TEN EQUATIONS THAT CHANGED THE WIRLD The brightest minds in history have used mathematics to lay the foundation for how we measure and understand our universe. Time and time again‚ we have proved that it only takes one simple formula to alter the course of humanity. Here are ten equations that did just that. ISSAC NEWTON’S LAW OF UNIVERSAL GRAVITATION Newton’s law explains why planets move the way they do‚ and how gravity works‚ both on earth and throughout the universe. First published in the
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established: a. directly by the 1933 Securities Act. b. by the Public Company Accounting Oversight Board. c. by the Financial Accounting Standards Board. d. by the Association of Certified Public Accountants. On March 1‚ 2006‚ the premium on a two-year insurance policy on equipment was paid amounting to $1‚800. At the end of 2006 (end of the accounting period)‚ the financial statements for 2006‚ would report a. Insurance expense‚ $750; Prepaid insurance $1‚050. b. Insurance expense‚ $900;
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Solving Exponential and Logarithmic Equations Exponential Equations (variable in exponent position) 1. Isolate the exponential portion ( base exp onent ): Move all non-exponential factors or terms to the other side of the equation. 2. Take ln or log of each side of the equation. • Make sure to use ln if the base is “e”. Then remember that ln e = 1 . • Make sure to use log if the base is 10. • If the base is neither “e” nor “10”‚ use either ln or log‚ your choice.. 3. Bring the power (exponent)
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balance each other out. Next we had to invest $25‚000 for business supplies. This will fall as a debit and credit line item under assets because we spend cash and the $25‚000 would increase the value of the business. Next we had to but the land for $150‚000. This was a debit and credit line item under assets because we used cash and credit $100‚000 under liability because we now owe a debt. After fully balancing the equation‚ we had $200‚ 00 in assets (what we invested) and $100‚000 in liabilities
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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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Coordinate Systems: A point P is described by three coordinates ‚ in cartesian (x‚y‚z)‚ in cylindrical (r‚ ϕ ‚z)‚ and in spherical (r‚θ‚ ϕ )‚ as shown. A point is also defined by the intersection of three orthogonal surfaces‚ as shown. Cartesian Cylindrical Spherical Transformation from Cylinder to Cartesian Coordinates Transformation from Cartesian to Cylindrical: Transformation
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Example 6.4: Application of General Equation for a Closed System Question A gas is contained in a cylinder fitted with a movable piston as presented in Figure E6.4.1. Figure E6.4.1: A cylinder fitted to a moving piston If the cylinder is placed in boiling water with the piston held in a fixed position‚ 5 kcal of heat is absorbed by the gas‚ which equilibrates at 150oC and a higher pressure. The piston is then released‚ and the gas does 250 J of work in moving to its new equilibrium position
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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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around an imaginary axis of the earth‚ with one revolution representing one day. However‚ this axis that goes through the earth from the North Pole to the South Pole is not just up and down‚ but is on a tilt of 23.5°. This tilted axis is the primary cause of the four seasons of the year - spring‚ summer‚
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Chemical Reactions I. Purpose – The purpose of this lab was to observe different type of chemical reactions to write and balance chemical equations. II. Hypothesis: If you mix two chemicals together‚ then they will change color and/or bubble/fix. III. Procedure - Workstation 1: 1. Light the Bunsen Burner 2. Add 5 – 8 mL of HCL to a test tube that’s in the test tube rack 3. Drop a 2 – cm piece of Mg ribbon into the test tube 4. Record Observations 5. Clean Workstation
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