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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The Drake Equation * The Drake Equation was created by Frank Drake in 1960. * estimate the number of extraterrestrial civilizations in the Milky Way. * It is used in the field of Search for ExtraTerrestrial Intelligence (SETI). * National Academy of Sciences asked Drake to organize a meeting on detecting extraterrestrial intelligence. Reason drake equation created * Drake equation is closely related to the Fermi paradox * The Drake Equation is: N = R * fp * ne * fl * fi
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Cause and Effect on The Cold Equation In the story "the Cold Equation" by Tom Godwin‚ the author created a cause and effect relationship by having Marilyn decide to stowaway on the emergency dispatch ship that only has enough fuel for one person. Because Marilyn decided to stowaway she ended her own life‚ forced Barton to deal with having to kill a woman‚ negatively affects the results of the mission to Woden‚ and for her parents and brother to deal with her death. Marilyn’s last moments of her life
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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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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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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 class of exact equations (equation
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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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velocity of the stream using Equation 1. (Eqn. 1) Where is the flowrate in m3/s and A is the cross-sectional area of the pipe. To find the flowrate‚ we multiply the flowmeter reading by the constant and convert from gallons to cubic meters as follows: The cross sectional area of the 7.75mm pipe is Plugging these values into Equation 1‚ we obtain a bulk velocity . With the bulk velocity value‚ we can find the Reynolds number of the flow using Equation 2. (Eqn. 2) Plugging
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Calorimetry Equations Monday‚ October 28‚ 2013 12:00 PM TOOL BOX q=mc∆T Water sp. Heat Calorimetry : the measurement of energy (calorie) Calorimeter : tool used to measure energy by Measuring the change in temperature Equation : q=mc∆T What is the difference between Calorimetry and Calorimeter? Quantity of Energy (Cal.) Mass (g) Specific heat (given) (Cal/g) Change in temperature (℃ ) (End-short) What is the dance that we learned
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