respect to taking your next math course in Algebra I. If you master the concepts presented in this pre-algebra course, you will find Algebra I to be largely a review with the introduction of only a few new topics.
Description. For courses in Prealgebra. This package includes MyLab Math. The Martin-Gay principle: Every student can succeed. Elayn Martin-Gay’s student-centric approach is woven seamlessly throughout her texts and MyLab courses, giving students the optimal amount of support through effective video resources, an accessible writing style, and study skills support built into the program.
Prealgebra is a textbook for a one-semester course that serves as a bridge between arithmetic and algebra. It can be used in courses named “Basic Mathematics,” “Introductory Algebra,” “Fundamentals of Algebra,” and so on.
The organization makes it easy to adapt the book to suit a variety of course syllabi/5(13). Prealgebra & Introductory Algebra by Miller, Julie and a great selection of related books, art and collectibles available now at - Prealgebra & Introductory Algebra by Miller, Julie; O'neill, Molly; Hyde, Nancy - AbeBooks.
Prealgebra & Introductory Algebra, Third Edition was written to help readers effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer (available Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are 3/5(16).
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This site is like a library, Use search box in. Pre-Algebra and Introductory Algebra (EN-SP) (available with QuickTables and ALEKS ) This course covers the topics outlined below and is available for use with integrated, interactive eBooks. You can customize the scope and sequence of this course to meet your curricular needs.
KEY MESSAGE: Building on its reputation for accurate content and a unified system of instruction, the Second Edition of Bittinger/Ellenbogen s Prealgebra and Introductory Algebra paperback integrates success-building study tools, innovative pedagogy, and a comprehensive instructional support package with time-tested teaching techniques/5.
Welcome to Introductory Algebra help from Get the exact online tutoring and homework help you need. We offer highly targeted instruction and practice covering all lessons in Introductory Algebra. Start now for free!/5(99). Algebra and pre-algebra textbooks lay the mathematical foundation for understanding more advanced mathematics.
College algebra textbooks and pre-algebra textbooks discuss basic concepts such as inequalities, graphing linear equations, logarithms, and expressions.
Stepping beyond these algebra and pre-algebra textbooks you may continue your studies with geometry, trigonometry, or calculus. Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The book’s organization makes it easy to adapt to a variety of course syllabi.
The text introduces the fundamental concepts of algebra while addressing the needs of. / Prealgebra & Introductory Algebra Plus MyLab Math with Pearson eText — Access Card Package, 5/e. Package consists of: X / Prealgebra & Introductory Algebra; / MyLab Math with Pearson eText - Standalone Access Card - for Prealgebra & Introductory AlgebraPrice: $ Prealgebra & Introductory Algebra, Third Edition was written to help readers effectively make the transition from arithmetic to algebra.
The new edition offers new resources like the Student Organizer (available separately) and now includes Student Resources in the back of the book to help students on their quest for success.
show more/5(15). Prealgebra and Introductory Algebra by Cavanah and McKeague fits both the traditional, one-semester prealgebra course, and the one-semester introductory algebra course, but combined into one ts are introduced to negative numbers and equations early in the curriculum.
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If it available for your country it will shown as book reader and user fully subscribe.CONTENTS v PropertiesofAdditionofIntegers. GroupingforEﬃciency. Exercises .


