2/20/2014 Frequently Used Equations - The Physics Hypertextbook Frequently Used Equations Mechanics velocity Δ s v= Δ t ds v= dt acceleration Δ v a= Δ t dv a= dt equations of motion v = 0+at v x =x0+v 0 +½ 2 t at weight W =m g momentum p =m v dry friction ƒ μ =N centrip. accel. v2 ac = r 2 ac =−ω r impulse J =F Δ t impulse–momentum F Δ= Δ t m v J =⌠ dt F ⌠ dt =Δ F p ⌡ kinetic energy potential energy ⌡ K =½ mv
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Real number Irrational numbers π ‚ √�� Rational numbers Integers Whole Natural 3 5 1 2 4 2 2 3 Rational Like: Integers {…‚ -3‚ -2‚ -1‚ 0‚ 1‚ 2‚ 3…….} Whole {0‚ 1‚ 2‚ 3…} Natural {1‚ 2‚ 3…} ‚ ‚ ‚ Properties of real numbers 1234- Reflexive property a=a Symmetric property a = b then b = a Transitive property a = b and b = c then a = c Principle of substitution if a = b then we can substitute b for a in any expirations Commutative properties a+b=b+a ‚ a.b=b.a Associative properties
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whether each statement is always‚ sometimes‚ or never true. 1. The graph of a quadratic function is a straight line. 2. The range of a quadratic function is the set of all real numbers. 3. The highest power in a quadratic function is 2. 4. The graph of a quadratic function contains the point (0‚ 0). 5. The vertex of a parabola occurs at the minimum value of the function. 6. The graph of a quadratic function that has a minimum opens upward. 7. The graphs of f(x) = ax2 and gx=
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was that you can make complex equations look simpler by making substitutions. Take the equation: 2tan2-3tan-2=0 To make this look simpler you can substitute u for tan to get: 2u2-3u-2=0 From there you can us the quadratic formula to get: u= -0.5‚ 2 With this you can now say tan=2 and tan=-0.5 which makes solving for much easier. In this case substitutions made solving much easier and less chaotic looking. The next thing we learned was to rewrite equations in a way that suits your purpose
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Title of Project An investigation into a quadratic expression used to represent a parabolic edge in designing a flower garden utilizing calculus to determine the maximum area of the lawn Purpose of the Project Mr. Jack is an avid gardener and he is considering a new design for his garden. He has a rectangular lawn measuring 5 metres by 3 metres and wants to dig up part of it to include a flower bed. He desires to have a parabolic edge for the flower bed as shown below in Figure 1.
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Quadratic Equations ax2 + bx + c = 0 Examples of Quadratic equations 1. x2 +2x – 8 = 0 2. x2 – 10x + 25 = 0 3. 3x2 + x - 2 = 0 Quadratic Formula If [pic] a x2 + b x + c = 0‚ then [pic] Finding the zeros of the quadratic functions - The zeros of a function are the input values which result in an output value of zero. One way of solving quadratic equations is using factoring Examples are the following: 1) x2 + 5x + 6 = 0 Set this equal to zero:
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Aryabhata (476–550 CE) was the first in the line of greatmathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Aryabhatiya (499 CE‚ when he was 23 years old) and the Arya-siddhanta. Name While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "bhatta" suffix‚ his name is properly spelled Aryabhata: every astronomical text spells his name thus‚[1] including Brahmagupta’s references to
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is continuous because it is associated with a measurement and its possible to have the same y value for different x values. And since the data is measuring height a decimal answer is possible. A function that would fit most of the data would be a quadratic function. The
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MATHEMATICAL METHODS PARTIAL DIFFERENTIAL EQUATIONS I YEAR B.Tech By Mr. Y. Prabhaker Reddy Asst. Professor of Mathematics Guru Nanak Engineering College Ibrahimpatnam‚ Hyderabad. SYLLABUS OF MATHEMATICAL METHODS (as per JNTU Hyderabad) Name of the Unit Unit-I Solution of Linear systems Unit-II Eigen values and Eigen vectors Name of the Topic Matrices and Linear system of equations: Elementary row transformations – Rank – Echelon form‚ Normal form – Solution of Linear Systems
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CONTENTS INTRODUCTION 3 DESCRIPTION 5 UNIT CREDIT 6 TIME ALLOTMENT 6 EXPECTANCIES 7 SCOPE AND SEQUENCE 8 SUGGESTED STRATEGIES AND MATERIALS 9 GRADING SYSTEM 10 LEARNING COMPETENCIES 11 SAMPLE LESSON PLANS 30 INTRODUCTION This Handbook aims to provide the general public – parents‚ students‚ researchers‚ and other stakeholders – an overview of the Mathematics program at the secondary level. Those in education‚ however‚ may use it as a
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