Visualizing the Domain and Range of the Composition of Functions

2005 ◽  
Vol 98 (5) ◽  
pp. 306-311
Author(s):  
Nial Neger ◽  
Michael Frame
Keyword(s):  
Graphical Method ◽  
Graphical Methods ◽  
Real Numbers ◽  
Straightforward Application ◽  
Restricted Domains ◽  
Teachers And Students ◽  
Addition And Subtraction ◽  
Composition Of Functions

Graphical methods for visualizing addition and subtraction of functions are familiar to every teacher. This article presents a simple graphical method for visualizing the composition of functions. This straightforward application enables users to find the domain and range of compositions. Finding the domain by standard approaches is challenging to the point that it often is ignored by composing functions with domains consisting only of real numbers. By contrast, finding the domain of the composition of functions with restricted domains is easy with this method. In addition, teachers and students can generate families of functions in which composition domains undergo all sorts of changes.

A Graphical Method for the Evaluation of Principal Strains From Normal Strains

1945 ◽  
Vol 12 (4) ◽  
pp. A209-A210
Author(s):  
Glenn Murphy
Keyword(s):  
Graphical Method ◽  
Graphical Methods ◽  
Principal Strains

Abstract Graphical methods are available for determining principal strains when observed strains are measured along gage lines which make angles of 45 deg or 60 deg with each other. In this paper the author presents a simplified graphical method for the general case in which angles between the gage lines may have any arbitrary values.

A Graphical Method of Solution for Travelling Waves on Transmission Systems with Attenuation

1975 ◽  
Vol 12 (1) ◽  
pp. 78-87
Author(s):  
P. S. Barnett
Keyword(s):  
Transmission Lines ◽  
Graphical Method ◽  
Travelling Waves ◽  
Graphical Methods ◽  
Transmission Systems ◽  
Method Of Solution

Graphical methods of solution for networks containing transmission lines with attenuation but no distortion are presented. These are similar to those available for the solution of travelling waves on lossless transmission lines using the Schnyder-Bergeron method. The equations used are derived and are of the same form as those used in the method of Schnyder and Bergeron. Examples illustrating the graphical methods are given.

scholarly journals Penerapan Metode Pembelajaran Matematika Berbasis ICT pada SDN 14 Kecamatan Lubuk Begalung Padang

2018 ◽  
Vol 1 (1) ◽  
pp. 91-99
Author(s):  
Ranti Eka Putri
Keyword(s):  
Teaching Methods ◽  
Teaching And Learning ◽  
Learning Objectives ◽  
Instructional Media ◽  
Emotional Climate ◽  
Adobe Flash ◽  
Teachers And Students ◽  
Addition And Subtraction ◽  
Time And Energy ◽  
Selection Of

Learning media is a container, facilities or facilities that can provide convenience to educators to convey messages or information to be received well and interesting by students. Selection of appropriate learning media will give effect and influence in realizing the achievement of learning objectives. With the availability of instructional media, educators can create classroom situations, determine what teaching methods will be used in different situations and create a healthy emotional climate among learners. In the process of teaching and learning at SDN 14 Padang, what happens in learning often happen the teaching process runs ineffectively. A lot of time, and energy wasted while the goal of learning cant be achieved even happen noises or voice that is not important in communication between teachers and students. For that purpose, it is designed the instructional media which is devoted to the field of mathematics study in discussing material about multiplication, division, addition and subtraction by using Adobe Flash CS3. Keywords : Learning Media, ICT, Adobe Flash CS3

Penjumlahan dan Pengurangan Bilangan Bulat Interaktif Berbasis Komputer

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Jalinus ◽  
Jesi Alexander Alim
Keyword(s):  
Elementary School ◽  
Elementary School Teachers ◽  
Mathematics Learning ◽  
Interactive Media ◽  
Fourth Grade ◽  
Teaching Materials ◽  
Mathematical Concepts ◽  
Teachers And Students ◽  
Computer Based ◽  
Addition And Subtraction