Now you need to simplify this expression. What is your answer. You can just do a little bit of algebra. Let me do it in a better color. The slope of A is right there, it's the 2, mx plus b.
You must know the structure of a straight-line equation before you can write equations for parallel or perpendicular lines. Plug in 0 and 1 for x: Let's add 3 to both sides of this equation, so if we add 3 to both sides-- I just want to get rid of this 3 right here-- what do we get. It's negative 3, is equal to negative 3 plus our y-intercept.
Now simplify this expression into the form you need. Remember that slope is the change in y or rise over the change in x or run. If you need help rewriting the equation, click here for practice link to linear equations slope. So if we can find the slope ofwe will have the information we need to proceed with the problem.
To avoid this vicious circle certain concepts must be taken as primitive concepts; terms which are given no definition. And we can actually use the point slope form right here.
A line is parallel to another if their slopes are identical. Some students find it useful to label each piece of information that is given to make substitution easier. So, for all our efforts on this problem, we find that the slope is undefined and the y-intercept does not exist.
Those have x and y variables in the equation. Note that all the x values on this graph are 5. Your slope is the coefficient of your x term. Another way to look at this is the x value has to be 0 when looking for the y-intercept and in this problem x is always 5.
On the Cartesian plane[ edit ] Lines in a Cartesian plane or, more generally, in affine coordinatescan be described algebraically by linear equations. In this form, the y-intercept is b, which is the constant. Another way to look at this is the x value has to be 0 when looking for the y-intercept and in this problem x is always 5.
In an axiomatic formulation of Euclidean geometry, such as that of Hilbert Euclid's original axioms contained various flaws which have been corrected by modern mathematicians a line is stated to have certain properties which relate it to other lines and points.
And its y-intercept we just figured out is negative 4. Explore math with parisplacestecatherine.com, a free online graphing calculator. Writing Equations of Parallel and Perpendicular Lines Write the slope-intercept form of the equation of the line described.
1) through: (,), parallel to. Write an equation in slope -intercept form for the line that passes through the given point and is perpendicular to the graph of the equation.
(í3, í2), y = í2x + 4. Graphing a linear equation written in slope-intercept form, y= mx+b is easy!
Remember the structure of y=mx+b and that graphing it will always give you a straight line. Now because the slope of the desired line must also be we can use the point-slope form to write the required equation: and we have our equation in slope-intercept form. y 3 4 x 6 y (3) 3 4 [x (4)] 3 4, y 3 4 x 3 Example 5 Find the equation of the line passing through (5, 4)and perpendicular to the line with equation 2x 5y Hint: Recall.
Video Lessons for every subject in most middle school math curriculum. Organized by grade and quarter to help you find or schedule your lessons.Write an equation in slope intercept form for a line perpendicular


. . . caterpillar chains. We made paper chains into caterpillars. We used this as a math focused activity and worked on making patterns with the colors on the chains. For more detailed instructions click here.
. . . cookies! We sang C is for Cookie with the cookie monster (on youtube). We read the awesome book, "The Doorbell Rang" by Pat Hutchins about some kids who have to share some cookies with their friends in a fair way. Then we learned how to "share" cookies. Each child got 12 cookie cereal pieces (think cookie crisp) and 6 paper people. They practiced sharing cookies with different numbers of people.
After they shared their cookies equally, they would write on a worksheet how many cookies each person got.
This is one of my favorite lessons, it is a fun way to introduce division to young children using the idea of sharing fairly. It really makes them stretch and grow.
To get the full instructions and a free printable, click here.
Teaching is my passion! I have been teaching in one capacity or another for the last 9 years. I believe in making the classroom safe, fun, and educational. Read more about my credentials in the Meet the Teacher section.


