10th algebra-lesson 1- part 1
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This document discusses linear equations using one or two variables. It defines a linear equation as having one or two variables, with no variables raised to a power greater than 1. Linear equations graph as straight lines when the pairs of values that satisfy the equation are plotted on a coordinate grid. The general form of a linear equation using two variables is presented as ax + by + c = 0, where a, b, and c are real numbers, a and b cannot both be 0, and c is a constant. Simultaneous equations are also introduced as two equations with the same two unknowns that must be solved together.
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The document discusses various mathematical methods including matrices, eigen values, quadratic forms, algebraic and transcendental equations, interpolation, curve fitting, numerical differentiation and integration, Fourier series and transforms, and partial differential equations. It provides the contents, recommended textbooks and references for further study on these topics which are important for engineering applications.Recently uploaded (20)
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APM People Interest Network Conference - Tim Lyons - The neurological levels ...Association for Project Management
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APM People Interest Network Conference 2025
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-Tim Lyons
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team-working: Harmony and tensions
With a background in projects spanning more than 40 years, Tim Lyons specialised in the delivery of large, complex, multi-disciplinary programmes for clients including Crossrail, Network Rail, ExxonMobil, Siemens and in patent development. His first career was in broadcasting, where he designed and built commercial radio station studios in Manchester, Cardiff and Bristol, also working as a presenter and programme producer. Tim now writes and presents extensively on matters relating to the human and neurological aspects of projects, including communication, ethics and coaching. He holds a Masters degree in NLP, is an NLP Master Practitioner and International Coach. He is the Deputy Lead for APMs People Interest Network.
Session | The Neurological Levels of Team-working: Harmony and Tensions
Understanding how teams really work at conscious and unconscious levels is critical to a harmonious workplace. This session uncovers what those levels are, how to use them to detect and avoid tensions and how to smooth the management of change by checking you have considered all of them.
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Oliver is a career project professional since 2011 and started volunteering with APM in 2016 and has since chaired the People Interest Network and the North East Regional Network. Oliver has been consulting in culture, leadership and behaviours since 2019 and co-developed HPTM??an off the shelf high performance framework for teams and organisations and is currently working with SAS (Stellenbosch Academy for Sport) developing the culture, leadership and behaviours framework for future elite sportspeople whilst also holding down work as a project manager in the NHS at North Tees and Hartlepool Foundation Trust.
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A Leadership and Culture Change expert, David is the originator of BTFA? and The Dux Model.
With a Masters in Applied Neuroscience from the Institute of Organisational Neuroscience, he is widely regarded as the Go-To expert in the field, recognised as an inspiring keynote speaker and change strategist.
He has an industrial engineering background, majoring in TPS / Lean. David worked his way up from his apprenticeship to earn his seat at the C-suite table. His career spans several industries, including Automotive, Aerospace, Defence, Space, Heavy Industries and Elec-Mech / polymer contract manufacture.
Published in Londons Evening Standard quarterly business supplement, James Caans Your business Magazine, Quality World, the Lean Management Journal and Cambridge Universities PMA, he works as comfortably with leaders from FTSE and Fortune 100 companies as he does owner-managers in SMEs. He is passionate about helping leaders understand the neurological root cause of a high-performance culture and sustainable change, in business.
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10th algebra-lesson 1- part 1
- 1. Chapter :1 ?Linear Equation Using two variables Mrs Amrita Kulthe, Pune 1 ݺߣs By: Mrs. Amrita Kulthe Secondary Teacher Pune
- 2. E x p r e s s i o n Mrs Amrita Kulthe, Pune 2 EXPRESSION
- 3. e.g. 2x+6=8 where a, b, and c are real numbers and . Linear Equations are also first-degree equations because the exponent on the variable is understood to be 1. a, x, b, c, +, = ( ?? + ? = ?) Linear equation using ONE variable Mrs Amrita Kulthe, Pune 3
- 4. What is Linear Equation? Linear Equations A linear equation looks like any other equation. It is made up of two expressions set equal to each other. A linear equation is special because: It has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make the linear equation true and plot those pairs on a coordinate grid, all of the points for any one equation lie on the same line. Linear equations graph as straight lines. Mrs Amrita Kulthe, Pune 4
- 7. Here We will Learn General Form Of Linear Equation using two variables.. ?? + ?? + ? = 0 Where 1) a, b, and c are REAL NUMBERs 2) a 0 , b 0 at the same time c is constant. For e.g. ?? + ?? + ? = ?, ?? ? ?? =9 Question Time: Why we can not take both values zero at the same time?
- 9. SIMULTANEOUS EQUATION : - Simultaneous equations are two equations, each with the same two unknowns and are "simultaneous" because they are solved together.
Editor's Notes
- #7: While solving an equation, you must always keep the following points in mind: The solution of a linear equation is not affected when: The same number is added to (or subtracted from) both the sides of the equation. You multiply or divide both the sides of the equation by the same non-zero number. Let us now consider the following situation: In a One-day International Cricket match between India and Sri Lanka played in Nagpur, two Indian batsmen together scored 176 runs. Express this information in the form of an equation. Here, you can see that the score of neither of them is known, i.e., there are?two unknown quantities. Let us use x and y to denote them. So, the number of runs scored by one of the batsmen is x, and the number of runs scored by the other is y. We know that ?x + y = 176?which is the required equation. This is an example of a linear equation in two variables. It is customary to denote the variables in such equations by x and y, but other letters may also be used. Some examples of linear equations in two variables are:
- #8: You have seen that every linear equation in one variable has a unique solution. When solving an?equation, multiplying?both?sides of the?equation?by?zero is not?a good choice. Multiplying?both?side of an?equation?by 0?will?always result in an?equation?of 0 = 0, but an?equation?of 0 = 0 does?not?help?you?know what the solution to the original?equation is.