Tujuan penelitian yang dilakukan adalah untuk melahirkan media interaktif berbasis komputer yang dapat digunakan untuk materi penjumlahan dan pengurangan bilangan bulat oleh guru dan siswa karena media interaktif berbasis komputer ini dapat menyampaikan konsep matematika khususnya penjumlahan dan pengurangan bilangan bulat menggunakan animasi yang menyenangkan sesuai dengan tahap berpikir siswa SD yang masih berada pada tahap konkrit atau semi abstrak. Jenis penelitian ini adalah penelitian pengembangan (development research) dengan rancangan penelitian (langkah-langkah) berikut: 1. tahap analisis meliputi: a) melakukan wawancara dengan guru kelas IV SD tentang pembelajaran matematika; b) menganalisis silabus mata pelajaran matematika kelas IV SD; c) menganalisis buku teks matematika yang digunakan oleh guru SD; d) mereview literature tentang bahan ajar. 2. Tahap Prototype, meliputi: a) tahap validasi,, mliputi validitas isi dan konstruk; b) tahap paktikalita, dilakukan uji coba pada SD Babussalam Pekanbaru; 3. Tahap penilaian, meliputi kegiatan dipusatkan untuk engevaluasi apakah prototype (uji coba) dapat dipakai sesuai yang diharapkan dan efektif meningkatkan kualitas pembelajaran. Hasil validasi dari para validator menunjukkan bahan ajar matematika interaktif berbasis computer pada materi penjumlahan dan pengurangan bilangan bulat telah valid (bahan ajar telah sesuai dengan yang diharapkan). Hasil ujicoba yang dilakukan pada kelas IV SD Babussalam Pekanbaru menunjukkan bahwa bahan ajar interaktif berbasis komputer pada materi penjumlahan dan pengurangan bilangan bulat sudah praktis, terbukti dari hasil deskripsi dan analisis data yang diperoleh dapat disimplkan bahwa bahan ajar efektif dalam memunculkan aktivitas belajar siswa dan dapat membuat siswa belajar mandiri dan menyenangkan.   The purpose of the research is to construct computer-based interactive media that can be used for the addition and subtraction of integers by teachers and students because this computer-based interactive media can convey mathematical concepts in particular integers using fancy animations according to students' thinking stages (Elementary school) who is still at a concrete or semi-abstract stage. This research is developmental research with the design of the study (steps) following: 1. the analysis phase includes: a) conducting interviews with fourth grade teachers about mathematics learning; b) analyze the syllabus of 4th grade elementary school mathematics subjects; c) analyze mathematical textbooks used by elementary school teachers; d) reviewing the literature on teaching materials. 2. The Prototype stage, includes: a) validation stage, including content and construct validity; b) paktikalita stage, conducted a trial on Babussalam Pekanbaru Elementary School; 3. The assessment phase, including activities focused on evaluating whether the prototype (trial) can be used as expected and effectively improving the quality of learning. The validation results from the validators show that the computer-based interactive mathematics teaching material in integer addition and subtraction material has been validated (expected). The results of experiments conducted at the fourth grade of Babussalam Pekanbaru Elementary School showed that interactive computer-based teaching materials in integer addition and subtraction material were practical, as evidenced from the results of the description and analysis of the obtained data that it could be effective in generating student learning activities and promoting students self-learning and interests.

scholarly journals Low-precision Logarithmic Number Systems

2021 ◽  
Vol 18 (4) ◽  
pp. 1-25
Author(s):  
Syed Asad Alam ◽  
James Garland ◽  
David Gregg
Keyword(s):  
Input Data ◽  
Global Optimum ◽  
Average Error ◽  
Conversion Error ◽  
Real Numbers ◽  
Number Systems ◽  
External Sources ◽  
Addition And Subtraction ◽  
Base Selection ◽  
Logarithmic Number

Logarithmic number systems (LNS) are used to represent real numbers in many applications using a constant base raised to a fixed-point exponent making its distribution exponential. This greatly simplifies hardware multiply, divide, and square root. LNS with base-2 is most common, but in this article, we show that for low-precision LNS the choice of base has a significant impact. We make four main contributions. First, LNS is not closed under addition and subtraction, so the result is approximate. We show that choosing a suitable base can manipulate the distribution to reduce the average error. Second, we show that low-precision LNS addition and subtraction can be implemented efficiently in logic rather than commonly used ROM lookup tables, the complexity of which can be reduced by an appropriate choice of base. A similar effect is shown where the result of arithmetic has greater precision than the input. Third, where input data from external sources is not expected to be in LNS, we can reduce the conversion error by selecting a LNS base to match the expected distribution of the input. Thus, there is no one base that gives the global optimum, and base selection is a trade-off between different factors. Fourth, we show that circuits realized in LNS require lower area and power consumption for short word lengths.

