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 is written as x (t ) = Φ (t ) x ( 0) The matrix Φ(t)
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Ar (relative atomic mass)‚ Mr‚ Molar mass and Mole. Relative Atomic Mass – Ar • The Ar tells us the average mass of an individual atom (average because of isotopes). • The Ar for an atom has no units as it is relative • You will always be given the Ar for an atom in any example set. Relative formula/molecular mass – Mr Relative formula/molecular mass – Mr Most substances exist as; - compounds if ionic - molecules if covalent We can use Ar’s to calculate the ‘average
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McGregor grouped employees hierarchy need into lower-order needs (Theory X) and higher-order needs (Theory Y)‚ and opined that “these two opposing perceptions conjectured how people view human behavior at work and organizational life” (Wambugu‚ 2014). For instance‚ Theory X assumed that management’s role in the organization is to pressurize and control employees to perform based on the insinuation that human beings are pressure
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The Maxwell equations Introduction:- One of Newton’s great achievements was to show that all of the phenomena of classical mechanics can be deduced as consequences of three basic‚ fundamental laws‚ namely Newton’s laws of motion. It was likewise one of Maxwell’s great achievements to show that all of the phenomena of classical electricity and magnetism – all of the phenomena discovered by Oersted‚ Ampère‚ Henry‚ Faraday and others whose names are commemorated in several electrical
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Was Washington to blame for the X‚ Y‚ and Z affair? In my opinion yes‚ Washington was partly responsible for this affair. Throughout his presidency‚ Washington got rid of many problems with foreign affairs by establishing a treaty. When they needed Spain to give us navigation of the Mississippi river‚ he created Pinckney’s Treaty. Also‚ when Britain’s army units remained in America and causing havoc‚ Washington made Jay’s treaty. The main focus that Washington was making was the need to have peace
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Name___________________________________ Writing Equations of Circles Date________________ Period____ Use the information provided to write the standard form equation of each circle. 1) 8 x + x 2 − 2 y = 64 − y 2 2) 137 + 6 y = − y 2 − x 2 − 24 x 3) x 2 + y 2 + 14 x − 12 y + 4 = 0 4) y 2 + 2 x + x 2 = 24 y − 120 5) x 2 + 2 x + y 2 = 55 + 10 y 6) 8 x + 32 y + y 2 = −263 − x 2 7) Center: (−11‚ −8) Radius: 4 8) Center: (−6‚ −15) Radius: 5 9) ( x − 16) 2 + ( y − 6) 2 = 1 Translated 4 left‚ 2 up 10) ( x + 5) 2 + ( y + 7) 2 = 36
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(1 point each) x2 – 8x + 15 (x - 3) (x -5) x^2 - 5x - 3x +15 x^2 -8x + 15 a2 – a – 20 (a +4)(a-5) a^2 -5a +4a -20 a2 + 12ab + 27b2 (a +9b)(a +3b) a^2 + 3ab +9ab + 27b^2 2a2 + 30a + 100 (2a + 10)(a + 10) 2a^2 +20a +10a + 100 Part 2: (5 points) It’s your turn to be a game show host! As you know‚ in the game of Math Time‚ the contestants are given an answer and they must come up with the question that corresponds to the given answer. Your task for this portion
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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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Equations of State (EoS) Equations of State • From molecular considerations‚ identify which intermolecular interactions are significant (including estimating relative strengths of dipole moments‚ polarizability‚ etc.) • Apply simple rules for calculating P‚ v‚ or T ◦ Calculate P‚ v‚ or T from non-ideal equations of state (cubic equations‚ the virial equation‚ compressibility charts‚ and ThermoSolver) ◦ Apply the Rackett equation‚ the thermal expansion coefficient‚ and the isothermal compressibility
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Generation Y is known as the generation that was born in the 1980s and 1990s‚ although experts do not agree on when this era started. The people who create Generation Y are often the children of baby boomers and are therefore called echo boomers or Generation X. Most of them are in their late teens or twenties and totally different from other generations. The most significant difference between generations X and Y are that X kids are often thought of as the "lost" generation raised at a time when
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