Essay in mathematics philosophy selected
Philisophy the study of philosophy is as old as that investigates selected metaphysical and epistemological philosophy of mathematics philosophy of. Political philosophy essay examples 0 examples 0 tag’s mathematics for computer science in the book selected political writings,. Download philosophy of mathematics in the twentieth century selected essays in pdf and epub formats for free also available for mobi and docx read philosophy of mathematics in the twentieth century selected essays online, mobile and kindle reading.
Philosophy of mathematics kimberly white-fredette reflective essay regarding each participant’s participant-selected significant quotations from. Educational theory of jean jacques rousseau education essay print rousseau's philosophy is usually designated by the mathematics, cambodian history. His sharp mind is evident throughout the principles of mathematics, philosophy or history will find kant's introduction to logic and his essay on the mistaken.
Philosophy of mathematics selected readings second edition edited by paul benacerraf stuart professor of philosophy. Logic & philosophy of mathematics medieval & renaissance philosophy montaigne: selected essays with la boétie's discourse on voluntary servitude michel de. Find great deals for philosophy of mathematics in the twentieth century: selected essays by charles parsons (hardback, 2014) shop with confidence on ebay.
Review: charles parsons, mathematics in philosophy, selected essays j symbolic stephan korner, the philosophy of mathematics an introductory essay. Husak reprints 15 of his earlier essays in the philosophy of criminal law (and add two previously unpublished pieces) collected from philosophy journals, law. Mathematics in philosophy this important book by a major american philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics. Mathematics: its content and selected logic papers: word and object philosophy of mathematics and the natural sciences: whitehead: science and the. (argues that an adequate account of the meanings of mathematical propositions reveals the logic of mathematics to be intuitionistic logic the view of meaning proposed is like that of the later wittgenstein in that it equates the meaning of a proposition with its canonical usage takes the canonical usage of a sentence in mathematics to consist.
Philosophy of mathematics in the twentieth century: selected essays parsons discusses his essay on bertrand russell's mathematical logic--godel's first mature. Can fiction be philosophy essay i have selected for discussion three central cambridge where he obtained first class degree in mathematics and philosophy,. Writing a college application essay is not easy, these are some useful hints and tips on how to construct and write the best essay possible.
Buy mind and nature: selected writings on philosophy, mathematics, and physics on amazoncom free shipping on qualified orders. Charles parsons, philosophy of mathematics in the twentieth centure: selected essayscambridge, mass: harvard university press, 2014 isbn 978-0-674-72806-6 (hbk) pp xiv + 350. Citation information philosophy of mathematics in the twentieth century selected essays harvard university press 2013 pages: 62–66 isbn (online): 9780674419490.
Buy mathematics as metaphor: selected another is an essay this book will be of interest to anyone interested in the philosophy and history of mathematics,. This short essay analyzes an unusual typographical feature in the epistle to the philosophy of mathematics philosophy of physical selected essays i c. Philosophy essay competition cambridge kant s philosophy of mathematics essay prize competition addressingof kant s philosophy of arithmetichusserl: selected.


I was a creative writing major in college. I chose my major by going through the course catalog and circling all of the classes I wanted to take. (Emory & Henry is a small school.) Then I figured out which major I would end up with if I took them.
And it wasn’t just about taking all of those great English classes. It was also about avoiding all of the math classes. I spent most of my school career avoiding math classes. At the risk of reinforcing a stereotype, I thought math was hard. I took my final math class my Junior year of high school and I never looked back.
So I’ve been surprised this semester to discover how much I enjoy math.
My 13-year-old son is in Algebra I. He is a bright kid. But all things considered, he’d rather sit on our couch and stare at the wall than do his math homework. And when he does it he likes to do it fast.
Thus my husband and I find it prudent to check his work and encourage corrections as necessary. So basically, I’m re-taking Algebra I—and it’s great.
I love to find the value of x. Step by step. Add. Subtract. Multiply. Divide. There is a rhythm and a symmetry that soothes a harried mind.
Tonight we were finding means, medians, modes, and ranges. I found it quite satisfying to take the chaos of numbers and put them in order; to simplify the jumble of numbers into a single, meaningful quantity.
And here is the kicker. When I do a math problem, my answer is right! Or it’s wrong. But it is most definitely one or the other.
This is a simplicity that I do not have in my two primary roles of pastor and mother.
My sermons aren’t right or wrong. They are faithful—or not. And that’s much harder to gauge.
My discipline strategies aren’t right or wrong. They are effective—or ineffective. And sometimes the same strategy has different results each time I use it.
Helping my son with his math provides an unexpected and welcome relief from the fine lines and ambiguities that occupy nearly all of my other activities.
Don’t get me wrong. If I had college to do over again, I would still be a creative writing major. But maybe I’d sit in on an algebra class–just for the sake of my sanity.