Study of the Enwrapping Profiles Associated with Rolling Centrodes by the Minimum Distance Method — Graphical Solution Developed in the CATIA Design Environment

2014 ◽  
Vol 656 ◽  
pp. 181-191
Author(s):  
Virgil Teodor ◽  
Silviu Berbinschi ◽  
Nicuşor Baroiu ◽  
Nicolae Oancea
Keyword(s):  
Minimum Distance ◽  
Graphical Method ◽  
Graphical Methods ◽  
Graphical Solution ◽  
Design Environment ◽  
Distance Method ◽  
Basic Theorem ◽  
Graphical Design

The issue of enwrapping surfaces study can be solved using the basic theorem Olivier or Gohman. Also, are known and used some specific theorems for the study of the enveloping of the helical surfaces. More, they were developed and applied complementary theorems as: “the minimum distance” method or “the inplane generating trajectories family”. The development of the graphical design environment allows the approach of the issue of surface enwrapping using the capabilities of this software. In this paper it is proposed a methodology for application of the “minimum distance method” for generation of the surface associated with a pair of rolling centrodes using various tools: rackgear tool and gear shaped tool. They are presented applications of this graphical method and the results. This proves the quality of the proposed method. The graphical methods have the advantages that are fast, rigorous and intuitive.

Using Clock Arithmetic to Teach Algebra Concepts

2005 ◽  
Vol 11 (2) ◽  
pp. 104-109
Author(s):  
Elizabeth M. Brown ◽  
Elizabeth Jones
Keyword(s):  
Middle School Students ◽  
Number System ◽  
Abstract Concepts ◽  
Real Numbers ◽  
School Students ◽  
Multiplicative Inverse ◽  
Finite Systems ◽  
Solving Equations ◽  
Original Number ◽  
Addition And Subtraction

Learning algebra concepts can be difficult for middle school students. One reason may be because we work in only one number system, the set of real numbers. Students have only one frame of reference to provide examples of abstract concepts, such as the additive and multiplicative identities, additive and multiplicative inverses, and connections among the operations. These concepts are essential in solving equations. For example, we can think of an equation like 3x + 4 = 7 in the following way: Begin with a number, multiply it by 3, and add 4. If the answer is 7, what number did we start with? To solve this type of equation algebraically, we just undo what was done to the original number, that is, we add -4, the additive inverse of 4, and multiply the result by 1/3, the multiplicative inverse of 3. We can also think of this as subtracting 4 and dividing by 3, because addition and subtraction are inverse operations as are multiplication and division. The ideas of inverse operations and inverse elements are, therefore, central to algebra. Many students understand these ideas well enough to do simple problems like 3x + 4 = 7 but get confused with more difficult problems, such as 3(x + 6) + 2 = 5x + 5, where it is not as easy to see the order in which to undo these operations. We use finite systems to help students understand these key concepts in algebra, including additive and multiplicative identities, additive and multiplicative inverses, closure, and the relationships between addition and subtraction and multiplication and division.

A three-dimensional graphical method for shear strain analysis

1994 ◽  
Vol 29 (4) ◽  
pp. 263-266
Author(s):  
S E-D Taher ◽  
A A Almusallam
Keyword(s):  
Graphical Method ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Graphical Methods ◽  
Strain Components ◽  
Graphical Technique ◽  
Shearing Strain ◽  
Original Construction

The efficiency of graphical methods for strain analysis depends merely on its simplicity and accuracy. For most strain definitions, the Mohr circle has proved to be the most powerful graphical technique. Unfortunately, its three-dimensional form has limitations concerning the determination of the shearing strain components on a general oblique plane. In this paper, the various deformation quantifiers and the existing extensions to Mohr's method which account for its drawbacks are briefly reviewed. A novel proposal to be appended to Mohr's original construction, allowing its complete generality, is given. It has the form of a simplified complementary triangular construction. A mathematical formulation of the suggested graphical techniques on the basis of Cauchy's formula and vector analysis is carried out.

