In the damped harmonic oscillator, we assume that the coefficients m, b, and k are positive. However, the rationale underlying the guess-and-test method made no such assumption, and the same analytic technique can be used if some or all of the coefficients of the equation are negative. In Exercises 5 and 6, make the same graphs and perform the same calculations as were specified in Exercises 1—4. What is different in this case?
6.
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- 2.4 Practice In Exercises 1–3, solve the equatior 1. 3x + 4 = 31 3-27 2. 7-3 In Exercises 4–6, solve the equatic 4. p = 2v; v In Exercises 7 and 8, name the pr 7. If x = y, then -2x = -2y. 8. If mZA = mZB and mZB In Exercises 9–11, use the prop 9. Addition Property of Equa!arrow_forwardExercises 38–40 will help you prepare for the material covered in the first section of the next chapter. In Exercises 38-39, simplify each algebraic expression. 38. (-9x³ + 7x? - 5x + 3) + (13x + 2r? – &x – 6) 39. (7x3 – 8x? + 9x – 6) – (2x – 6x? – 3x + 9) 40. The figures show the graphs of two functions. y y 201 10- .... -20- flx) = x³ glx) = -0.3x + 4x + 2arrow_forward*There are two solutions to the equation (x – 1)3 – 9 = 0. Find both and enter them below as whole numbers.arrow_forward
- You may find it helpful to review the information in the Reasonable Answers box from this section before answering Exercises 13–16. Verify that the solutions you found to Exercise 9 are indeed homogeneous solutions.arrow_forwardQuestion 2 Evaluate 2x /xb +c + D. 9.arrow_forwardExercises 7–12: Determine whether the equation is linear or nonlinear by trying to write it in the form ax + b = 0. 7. 3x – 1.5 = 7arrow_forward
- In Exercises 9–12, find all real solutions to the equations.arrow_forwardFor Exercises 54–60, a. List all possible rational roots or rational zeros. b. Use Descartes's Rule of Signs to determine the possible number of positive and negative real roots or real zeros. c. Use synthetic division to test the possible rational roots or zeros and find an actual root or zero. d. Use the quotient from part (c) to find all the remaining roots or zeros. 54. f(x) = x' + 3x² – 4 55. flx) = 6x + x² – 4x + 1 %3D 56. 8x - 36xr? + 46x - 15 = 0 57. 2x + 9x2 - 7x + 1 = 0 58. x* - x - 7x2 + x + 6 = 0 59. 4x* + 7x - 2 = 0 60. f(x) = 2x* + x³ – 9x² – 4x + 4arrow_forward(1 point) Suppose that c · + d. 4 Find the values of c and d. c = d =arrow_forward
- Please give the reasoning for each of your answers (Y/N) for the table. Thank you!arrow_forwardIn Problems 37–42, analyze each rational functionarrow_forwardSubtract 1.2a“ – 0.7a from the sum of 0.6 a4 + 1.5a and 0.4 a4 - 1.1a First, we will translate the words of the problem into mathematical symbols. Then we will perform the indicated operations. The words of the problem contain the key phrases subtract from and sum. Since 1.2a4 – 0.7a is to be subtracted from the sum, the order must be reversed when we translate to mathematical symbols. Subtract 1.2a4 0.7a from the sum of 0.6a + 1.5a and 0.4a4 1.1a. [(0.6 a4 + 1.5a) + (0.4 at – 1.1a) ] - (1.2a* – 0.7a) Use brackets [ ] to enclose the sum. Next, we remove the grouping symbols to obtain 0.6 a4 + 1.5a + 0.4 at – 1.1a -1.2a4 + 0.7a Change the sign of each term within (1.2a4 - 0.7a) and drop the parentheses. at+ a Combine like terms. %D Subtract -0.6q? – 0.6q from the sum of 0.1q? - 0.6q and 0.3q² + 0.1q.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage