CHAPTER 2 FIRST ORDER DIFFERENTIAL EQUATIONS 2.1 Separable Variables 2.2 Exact Equations 2.2.1 Equations Reducible to Exact Form. 2.3 Linear Equations 4. Solutions by Substitutions 2.4.1 Homogenous Equations 2.4.2 Bernoulli’s Equation 2.5 Exercises In this chapter we describe procedures for solving 4 types of differential equations of first order‚ namely‚ the class of differential equations of first order where variables x and y can be separated‚ the
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Upstream: 60 = 6(b-c) Downstream: 60 = 3(b+c) There are now two separate equations: 60 = 6b - 6c and 60 = 3b + 3c Solve both equations for b: b = 10 + c b = 10 - c Now make both equations equal each other and solve for c: 10 + c = 10 - c 2c = 0 c = 0 The speed of the current was 0 mph Now‚ plug the numbers into one of either the original equations to find the speed of the boat in still water. I chose the first equation: b = 10 + c or b = 10 + 0 b = 10 The speed of the boat in still water must
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The Putting Out-Systems and its effects on production labor and accumulation of Profit Priscilla Palomo Period Paper 2 US History DE 3/4B-S53 12/2/2013 The Putting-Out System is a production of goods at home under the supervision of a merchant that also gave control of production to merchant capitalist. Agricultural laborers and farmers were the ones who would perform certain tasks and would benefit by making money on the side with spare time on their hands. The system later economically
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the combustion of ethanol to provide energy for a small explosion. The chemical equation that describes the combustion of ethanol is shown below. (Note: Hover over the equations in this Introduction with your cursor to view enlarged formulas.) Equation 1: C2H6O+3O2→3H2O+2CO2+heat Ethanol: C2H6O Oxygen: 3O2 Water: H2O Carbon dioxide: CO2 The chemical equation states that ethanol (C2H6O)
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On Mathieu Equations by Nikola Mišković‚ dipl. ing. Postgraduate course Differential equations and dynamic systems Professor: prof. dr. sc. Vesna Županović The Mathieu Equation An interesting class of linear differential equations is the class with time variant parameters. One of the most common ones‚ due to its simplicity and straightforward analysis is the Mathieu equation. The Mathieu function is useful for treating a variety of interesting problems in applied
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2 CALCULATIONS For the sample calculations‚ we looked at the first sample point of the flow in Pipe 1‚ the smallest diameter smooth copper tube: The first step in determining the properties of the flow is finding the density and kinematic viscosity of the water. At 296.51 K‚ water has the following properties1: From this we can determine the bulk velocity of the stream using Equation 1. (Eqn. 1) Where is the flowrate in m3/s and A is the cross-sectional area of
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CHEMISTRY TOPIC 11 CHEMICAL CALCULATIONS CHEMICAL CALCULATIONS INTRODUCTION The first part of this ‘Chemical Calculations’ topic will help us to work out QUANTITIES involved in a reaction; For example‚ a manufacturer might want to know‚ How much ammonia will I produce from 20 tonnes of nitrogen in the Haber Process? To do these calculations you will need to be familiar with the term Ar (relative atomic mass)‚ Mr‚ Molar mass and Mole. Relative Atomic
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The Triathlon Equation Those who are interested in doing the triathlon often do not know how to do their training effectively. First you must build a base. This means you must start with endurance only a few times a week‚ progressing to 6 days a week with one rest day. You should only do 1 activity a day‚ with 1 brick workout a week. A brick workout simulates what it feels like to do two of the activities back to back so that it is easier come race day. Brick examples include: 1.) swim 300m
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Quadratic Equation: Quadratic equations have many applications in the arts and sciences‚ business‚ economics‚ medicine and engineering. Quadratic Equation is a second-order polynomial equation in a single variable x. A general quadratic equation is: ax2 + bx + c = 0‚ Where‚ x is an unknown variable a‚ b‚ and c are constants (Not equal to zero) Special Forms: * x² = n if n < 0‚ then x has no real value * x² = n if n > 0‚ then x = ± n * ax² + bx = 0 x = 0‚ x = -b/a
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ME 381 Mechanical and Aerospace Control Systems Dr. Robert G. Landers State Equation Solution State Equation Solution Dr. Robert G. Landers Unforced Response 2 The state equation for an unforced dynamic system is Assume the solution is x ( t ) = e At x ( 0 ) The derivative of eAt with respect to time is d ( e At ) dt Checking the solution x ( t ) = Ax ( t ) = Ae At x ( t ) = Ax ( t ) ⇒ Ae At x ( 0 ) = Ae At x ( 0 ) Letting Φ(t) = eAt‚ the solution
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