THEORETICAL STUDY ON MICROWAVE ASSISTED BONDING OF POLYMER BASED MICROFLUIDIC DEVICES By KASI BALAMURUGAN MANI A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN MECHANICAL ENGINEERING WASHINGTON STATE UNIVERSITY School of Mechanical and Materials Engineering May 2013 To the Faculty of Washington State University: The members of the Committee appointed to examine the thesis of KASI BALAMURUGAN MANI‚ find it satisfactory and recommend that it
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SL Math Internal Assessment: Stellar Numbers 374603 Mr. T. Persaud Due Date: March 07‚ 2011 Part 1: Below is a series of triangle patterned sets of dots. The numbers of dots in each diagram are examples of triangular numbers. Let the variable ‘n’ represent the term number in the sequence. n=1 n=2 n=3 n=4 n=5 1 3 6
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–––– Run ∆y y 2 - y1 ––– = ––––––– ∆x x 2 - x1 1- Solve for y to put the equation in slope intercept form. 2- Plot the y-intercept. 3- Using the slope as a fraction‚ rise y and run x to get second point. 4- Graph the line. Ex: 2x+3y=12 -2x -2x ––––––––– 3y=-2x+12 –– –––– 3 3 y= -2/3x+4 m= -2/3 b= 4 Horizontal and Vertical Lines: - A Horizontal Line has the form y=#. (In an equation of a horizontal line‚ there is no x) - The slope of a horizontal line is 0. Picture:
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for one variable from one equation into the other equation -To solve a linear system by substitution: Step 1: Solve one of the equations for one variable in terms of the other variable Step 2: Substitute the expression from step 1 into the other equation and solve for the remaining variable Step 3: Substitute back into one of the original equations to find the value of the other variable Step 4: Check your solution by substituting into both original equations‚ or into the statements of
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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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15= 25a+ 5b +c • Solve for c in equation 5 15= 25a+ 5b+c 15-c= 25a+b 3-c= 5a+b -c= 5a+b-3 c= -5a –b+3 This will be known as equation 6 • Solve for b using equation 4 10=16a+4b+c 10+4b=16a+c -5 + b= -4a +c 2 b= -4a+ 5 + c 2 This will be known as equation 7 • Solve for c using equation 3 6=9a+3b+c -c+6 = 9a+3b
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Summer 2010-3 CLASS NOTES CHAPTER 1 Section 1.1: Linear Equations Learning Objectives: 1. Solve a linear equation 2. Solve equations that lead to linear equations 3. Solve applied problems involving linear equations Examples: 1. [pic] [pic] 3. A total of $51‚000 is to be invested‚ some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3‚000‚ how much will be invested in each type
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mass-spring-damper system. The governing differential equation of a mass-spring-damper system is given by m x + c x + kx = F . Taking the Laplace transforms of the above equation (assuming zero initial conditions)‚ we have ms 2 X ( s ) + csX ( s ) + kX ( s ) = F ( s )‚ X ( s) 1 ⇒ = . 2 F ( s ) ms + cs + k Equation (1) represents the transfer function of the mass-spring-damper system. Example 2 Consider the system given by the differential equation y + 4 y + 3 y = 2r (t )‚ where r(t) is the input to
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order to find the vertex of the quadratic equation‚ begin by using the proper formula - b / 2(a) to find it. In the equation there is an (a) (b) (c) which is needed for the vertex equation. First look at the equation and determine what are the values of the three variable. In this case (a)= 2‚ (b)= 8‚ (c)= 5. Now plug them in properly into the vertex equation. * Notice in the vertex equation there is a negative sign!!! DO NOT FORGET! When plugged into the equation‚ it should state -8 / 2(2). Now use
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radius. Rewriting the equation with one variable would result in a polynomial equation that you could solve to find the radius. 3. Rewrite the formula using the variable x for the radius. Substitute the value of the volume found in step 2 for V and express the height of the object in terms of x plus or minus a constant. For example‚ if the height measurement is 4 inches longer than the radius‚ then the expression for the height will be (x + 4). 4. Simplify the equation and write it in standard
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