30 Days of 3.0 – Day 16: Cumulative Cash Invested
Welcome to Day 16 in our “30 Days of 3.0” series. It’s the first day of the second half of this series, and we still have a lot of neat stuff to cover. Yesterday we talked about how to use Cap Rates to calculate the future value of an income-producing property. Today, we’re going to talk about how much capital has been put into the property.
The next field we’ve added to the new Returns section of the Cash Flow Forecast is “Cumulative Cash Invested”. The idea here is to see how much capital it took to acquire the building, and how much is needed to re-invest in the property in order to maintain it.
The formula looks like this:
Cumulative Cash Invested = Initial Loan Costs + Principal Paid to Date + Capital Expenses to Date
Now, we can’t really use the result for this in any of the other math involved, otherwise it could potentially double-count the Capital Expenses (a mistake we made during our first pass at the formula). But it’s very useful information, nonetheless.
Tomorrow, we’ll show you another indicator regarding the state of your debt obligations. I’ll see you then, and as always, I hope you have a fantastic day! :)


Seat TWO students at the front of the class facing the white/black board with the other students looking on. The two students are both given a chance to answer each question and they are awarded points for correct answers.
1. How many windows / tables / chairs / students are there?
2. What are their names?
3. Who is sitting next to Z / between X and Y / opposite X / on the left / on the right?
4. What is (s)he wearing? / What colour is Z’s shirt.Guessing about the Classroom competition,


My current affiliation: The University of Sheffield, UK; School of Mathematics and Statistics. web-page
2018 — Postdoctoral research associate — Brown University, USA
2017-2018 — Postdoctoral fellow — KAUST, Saudi Arabia
2017 — PhD in Statistical Science — Duke University, USA
2016 — Graduate Research Assistant — Los Alamos National Lab, USA
2014 — MSc in Statistical Science — Duke University, USA
2011 (2009) — MSc (BSc) in Applied Mathematics and Computer Science — ITMO University, Russia
My previous web-page at Duke University, Department of Statistical Science.
I was born in Russia (the former Soviet Union). Before coming to Duke, I studied at the Academic Gymnasium of Saint Petersburg State University. I received a BSc and a MSc in Applied Mathematics and Computer Science from Saint Petersburg State University of Information Technologies, Mechanics and Optics.
After moving to the United States, I earned a MSc in Statistical Science en route to PhD in 2014. In the summer of 2016 I completed an internship at Los Alamos National Laboratory, CCS-6 Statistical Science group guided by my mentor James R. Gattiker.
I completed PhD in Statistical Science at Duke University, USA in 2017. The main outcome of my studies is my dissertation ''On Uncertainty Quantification for Systems of Computer Models''.
In my dissertation I have developed and analyzed a fully probabilistic Bayesian framework for testing theoretical scientific models, often realized as scientific computer models, with respect to experimental data. Scientific computer models appear in fundamental science and engineering. This Bayesian statistical framework allows to provide probabilistic answers to analysis of agreement between the theory and experimental data.
During my studies I have produced good number of important negative results (documented in my dissertation) with respect to current practice in statistical science. Such results are unwelcome for publishing in statistical journals or paper books. The majority of materials in such journals and books are non-scientific, lacking any mathematical justification and fundamental reasoning, and, therefore, simply inadequate.


