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Absolute value notes

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1-4, 1-6 Solving Absolute Value Equations and Inequalities Absolute value: distance from zero on a number line. Since distance in a nonnegative, the absolute value of a number is always positive. The symbol lxi is used to represent the absolute value of a number x. I units 4 units I I I I 1 I 3 4 5 Solving Absolute Value Equations: For any real numbers a and b, where b ~! 0, if Jal = then a = b or ?a = b. The second case is often written as a = ?b. Steps 1. Isolate the Absolute Value expression 2. Rewrite equation without the I I symbols. a. One with positive answer b. One with negative answer Ex 1: Jx-51=7 x-c3- ?t-3 k'3 + 3. Solve each equation '7 2\: flL1 - '7 I 2 - \ - 4. Check your answers (plug back into I T

Calculus 1 Exam 3 4of4

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18) Find the center, foci, and vertices of the ellipse, and determine the length of the major and minor axes. Then sketch the graph. a) b) Center: Foci: Vertices: 19) Find the solutions of the system of equation. 20) The population of a certain city was 112,000 in 2006, and the observed doubling time for the population in 18 years. a) Find an exponential model for the population t years after 2006. b) Find an exponential model for the population t years after 2006. 21) Find the for the given system of equations.
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Calculus 1 Exam 3 2of4

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8) Find the inverse function of f. 9) Find the exact solution and rounded to four decimal places solution of the exponential equation. 10) Find the solution using Gaussian elimination or Gauss ? Jordan elimination. 11) Determine whether the system of linear equations is inconsistent or dependent. If it is dependent, find the complete solution. Find the solution using Gaussian elimination or Gauss ? Jordan elimination 12) Graph the solution set of the system of inequality. 13) Use Cramer?s Rule to solve the system.
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Summary of Shang dynasty

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SHANG DYNASTY TOP TEN 1. Technological: paper was invented. 2. Oracle bones are found to have been a huge part 3. Writing system ----- pictographic 4. Believed and worshiped a higher god who was superior to lesser gods such as the sun, moon and rain. 5. The Shang dynasty had an aristocracy with a king ruling over military dignity. 6. First ruler, Tang, learned a lot about the downfall of prior dynasty and was the most influential of all the king's to come. 7. Ancestor worship : People offered up their ancestor's souls to God.
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