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4.4 system of linear equations 2
The document discusses solving systems of linear equations with three variables. The standard method is elimination, where one extracts a system of two equations with two unknowns from the original system of three equations. One solves the system of two equations and plugs the answers back into the original system to find the third variable. This process generalizes to systems with N equations and N unknowns by repeatedly extracting and solving smaller systems until reaching a system of two equations. An example problem demonstrates applying this method to find the price of hamburgers, fries, and sodas given three equations relating purchases to total costs.
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The document discusses solving systems of linear equations with three variables. The standard method is elimination, where one extracts a system of two equations with two unknowns from the original system of three equations. One solves the system of two equations and plugs the answers back into the original system to find the third variable. This process generalizes to systems with N equations and N unknowns by repeatedly extracting and solving smaller systems until reaching a system of two equations. An example problem demonstrates applying this method to find the price of hamburgers, fries, and sodas given three equations relating purchases to total costs.
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1.7 derivative
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1.2 review on algebra 2-sign charts and inequalities
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t1 angles and trigonometric functions
There are two main systems for measuring angles: the degree system and radian system. The degree system divides a full rotation into 360 equal degrees, while the radian system defines an angle as the arc length cut out on a unit circle. There are also two important types of right triangles used in trigonometry: the 45-45-90 triangle where the two legs have length a and the hypotenuse has length a√2, and the 30-60-90 triangle where one leg has length a, the other has length a/2, and the hypotenuse has length 2a.
2.1 limits i
The document discusses limits and derivatives. It explains that in calculating the derivative of f(x)=x^2 - 2x + 2, the slope formula was simplified. As h approaches 0, the chords slide towards the tangent line, so the slope at (x,f(x)) is 2x-2. It then provides definitions and explanations for what it means for a variable to approach 0 from the right, left, or in general, to clarify the procedure of obtaining slopes using limits.
Schedule Y
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This document contains 8 questions on topics in applied mathematics for a Masters degree examination. The questions cover a range of numerical methods including Muller's method, Bairstow's method, Gauss-Seidel method, cubic spline interpolation, and the Numerov method. Other questions address linear algebra topics such as basis vectors, subspaces, linear transformations, and inverses. Students are asked to prove theorems about graphs, vector spaces, and matrix eigenvectors. Calculations involve solving systems of equations, finding roots of polynomials, and maximizing profit under constraints.
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The document discusses evaluating the formula log[(2x+1)/(sin1/3(x)+1)] at x=0 and x=10 degrees using a scientific calculator. It explains that the answer is 0 at x=0 and approximately 1.13 at x=10 degrees. It then describes the keyboard of a typical scientific calculator, noting the number, operation, yx, sin, log and formula keys. The rest of the document provides examples and definitions of algebraic, trigonometric and exponential-log formulas.
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1.7 derivative
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The document discusses sign charts and inequalities. It explains that sign charts can be used to determine if expressions are positive or negative by factoring them and evaluating at given values of x. Examples are provided to demonstrate how to construct a sign chart by: 1) solving for where the expression equals 0, 2) marking these values on a number line, and 3) evaluating the expression at sample points in each segment to determine the signs in between values where the expression equals 0. The sign chart then indicates the ranges where the expression is positive, negative or zero.
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There are two main systems for measuring angles: the degree system and radian system. The degree system divides a full rotation into 360 equal degrees, while the radian system defines an angle as the arc length cut out on a unit circle. There are also two important types of right triangles used in trigonometry: the 45-45-90 triangle where the two legs have length a and the hypotenuse has length a√2, and the 30-60-90 triangle where one leg has length a, the other has length a/2, and the hypotenuse has length 2a.
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The document discusses limits and derivatives. It explains that in calculating the derivative of f(x)=x^2 - 2x + 2, the slope formula was simplified. As h approaches 0, the chords slide towards the tangent line, so the slope at (x,f(x)) is 2x-2. It then provides definitions and explanations for what it means for a variable to approach 0 from the right, left, or in general, to clarify the procedure of obtaining slopes using limits.
Schedule Y
Schedule Y amended version 2005,
I hope this is useful to All Clinical Research Professionals.
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1.2 review on algebra 2-sign charts and inequalities
1.2 review on algebra 2-sign charts and inequalities