Math141HW5F11Shortened

Math141HW5F11Shortened - (Exercises for Chapter 7: Systems...

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(Exercises for Chapter 7: Systems and Inequalities) E.7.1 CHAPTER 7: Systems and Inequalities (A) means “refer to Part A,” (B) means “refer to Part B,” etc. (Calculator) means “use a calculator.” Otherwise, do not use a calculator. SECTIONS 7.1-7.3: SYSTEMS OF EQUATIONS When solving a system, only give solutions in ± 2 , the set of ordered pairs of real numbers. All such solutions correspond to intersection points of the graphs of the given equations. If there are no such solutions, write ± , the empty set or null set. Write solutions in a solution set as ordered pairs of the form x , y () . Unless otherwise specified, do not rely on graphing or “trial-and-error point-plotting.” 1) Consider the system x + y = 5 5 x ± 3 y = ± 23 ² ³ ´ . (A-E) a) The graphs of the equations in the system are distinct lines in the xy -plane that are not parallel. How many solutions does this system have? b) Solve the system using the Substitution Method. c) Solve the system using the Addition / Elimination Method. 2) Consider the system x 2 + y 2 = 2 y = x + 2 ± ² ³ . (A-D) a) Find the solution set of the system. b) Use the solution set from a) to graph the equations in the system in the usual xy -plane. 3) Consider the system x 2 + y 2 = 3 2 y 2 = x 2 ± ² ³ ´ ³ . (A-D) a) What are the graphs of the equations in the system in the usual xy -plane? b) How many solutions does the system have? c) Find the solution set of the system.
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(Exercises for Chapter 7: Systems and Inequalities) E.7.2 4) Consider the system x = y 2 x = 4 ± y 2 ² ³ ´ µ ´ . (A-D; Section 1.8) a) What are the graphs of the equations in the system in the usual xy -plane? b) How many solutions does the system have? c) Find the solution set of the system. 5) Consider the system x 2 + y = 0 y ± x 2 = 1 ² ³ ´ µ ´ . (A-D, F) a) Sketch graphs of the equations in the system in the usual xy -plane. b) Based on your graphs in a), find the solution set of the system. c) Verify the solution set by using the Substitution Method or the Addition / Elimination Method to solve the system. 6) Solve the following systems. (A-D, F) a) y = 3 x 2 ± x y = 2 x 2 ± 3 x + 8 ² ³ ´ µ ´ b) x 2 + 4 y 2 = 2 3 x ± 2 y = ± 4 ² ³ ´ c) x 2 + y 2 = 1 x 2 ± y 2 = 4 ² ³ ´ µ ´ 7) ADDITIONAL PROBLEM. Solve the system 0 = 0 0 = 1 ± ² ³ . (A-D, F)
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(Exercises for Chapter 7: Systems and Inequalities) E.7.3 SECTION 7.4: PARTIAL FRACTIONS 1) Write the PFD (Partial Fraction Decomposition) Form for the following. Do not find the unknowns ( A , B , etc.). (A-C) a) 1 x + 4 () x ± 3 x 2 + 1 b) x + 5 x 3 x ± 1 2 x 2 + 3 2 c) 3 t 2 + 2 t ± 2 t 2 2 t + 5 3 2 t 2 + 5 t 2 + t + 1 2) Write the PFD (Partial Fraction Decomposition) for the following. (A-G) a) 3 x ± 5 x 2 ± 5 x + 6 b) 2 x 2 ± 3 x + 19 x 3 + 4 x 2 ± 7 x ± 10 . (Hint: Use the Rational Zero Test and Synthetic Division.) c) 9 x 2 + 14 x + 6 2 x 3 + x 2 d) x + 1 x 2 ± 8 x + 16 e) 8 x 2 + 7 x + 12 x + 2 x 2 + 1 f) 5 x 2 ± 5 x + 12 x 3 ± 5 x 2 + 3 x ± 15 . (Hint: Use Factoring by Grouping.) g) ± 5 x 2 ± 8 x ± 3 x 3 + x 2 + x h) 5 t 3 ± t 2 + 20 t ± 8 t 2 + 4 2 3) A student writes: x 4 x + 3 x + 5 = A x + 3 + B x + 5 . Is this appropriate? Why or why not?
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(Exercises for Chapter 8: Matrices and Determinants) E.8.1 CHAPTER 8:
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Math141HW5F11Shortened - (Exercises for Chapter 7: Systems...

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