Simple graphical methods for estimating the confidence region about the orientation of the intersection of two planes

1978 ◽  
Vol 15 (10) ◽  
pp. 1598-1604 ◽  
Author(s):  
D. Cruden ◽  
D. Kelker
Keyword(s):  
Structural Geology ◽  
Rock Mechanics ◽  
Graphical Method ◽  
Confidence Region ◽  
Acute Angle ◽  
Graphical Methods ◽  
Graphical Construction ◽  
Large Size ◽  
Common Plane ◽  
The Common

We give a simple graphical method for the construction on a stereonet of the confidence region for the orientation of the line of intersection of two planes. The method applies when the poles to the planes have been estimated by large and approximately equal numbers of measurements which may be treated as samples from two Fisher distributions of equal and large precision parameters. The method requires the estimation of the acute angle between poles to the planes and the range of the plunges of the poles.When the samples of poles are samples of large size from two Bingham distributions tightly clustered about their common plane, a more complex graphical construction is available. It requires the estimation of scatter of the poles in and perpendicular to the common plane and some simple calculations.The methods are applicable to a variety of problems in structural geology and rock mechanics.

scholarly journals Optimisasi Jumlah Produksi dalam Memperoleh Keuntungan Maksimal Pada Penjualan Dompet dan Tas Jimshoney “NAYA Online Shopping”

2020 ◽  
Vol 1 (1) ◽  
pp. 45-52
Author(s):  
Rochmat Umar
Keyword(s):  
Linear Programming ◽  
Operational Research ◽  
Online Shopping ◽  
Graphical Method ◽  
Optimal Solution ◽  
Sensitivity Test ◽  
Graphical Methods ◽  
Maximum Capacity ◽  
Maximum Profit ◽  
Research Techniques

ABSTRACT Linear programming is one of the most widely used operational research techniques in practice and is known for being easy to understand. The method in solving linear programming in "Naya Online Shopping" is by the graphical method and compared with LINGO software. The purpose of the completion of linear programming is to optimize the amount of production in obtaining maximum profits. And an optimal solution is obtained, namely a maximum profit of IDR 1,750,000. with 50 bags of "ting-ting bags" to be purchased from agents and many "crown wallets" to be purchased from agents of 100 pieces. From the maximum capacity of the shelter 150 pieces can be maximized by purchasing as many as 50 bags and purchasing 100 pieces of wallet. From the sensitivity test, it can be concluded that each capital increase or reduction of IDR 750,000 will result in a gain or loss of IDR 12,500. Completion of linear programming with research into the operation of graphical methods and LINGO software obtained the same value. Keywords: Linear programming, Operations of graphical method operations, LINGO software, sensitivity test ABSTRAK Linear progamming adalah salah satu teknik riset operasi yang paling banyak dipergunakan dalam praktik dan dikenal karena mudah dipahami. Metode dalam penyelesaian linear progamming pada “Naya Online Shopping” yaitu dengan metode grafik dan dibandingkan dengan software LINGO. Tujuan dari penyelesaian linear progamming ini adalah untuk mengoptimalkan jumlah produksi dalam memperoleh keuntungan maksimal. Dan didapatkan solusi optimal yaitu keuntungan maksimum sebesar Rp1.750.000, dengan banyaknya tas “ting-ting bag” yang akan dibeli dari agen sebanyak 50 buah dan banyaknya dompet “crown wallet” yang akan dibeli dari agen sebanyak 100 buah. Dari kapasitas maksimal penampungan 150 buah dapat dimaksimalkan dengan pembelian tas sebanyak 50 buah dan pembelian dompet 100 buah. Dari uji sensitivitas dihasilkan bahwa setiap penambahan atau pengurangan modal sebesar Rp750.000, maka akan didapatkan keuntungan atau kerugian sebesar Rp12.500,. Penyelesaian linear progamming dengan riset operasi metode grafik dan software LINGO didapatkan hasil yang sama nilainya. Kata Kunci: Linear progamming, Riset operasi, Software LINGO, Optimasi, Pemodelan Matematik.

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