To solve a system of equations by addition or subtraction (or elimination)‚ you must eliminate one of the variables so that you could solve for one of the variables. First‚ in this equation‚ you must look for a way to eliminate a variable (line the equations up vertically and look to see if there are any numbers that are equal to each other). If there is lets say a –2y on the top equation and a –2y on the bottom equation you could subtract them and they would eliminate themselves by equaling zero
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Differential Equations Second Order Differential Equations Introduction In the previous chapter we looked at first order differential equations. In this chapter we will move on to second order differential equations. Just as we did in the last chapter we will look at some special cases of second order differential equations that we can solve. Unlike the previous chapter however‚ we are going to have to be even more restrictive as to the kinds of differential equations that we’ll look at
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Apex is a medium-sized chemical manufacturer with annual sales of $60 million that must make a crucial decision on how to allocate its limited resources. These types of decisions often occur during the S&OP process and are made using product data‚ market analysis‚ risk tolerance‚ culture‚ and a little bit of luck. However‚ making long-term investments based on luck is not a business plan I would be comfortable with. Fortunately for the Executives at the Apex Company they can assess potential business
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Solving systems of linear equations 7.1 Introduction Let a system of linear equations of the following form: a11 x1 a21 x1 a12 x2 a22 x2 ai1x1 ai 2 x2 am1 x1 am2 x2 a1n xn a2 n x n ain xn amn xn b1 b2 bi bm (7.1) be considered‚ where x1 ‚ x2 ‚ ... ‚ xn are the unknowns‚ elements aik (i = 1‚ 2‚ ...‚ m; k = 1‚ 2‚ ...‚ n) are the coefficients‚ bi (i = 1‚ 2‚ ...‚ m) are the free terms
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In the poem “An Equation for My Children” by Wilmer Mills‚ the speaker wants to find out the relationship between his family life and mathematics. Initially‚ the speaker reveals his fascination with Pythagoras’ work‚ which inspired him to go on a quest to finding out how his family life revolved around Pythagoras’ complex theorems. Along the way‚ the speaker finds his investigation so elusive that it feels as if he asked Pythagoras himself to calculate the mathematical equation of a “music tuning
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CHM1022 Tutorial 2 – Semester 2‚ 2012 (Chemical Equilibria) 1. The reaction 2 HCl(g) +I2(s) [pic] 2 HI (g) + Cl2(g) has Kc = 1.0 x 10-34 at 25˚C. If a 1.00 L reaction vessel initially contains 0.100 mol of each HCl and solid I2‚ what are the concentrations of HI and Cl2 at equilibrium? 2. Consider the following gas-phase reaction and equilibrium constant at 25 oC: 4 HCl(g) + O2(g) [pic] 2 Cl2(g) + 2 H2O(g) The concentrations of all species were measured at a particular
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neither be created nor destroyed. In this experiment‚ the mass of the metal was not destroyed or created; the metal’s mass was simply changed into a compound form once the gas reacted to it. The net mass of the reactant side of the equation and the product side of the equation should be equal if the experiment is done correctly. The molecular formula represents the number of all elements in a compound. The empirical
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Chemical Change Lab Name Data Table 1: |Chemicals |Well # |Reaction on White Paper |Reaction on Dark Paper | |NaHCO3 + HCl |A6 |Remains clear. |Remains clear. | |HCl + Blue Dye |B6 |Orange color. |Cannot distinguish color
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Rational Equations Rational equations can be used to get a general idea about the rate at which a job can be completed. This can be really useful for business owners and other areas of daily life. Here is an example: Scenario: Sue can paint the garage in 4 hours and Joe has carpal tunnel so he is slower and can paint the same garage in 6 hours. How long (number of hours) will it take Sue and Joe to paint the garage if they work together? Solution: Sue can paint of the garage in 1 hour. Joe
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Abstract Chemical equilibrium occurs when a reversible reaction is happening forward and backward‚ at the same time by the same amount‚ is equal. Two procedures were made. First is the Effect of Concentration on Equilibrium. The solution became orange when it was diluted with ammonium hydroxide and the solution became yellow when water was added to the solution. In the second‚ Effect of Temperature on Equilibrium‚ the solution turned into a light brown gas when it was placed in the refrigerator
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