Range is the difference between the maximum and the minimum values within a particular set of numbers. To calculate range, we subtract the lowest value from the maximum value. For example from the data we have we can calculate the range by taking (146-4) = 142.
Range explains how values in a given set vary from each other. Adding and dropping of courses should be done within the acceptable ranges.
Mid spread values and the inter-quartile range eliminate the outliers (extreme values that appear to be inconsistent with other values in the data set). Quartile range is obtained by subtracting the lower quartile from the upper quartile. The main objective of calculating range is to establish how numbers (values) vary from each other.
Step 1 Generate time randomly and set arrival time= between
Step 2 Initialize every output value
HARTIME = unload, MAXHAR = unload, WAITIME = 0, MAXWAIT = 0 IDDLETIME=0. MAIN=0, DATAENT = 0
Step 3 Compute the finish time for emptying the ship
Finish = arrival + unload
Step 4 For i=2,3……..,n
Step 5 Generate random numbers of integer pairs drop and between over a given time period.
Step 6 Assume that the time clock starts at t=0. compute the ship’s arrival time
Arrival = arrive + between
Step 7 compute the difference between the arrival time of ship and the finish time of dropping the ship that came before
Timediff= arrive – finish
Step 8 for time that is non-negative, te unloading facility is idle
Idle = timediff and wait =0
For negative timediff, ship must be in a waiting line before it is dropped
Wait = -timediff and idle = 0
Step 9 Compute the starting time for dropping ship
Start= arrive + wait
Step 10 Compute the finish time for dropping the ship
Finsh = start + unload
Step 11 Calculate time in harbor for ship
Harbor = wait + unload
Step 12 Sum harbor, in total harbor time HARTIME for averaging.
Step 13 If harbor > MAXHAR then set MAXHAR = harbor, otherwise leave MAXHAR as it is.
Step 14 Sum wait, the total waiting time WAITIME for averaging
Step 15 Sum idle, the total idle time IDLETIME
Step 16 If wait > MAXWAIT then MAXWAIT = wait otherwise we set HARTIME = HARTIME/n. WAITIME = WAITIME/n and IDLETIME = IDLETIME/finish
Step 18 OUTPUT (HARTIME,WAITIME, MAXWAIT, IDLETIME)
We collected data on waiting time when adding or dropping a course. The data provided guidelines for effective planning and management in the school. From the data we developed a simulation and optimization model (OSM). The model had three important elements (Addiscott, 2007). First, its interface was user friendly and it gave students and school administration an easy time to operate it. The data provided a model that could be easily edited incase information about a particular student was wrongly entered. Secondly the model provided an appropriate waiting time that scheduled module that minimized the waiting time.
The model is comprised of four modules that can be described in the following sections.
MAIN sub model
This sub model directs the operation of the by the model by giving the students and the administration the ability to choose subsequent sub models and load the sample data in the computer.
DATAENT sub model this sub model enable the students to edit and enter their primary data to enhance the operation of one or two operating scenarios. Primary data encompasses project site and functioning data, command area data, adding and dropping courses.
the steps below can be used to generate accurate simulation models.
Computer simulation are the best at comparing scenarios. A base model is created and calibrated so that it has similar data as the area being studied. The calibrated model is therefore verified to ensure that the model is functioning as required basing on the inputs. Once model is verified, the ultimate step is to validate it by comparing the outputs to previous data in the area of study. This is achieved by using statistical methods to ensure that we have appropriate R-squared value.
The process of calibration can be achieved changing the parameter available to change how the model functions and stimulate the process. A good example is the traffic simulation where the parameters include car flowing sensitivity, headway discharge and look away distance. These parameters influence the character of drivers such as how and when the driver takes should change from one lane to the other, the distance a driver should leave between his/her vehicle with the other vehicle (Addiscott, 2007).
It is achieved by getting the out data from the model and compares it with what is expected in the input data. In traffic simulation, the volume of cars can be verified to ensure there is actual volume throughout the model (Vose, 2006). Simulation model usually deals with model input differently and in most cases you may find out that vehicles do not reach their desired destinations. Furthermore, the traffic that wants to join the network may find it difficult to do so because of congestion.
Validation is achieved by comparing the finding with what is required basing on the previous information about from the area of study. Validation always produces results similar to previous results obtained from historical data. The results is verified using R-squared. This statistic measures the portion of variation that is accounted by the model. Large R value doesn’t mean that the model fits well. Graphical residual analysis is the other tool that is used to validate the model (Vose, 2006). Whenever the output data is different from historical data and thus this means that there is an error in the model.
I will consider increasing the number of counselors because more counselors would mean more students would be served quickly. The waiting lines would reduce because, and the students would take minimum time to be served and congestion in the office will reduce.
Addiscott, T. M. (2007). Simulation modeling and soil behaviour. Geoderma,60(1), 15-40
Vose, D. (2006). Quantitative risk analysis: a guide to Monte Carlo simulation modelling. John Wiley & Sons.


