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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Mass Relationships in a Chemical Reaction – Lab Christian Lecce Mr. Ribarich Wednesday‚ February 20st‚ 2013 Purpose To determine the mass of copper formed when excess aluminum is reacted with a given mass of a copper salt (Copper Chloride dihydrate)‚ and the mole-to-mole ratio between the reactant and the product of a chemical reaction. Apparatus * 150ml beaker * Stirring rod * Ruler * Hotplate * Tweezers * 50ml graduated cylinder Materials * Copper
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Experiment 4: Developmental of an Equation Purpose While performing this lab‚ the student will learn how to determine the formula of the ionic solid produced from the reaction. Also‚ the student will learn to write the chemical equation corresponding to the reaction. Procedure Please refer to General Chemistry Laboratory Experiments‚ Volume 1‚ 2011‚ by Robert Tatz and Judith Casey‚ Exp 4‚ pages 32-33‚ for proper procedure. Data See attached sheet. Report Questions 1. The charge on an
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08.03 Factoring Trinomials x2 + bx + c Part 1 Factor each trinomial below. Please show your work and check your answer. (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
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329 Quadratic Equations Chapter-15 Quadratic Equations Important Definitions and Related Concepts 1. Quadratic Equation If p(x) is a quadratic polynomial‚ then p(x) = 0 is called a quadratic equation. The general formula of a quadratic equation is ax 2 + bx + c = 0; where a‚ b‚ c are real numbers and a 0. For example‚ x2 – 6x + 4 = 0 is a quadratic equation. 2. Roots of a Quadratic Equation Let p(x) = 0 be a quadratic equation‚ then the values of x satisfying p(x) = 0 are called its roots or
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Establishment of a Chemical Equation Using the Method of Continuous Variation. b) Purpose: the continuous variation method is used to establish a chemical equation by displaying on a line graph the change/difference in temperature caused by the composition of acids and bases in the solution. II. Apparatus and Materials: A) Goggles B) Acid C) Base D) Digital Thermometer E) Pipet (10ml and 100 ml) F) Buret G) Plastic foam cup H) Beaker III. Outline of Procedure: For each system
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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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Reactions in Aqueous Solutions: Metathesis Reactions and Net Ionic Equations Introduction: Metathesis or double decomposition reactions are a reaction in which two compounds react to form two new compounds‚ with no changes in oxidation number. The ions of two compounds exchange partners. AX + BY AY + BX This reaction can occur between two inorganic salts when one product is insoluble in water‚ driving the reaction forward. A typical example is as followed and is considered a molecular equation
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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 +
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THE ACCOUNTING EQUATION The accounting equation can be described as of the basis of accounting. This is because it describes the double entry principle of book-keeping. It is a representation of how funds are raised to finance Assets. The equation is illustrated below: Asset = Capital + Liabilities For example‚ a girl needs to buy a laptop costing £500. She already had £250 in personal savings and then took a loan of £250 from her boyfriend. Here is the equation again: Asset Capital
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