X(horizontal) position‚ Y (vertical) position and Z (through) position. It is used in graphics and in positioning text on documents. -Algebraic equations involving the coordinates of the points lying on the shape. For example‚ a circle o f radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4. A system
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SC 4. If the second paragraph is retained‚ the phrasing must be altered.
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_________________ Teacher: _______________ Reviewer: Quadratic Equations I. Multiple Choice: Choose the letter of the correct answer. Show your solution. 1. What are the values of x that satisfy the equation 3 – 27x2 = 0? A. x = [pic]3 B. x = [pic] C. x = [pic] D. x = [pic] 2. What are the solutions of the equation 6x2 + 9x – 15 = 0? A. 1‚ - 15 B. 1‚ [pic] C. – 1‚ - 5 D. 3‚ [pic] 3. For which equation is – 3 NOT a solution? A. x2 – 2x – 15 = 0 C. 2x2
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Differential Equations Exercises 2.1 1. y 2. y y x t x t 3. y 4. y y x x t 5. y 6. y x x 7. y 8. y x x 17 Exercises 2.1 9. y 10. y x x 11. y 12. y x x 13. y 14. y x x 15. Writing the differential equation in the form dy/dx = y(1 − y)(1 + y) we see that critical points are located at y = −1‚ y = 0‚ and y = 1. The phase portrait is shown below. -1 y 5 4 3 2 1 1 2 x
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Writing ionic equations for redox reactions You can split the ionic equation into two parts‚ and look at it from the point of view of the magnesium and of the copper(II) ions separately. This shows clearly that the magnesium has lost two electrons‚ and the copper(II) ions have gained them. These two equations are described as "electron-half-equations" or "half-equations" or "ionic-half-equations" or "half-reactions" - lots of variations all meaning exactly the same thing! Any redox reaction
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A NET IONIC EQUATION EXAMPLE: KCl(aq) + Pb(NO3)2(aq) ( 1. a. Take only one of the first cation(s) and match it with one of the second anion(s). (Write the cation first) b. Take only one of the second cation(s) and match it with one of the first anion(s). (Write the cation first) KCl(aq) + Pb(NO3)2(aq) ( KNO3 +PbCl 2. Correct the formulas of the products based on the charges of the ions. KCl(aq) + Pb(NO3)2(aq) ( KNO3 +PbCl2 ◄ 3. Balance the equation 2 KCl(aq)
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Balancing Chemical Equations Answer Key Vocabulary: coefficient‚ combination‚ compound‚ decomposition‚ double replacement‚ element‚ molecule‚ product‚ reactant‚ single replacement‚ subscript Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is to activate prior knowledge and get students thinking. Students are not expected to know the answers to the Prior Knowledge Questions.] The scouts are making s’mores out of toasted marshmallows‚ chocolate
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Chapter One The Accounting Equation and Double-entry Bookkeeping I. Learning objectives After completing this session‚ students should be able to (1) Define assets‚ liabilities‚ owner’s equity‚ revenue and expenses; (2) Understand the functions of the fundamental accounting equation; (3) Record business transactions and illustrate their effects on the fundamental accounting equation; (4) Understand the accounts payable‚ accounts receivable‚ prepaid insurance‚ and drawing accounts;
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P0 P1/D1 Pt/Dt Rate of Return of Stock r = (D1 + P1)/P0 - 1 Given annual growth rate g1‚ g2‚ then g3 remained constant forever: Di = Di-1*(1+r) P2 = D3 /(R-g) P0 = D1 /(1+r)+ (D2+P2)/(1+r)2 Variation: quarterly basis Di = Di-1*(1+r)4 P2 = D3 /(R-g/4) Variation2: Change of Growth Find the R before Change: P0 = D1 /(R+g) Use it to find future P P1 = D2 /(R+gnew) Bond Repayment = total bond*(face value + last payment price) Efficient Market -Stock prices fully reflect available information
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period of time. General kinetic rate equation is: Where [A] and [B] are the concentration of the species in the reaction. The variable k is the rate constant‚ which is a function of time and catalyst presence. The variables m and n are the order of reaction for their respective species concentration. The higher the value of the reaction order the larger the effect of that specie’s concentration on the rate of the reaction. So for the chemical equation for this experiment: The reaction rate
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