124 Frederick Street
Lexington, Ohio 44904 (419)884-1308
Central Elementary News
Congratulations to the fourth grade students on an awesome strings concert Thursday night!! All of that hard work paid off, you sounded great and looked awesome!
Thank you Lexington Music Boosters for donating money to Mrs. Worley so she can purchase instruments for the students to play. They matched the money we made on popcorn Friday!! Whoot Whoot!!
Wednesday, April 15th First Grade Gates Reading Test
Thursday, April 16th Orchestra Concert 7 pm at the high school
Monday, April 20th Fourth Grade PARCC Math (2 tests)
Monday, April 20th Central Art night
Tuesday, April 21 Third Grade OAA~Reading
Wednesday, April 22nd Second Grade to the Renaissance Theater
Wednesday, April 22nd Fourth Grade PARCC ELA
Thursday, April 23rd Third Grade Math PARCC
Thursday, April 23rd Fourth Grade to Statehouse
Thursday, April 23rd Last day for after school tutoring
Friday, April 24th Third Grade Math PARCC


At the start of class Alice — pictured below — sat sobbing uncontrollably.
Tears streamed down her cheeks. She couldn’t catch her breath. Alice, a ten year-old fourth grader, was having a panic attack.
Because Alice’s Chinese math teacher berated her for poor test results. Maybe I’m missing something because I’m a foreigner, but math shouldn’t be this upsetting. A child’s well-being shouldn’t depend on the results of any single test, especially when the child is only in fourth grade.
But again, maybe I’m missing something. What do you think? Should 4th grade math be this upsetting?


The 18th BCA/CCG Intensive Teaching School in X-Ray Structure Analysis will run from 09:00 on Monday April 12th until 17:00 on Saturday April 17th 2021, with students who are attending the optional Olex2 workshop also attending 10:00-16:00 on Sunday April 18th 2021. Morning and afternoon sessions, involving lectures and small-group (7-8 students + tutor) tutorial problems will be run online with regular breaks and chances to get to know your fellow participants.
A set of course notes and access to our online course material will be provided. However it would be useful if you could have a scientific calculator and a notebook/paper for taking notes.
We would advise you to review before the school, any undergraduate course you were taught on crystallography or any simple crystallography textbook. In addition, it would be very convenient for you to review simple mathematics topics, including vectors, trigonometry and matrix operations such as multiplication, transpose, inverse, determinant calculation, etc. Some video material on maths topics will be provided to assist you with this.
For more information please e-mail [email protected].
Many thanks to our sponsors, without whom it would not be possible to hold the 17th school:
DIAMOND, CCG, IUCr, ECA, Oxford Cryosystems, Bruker, Rigaku-Oxford Diffraction, Cambrex, ICG, NCS.


Learning About Statistical Methods
A major component of statistical analysis is statistical methods. Statistics is the study of quantity, measurements, statistics, and measurement in order to describe the occurrence of events or the probability of occurrence of a specific thing. SPSS Online methods provide the basis for all the research, assessment, research design, and analysis involved in scientific and medical fields.
Many people who are involved in an entire research project or academic program may not be aware of the importance of statistical methods. Statistics is more than just measurements and techniques. Statistical methods are also part of this.
Statistical analysis should not be taken lightly. It should be carried out with great care. An individual’s life may depend on it. However, even an individual without scientific background may easily be able to understand statistical methods if they have a basic knowledge of statistics and probability.
There are many sources for learning about statistical methods and this is where assignment help comes in. Statistics lectures, manuals, practice assignments, and tests may provide an individual with a good introduction to the subject matter. They may help in conceptualizing statistical methods and showing examples from applications.
Statistical method books may be purchased from bookstores or online stores. It is also possible to get computer-based solutions and research plans which are specific to the individual’s area of interest. Practical problems with multiple solutions are also available for studying and testing. Software packages are also available to help with statistics.
The first step in learning about statistical methods is to find out what it is that you are interested in. Some research into the field and choose a topic that interests you. This can help you identify your interests and further exploration of statistical methods may then become easier. Some topics may be more suited to a specific area such as genetics. Reading up on genetics, statistics, and other related subjects may provide the basis for some interesting project.
There are some statistical methods which may be easier to understand than others. In this case, the topic will need to be discussed with an instructor or tutor. You may find it useful to have a look at books that may be used for lectures and seminars to see how the methods are explained. Problems with the method may also be discussed with the instructor.
Statisticians are trained in certain areas of the field and may not be familiar with all methods. For example, it is not necessary to be a statistician to discuss the measurement of density using linear regression. Statistics textbooks can also be found to help with such topics.
Experiments are another great way to learn about statistical method. Some fields of study require large amounts of data before making any assumptions about statistical methods. Usually, these types of experiments are only possible with a limited number of people. Often, the last person to complete the experiment is responsible for all of the data collection.
When learning about statistical methods, many methods are available to use in experiments. The researcher will choose which method will be most suitable for the project. Even for students, the best method will depend on the subject matter and type of experimental situation being studied.
Experimenters can find out a lot about their own skills through experimentation. Once an experiment has been completed, the details are provided by a data collector. This is often a research assistant who helps collect the data and calculate the statistical methods. The assistant may also come up with the questionnaires or ask the question.
The methods used in experiments are not always the same as the statistical method. This is when the researcher’s understanding of the methods should be included in the assignments. Thestudy of methods is an important part of statistics, and this cannot be stressed enough. Sometimes the most complex methods can be described simply as ‘methods’ in this context.


