Model A The very first differential equation that one typically encounters is the equation that models the change of a population as being proportional to the number of individuals in the population. In symbols‚ if P(t) represents the number of individuals in a population at time ‚ then the so called called exponential growth model is: Recall that the general solution of this differential equation is . Recall also that in order to
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Algebra 222 week 4 Quiz CLOSE WINDOW Week 4: Quadratic Equations and Functions‚ Date Submitted: 10/26/2014 1. Finding the roots of a quadratic equation with leading coefficient 1 Solve for y . =+y2−3y40 If there is more than one solution‚ separate them with commas. If there is no solution‚ click on "No solution." You answered correctly: =y− 4‚1 2. Finding the roots of a quadratic equation with leading coefficient greater than 1 Solve for v . =2v2+3v2 If there is more than one solution
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if loga m = loga n‚ then m=n Typeset by AMS-TEX 2 29. if a + ib = 0 √ −1‚ then a = b = 0 √ where i = −1‚ then a = x and b = y where i = 30. if a + ib = x + iy‚ 31. The roots of the quadratic equation ax2 +bx+c = 0; a = 0 are The solution set of the equation is −b ± √ b2 − 4ac 2a √ √ −b + ∆ −b − ∆ ‚ 2a 2a where ∆ = discriminant = b2 − 4ac 32. The roots are real and distinct if ∆ > 0. 33. The roots are real and coincident if ∆ = 0. 34. The roots are
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beginning of a reaction are present at the end of the reaction—they have just been rearranged to bond differently and form new substances. It is important that chemical equations represent this law by always having equal numbers of each type of atom on both sides of the equation; chemists call this “balanced.” In a balanced equation‚ each type of element must appear on both sides of the arrow the same number of times. Sometimes it can be difficult to observe what happens to all of the atoms in a chemical
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trials of the reaction were run at different temperatures (over a range of 40.5 ºC) maintaining the reactants concentration constant‚ and the Activation Energy was determined by means of the graphical analysis of the linearized for of the Arrhenius equation. The Activation energy was estimated to be 74kJmol-1‚ which represents a 9.9% error with respected to the accepted value of 82kjmol-1. | Introduction: Chemical reactions are omnipresent. They are the hidden engine of life‚ not only in terms
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Emmitt Smith & His Annual Rushing Yards Emmit Smith announced his retirement February 3‚ 2005. It was a very emotional moment for Smith‚ who has played running back in the NFL for fifteen years (thirteen of those years for the Dallas Cowboys). As Smith announced his retirement tears began to flow down his face stating "It’s been a tremendous ride." Over his career in the NFL‚ Smith has racked up many impressive statistics and awards. Smith has played on three Super Bowl championship teams (including
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The Parabola What is a Parabola? A quadratic expression is an expression in which the highest power of is 2. Consider the following: The above equations are all quadratic expressions as the highest power of is 2. When a quadratic function is graphed‚ the resulting curve is called a parabola‚ as demonstrated in figures 1 and 2. Real Life Application A quadratic function and parabola can be used when undertaking a new business venture to determine the optimum sales price of a particular
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Maximum Marks : 100 Note : Question no. one is compulsory. Attempt any three questions from four. 1. (a) For what value of ’k’ the points ( - k + 1‚ 2 k)‚ (k‚ 2 - 2 k) and ( - 4 - k‚ 6 - 2 k) are collinear. (b) Solve the following system of equations by using Matrix Inverse Method. 3x+ 4y+ 7z= 14 2x-y+ 3z= 4 2x + 2y - 3z = 0 (c) Use principle of Mathematical Induction to prove that : 1 ± 1 ± 1x2 2x3 (d) 1 n (n+1) n+1 5 5 5 5 -‚ How many terms of G.P ‚[3 3‚ 3 /3 Add upto 39 + 13 BCS-012
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3 so f 0.484 We will use t d t dM (1 f ) and t dM from table 7.1 t dM‚D2O 4.3e 2; t dM‚Be 3.9e 3; t dM‚C 0.017 Then‚ t d‚D2O =0.022188sec;t d‚Be =2.0124e-3sec;t d‚C 8.772e 3sec 7.5 One‐delayed‐neutron group reactivity equation; lp 1 lp where 0.0065; 0.1sec1 1 lp For lp 0.0sec For lp 0.0001sec For lp 0.001sec Note:In this question examine the figure 7.2 and see that to give a constant period value ‚say
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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. BaCl2(aq) + 2AgNO3(aq)
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