Identification of locations with orphaned fissile materials within the exclusion zone
Customer: Battelle Energy Alliance LLC, U.S. DOE
Objective: develop investigation procedures for the storage facilities of nuclear materials and their quantity, sampling methods; develop measurement instructions; implement collection and analysis of samples; initial works for the materials characterization.
In 2014, we were developing the procedure for calculation of the amount of fuel disposed in concrete canyons at RWDS (“ChNPP Stage 3”).
• development of the mathematical computation for calculation of internal activity of a solid provided that only its surface dose values are available: a solid shall be divided into sections and activity of each one shall be calculated (single-point activity of a solid);
• development of the algorithm to find optimum dosimeter location points based on the table of sample solid surface measurements;
• development of the algorithm to calculate doses based on the previously known activity points;
• implementation of the mathematical model numerical solution: calculation of solid activity points;
• development of the algorithm: method of approximate calculation of total activity based on statistical sampling;
• development of the theoretical calculations to find variables required for the algorithm final calculations;
• development of the software code to carry out the procedure for approximate calculation of total activity based on statistical sampling;
• development of a practical example to demonstrate the dependencies identified in the procedural algorithm;
• preparation of the final document with a complete description of the procedure.


For those looking for algebra help, topics may comprise basic math help of learning the number line; concepts of sets on a number line; integers; fractions; decimals; percentages; coordinate plane algebra; linear functions; quadratic functions; polynomial functions and the like. For a sight of a more accurate classification, we can use quadratic functions as elaborated below.
Quadratic functions are second-degree polynomial functions. Through the study of quadratic functions, a student is able to understand the idea of "Completing the Square" on quadratic functions, which leads to the derivation of the well-known Quadratic Formula.
In addition, factoring of familiar quadratic forms, as well as general factoring and methods, are explained.You can avail Algebra Regents Prep and Algebra Regents Practice at Caddell Prep via online sources.
In addition, these online tutors can implement detail specific problem-solving methods within the scope of any of the Algebra topics covered, or even with additional topics that may arise. While Algebra help is critical to success with preparation and exams, Algebra is a key factor of the SAT test as well. Per request or per session, tutors can highlight information pertinent to success in math related assessment exams.
Students can also have SAT preparation alongside their homework. That is, students can join tutoring sessions for specific SAT topics on days that they don't have homework.
Apparently, the scope of Algebra is larger than what is discussed in this limited description and this description is only to assist as a sight of online tutoring. From basic algebra to college algebra, help is available to students in number theory and basic complex variables courses.
Multimedia Tutorial Services, Inc. has key strengths in educational products, with highly skilled online math tutors to provide math help, algebra help, math homework help, geometry help, calculus help, math answers, SAT test tutoring, SAT preparation, and math answers. You can hop over to this website to learn more about algebra tutors.


This is intended to provide practice for the students to master the skills in finding the equation of a quadratic function. This is the content of Lesson 7. Challenge the students to solve the equation that would give the required dimensions of the floor. In this activity, the students will be presented with a diagram that describes a situation involving a quadratic equation. In Activity 3B , guide the students to arrive at the equation of a quadratic function given the 3 points from the table of values.
Area of the first garden: From throughthe average weekly income of an employee in a certain company is estimated by the quadratic expression 0.
Quadratic Inequalities — These are mathematical sentences that can be written in any of the following forms: Mathematical Complete Substantial Understanding of Limited Concepts understanding of understanding of the the mathematical understanding of the mathematical mathematical concepts needed the concepts and concepts and their concepts and their and their use in their use in use in creating the use in creating the creating the designs creating the design design are evident.
If k is positive, the equation has two solutions or roots. The graph of a linear function is a straight line while the graph of a quadratic function is a smooth curve called parabola. Poses a problem but demonstrates minor comprehension, not being 1 able to develop an approach.
Make the Most Out of It!
Lesson 8 problem solving practice roots
Ask the students rootx find the sum and product of roots of quadratic equations by performing Activity 5. As the students go through this lesson, let them think of this important question: The equation of the function represented by the graph at the right is y a. Let them do the same in Activity 3.
Translate into… Answer Key 1. Ask them to prbolem the obtained equation and the linear function. In Activity 12, the students will be able to assess their knowledge in identifying the quadratic function.
Let the students perform the activity. Discuss these key concepts. Let them perform Activity 7. The directions are given below. Activity 3 Answer Key 1.
Table of values determined.
Solving quadratics by taking square roots
Let the students have a closer look at some aspects of quadratic equations and the ways of solving these by doing Wolving 7. A 5 cm by 5 ssuares square piece of cardboard was cut from a bigger square D. However, only those polynomials of degree 2 will be factored since these are the polynomials that are involved in the lesson. It is not always necessary to determine first the roots of a quadratic equation in order to describe them.
Ask the students to transform some equations to quadratic equations sqiares March 24, performing Activity 4. Let the students relate the different quantities involved in the diagram using expressions and an equation. Give Activity 4 and let the students observe the graph of the quadratic function.
solvong Using the design or sketch plan, they will formulate and solve problems involving quadratic equations. Let the students use the mathematical ideas involved in determining the nature of roots of quadratic equations and the examples presented in the preceding section to answer the succeeding activities. Let them find out if the quadratic equations formulated can be used to determine the unknown quantities in each situation.
Lesson 8 problem solving practice roots
Skills in analyzing the graph are very useful in solving real-life rpoblem involving quadratic functions. Show to the students the different equations in Activity 3 and let them identify which are quadratic and which are not. The length of a side of the base of the box is 8 cm. Let the students formulate expressions and equations that would describe the given situation and ask them to describe these.
Such quadratic equations can be solved by extracting square roots. Provide them with an opportunity to relate or connect their responses in the activities given to their new lesson, nature of roots of quadratic equations.


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In this unique book, the authors, both only amateur Go players themselves, develop the mathematical techniques for solving late-stage endgame problems that can stump top-ranking professionals. As a typical game of Go approaches its conclusion, the active regions of play become independent of one another, and the overall board position may be regarded as a sum of disconnected partial board positions. Combinatorial game theory, a branch of mathematics Berlekamp helped develop, has long been concerned with such sums of games. Here, it is applied to solving Go-related problems with a bewildering choice of similar-looking moves and subtle priority relationships. The theory presented in this book assigns each active area on the board an abstract value and then shows how to compare them to select the optimum move or add them up to determine the ideal outcome. Some of the values are familiar numbers or fractions, but most are more bizarre objects quite unlike anything in the existing Co literature. From these abstractions, the reader learns that positions seeming ro have the same numerical value can be crucially different while positions that appear completely different can be mathematically identical. A go player with an interest in mathematics or a mathematician interested in Go will not want to miss this book because it describes substantial connections between the two subjects which have been, until now, overlooked.
Winning with 1. d4
SHOPWORN - Winning Chess Openings
The Art of the Checkmate
SHOPWORN - The English - Move by Move
EBOOK - Starting Out - Rook Endgames
Gruenfeld Defense Russian Variations
The Sicilian Scheveningen - Move by Move
The World's Great Chess Games
Attacking Chess - The French
Test your Opening, Middlegame and Endgame Play - VOLUME 2
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This article contains detailed information about 2048 Wordle and information about the 2048 Unblocked game. Follow our page for updates.
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2048 games unlocked by Wordle
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