Prealgebra & Introductory Algebra (4th Edition)
4th Edition
ISBN: 9780321955791
Author: Elayn Martin-Gay
Publisher: PEARSON
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Question
Chapter 3.3, Problem 3CE
To determine
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Chapter 3 Solutions
Prealgebra & Introductory Algebra (4th Edition)
Ch. 3.1 - Prob. 1CCCh. 3.1 - Prob. 2CCCh. 3.1 - Prob. 1PCh. 3.1 - Prob. 2PCh. 3.1 - Prob. 3PCh. 3.1 - Prob. 4PCh. 3.1 - Prob. 5PCh. 3.1 - Prob. 6PCh. 3.1 - Prob. 7PCh. 3.1 - Prob. 8P
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Prob. 7IRCh. 3.IR - Prob. 8IRCh. 3.IR - Prob. 9IRCh. 3.IR - Prob. 10IRCh. 3.IR - Prob. 11IRCh. 3.IR - Prob. 12IRCh. 3.IR - Prob. 13IRCh. 3.IR - Prob. 14IRCh. 3.IR - Prob. 15IRCh. 3.IR - Prob. 16IRCh. 3.IR - Prob. 17IRCh. 3.IR - Prob. 18IRCh. 3.IR - Prob. 19IRCh. 3.IR - Prob. 20IRCh. 3.IR - Prob. 21IRCh. 3.IR - Prob. 22IRCh. 3.IR - Prob. 23IRCh. 3.IR - Prob. 24IRCh. 3.IR - Prob. 25IRCh. 3.IR - Prob. 26IRCh. 3.IR - Prob. 27IRCh. 3.IR - Prob. 28IRCh. 3.IR - Prob. 29IRCh. 3.IR - Prob. 30IRCh. 3.IR - Prob. 31IRCh. 3.IR - Prob. 32IRCh. 3.IR - Prob. 33IRCh. 3.IR - Prob. 34IRCh. 3.IR - Prob. 35IRCh. 3.IR - Prob. 36IRCh. 3.IR - Prob. 37IRCh. 3.IR - Prob. 38IRCh. 3.IR - Prob. 39IRCh. 3.IR - Prob. 40IRCh. 3.3 - Prob. 1CCCh. 3.3 - Prob. 1PCh. 3.3 - Prob. 2PCh. 3.3 - Prob. 3PCh. 3.3 - Prob. 4PCh. 3.3 - Prob. 5PCh. 3.3 - Prob. 1VRVCCh. 3.3 - Prob. 2VRVCCh. 3.3 - Prob. 3VRVCCh. 3.3 - Prob. 4VRVCCh. 3.3 - Prob. 5VRVCCh. 3.3 - Prob. 6VRVCCh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - 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Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46ECh. 3.4 - Prob. 47ECh. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Prob. 50ECh. 3.4 - Prob. 51ECh. 3.4 - Prob. 52ECh. 3.4 - Prob. 53ECh. 3.4 - Prob. 54ECh. 3.4 - Prob. 55ECh. 3.4 - Prob. 56ECh. 3.4 - Prob. 57ECh. 3.4 - Prob. 58ECh. 3.4 - Prob. 59ECh. 3.4 - Prob. 60ECh. 3.GA - Prob. 1GACh. 3.GA - 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- 5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I purposefully removed the units- don't worry about them. Assume no conversions are needed.) a) Find the equation for the displacement of the spring mass at time t. b) Write the equation for the displacement of the spring mass in phase-mode form. c) Characterize the damping of the spring mass system as overdamped, underdamped or critically damped. Explain how you know. D.E. for Spring Mass Systems k m* g = kLo y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo m 2 A₁ = √c₁² + C₂² Q = tan-1arrow_forward4. Given the following information determine the appropriate trial solution to find yp. Do not solve the differential equation. Do not find the constants. a) (D-4)2(D+ 2)y = 4e-2x b) (D+ 1)(D² + 10D +34)y = 2e-5x cos 3xarrow_forward9.7 Given the equations 0.5x₁-x2=-9.5 1.02x₁ - 2x2 = -18.8 (a) Solve graphically. (b) Compute the determinant. (c) On the basis of (a) and (b), what would you expect regarding the system's condition? (d) Solve by the elimination of unknowns. (e) Solve again, but with a modified slightly to 0.52. Interpret your results.arrow_forward
- 3. Determine the appropriate annihilator for the given F(x). a) F(x) = 5 cos 2x b) F(x)=9x2e3xarrow_forward12.42 The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, 0= FT T + 200°C 25°C 25°C T22 0°C T₁ T21 200°C FIGURE P12.42 75°C 75°C 00°C If the plate is represented by a series of nodes (Fig. P12.42), cen- tered finite-divided differences can be substituted for the second derivatives, which results in a system of linear algebraic equations. Use the Gauss-Seidel method to solve for the temperatures of the nodes in Fig. P12.42.arrow_forward9.22 Develop, debug, and test a program in either a high-level language or a macro language of your choice to solve a system of equations with Gauss-Jordan elimination without partial pivoting. Base the program on the pseudocode from Fig. 9.10. Test the program using the same system as in Prob. 9.18. Compute the total number of flops in your algorithm to verify Eq. 9.37. FIGURE 9.10 Pseudocode to implement the Gauss-Jordan algorithm with- out partial pivoting. SUB GaussJordan(aug, m, n, x) DOFOR k = 1, m d = aug(k, k) DOFOR j = 1, n aug(k, j) = aug(k, j)/d END DO DOFOR 1 = 1, m IF 1 % K THEN d = aug(i, k) DOFOR j = k, n aug(1, j) END DO aug(1, j) - d*aug(k, j) END IF END DO END DO DOFOR k = 1, m x(k) = aug(k, n) END DO END GaussJordanarrow_forward
- 11.9 Recall from Prob. 10.8, that the following system of equations is designed to determine concentrations (the e's in g/m³) in a series of coupled reactors as a function of amount of mass input to each reactor (the right-hand sides are in g/day): 15c3cc33300 -3c18c26c3 = 1200 -4c₁₂+12c3 = 2400 Solve this problem with the Gauss-Seidel method to & = 5%.arrow_forward9.8 Given the equations 10x+2x2-x3 = 27 -3x-6x2+2x3 = -61.5 x1 + x2 + 5x3 = -21.5 (a) Solve by naive Gauss elimination. Show all steps of the compu- tation. (b) Substitute your results into the original equations to check your answers.arrow_forwardTangent planes Find an equation of the plane tangent to the following surfaces at the given points (two planes and two equations).arrow_forward
- Vectors u and v are shown on the graph.Part A: Write u and v in component form. Show your work. Part B: Find u + v. Show your work.Part C: Find 5u − 2v. Show your work.arrow_forwardVectors u = 6(cos 60°i + sin60°j), v = 4(cos 315°i + sin315°j), and w = −12(cos 330°i + sin330°j) are given. Use exact values when evaluating sine and cosine.Part A: Convert the vectors to component form and find −7(u • v). Show every step of your work.Part B: Convert the vectors to component form and use the dot product to determine if u and w are parallel, orthogonal, or neither. Justify your answer.arrow_forwardSuppose that one factory inputs its goods from two different plants, A and B, with different costs, 3 and 7 each respective. And suppose the price function in the market is decided as p(x, y) = 100 - x - y where x and y are the demand functions and 0 < x, y. Then as x = y= the factory can attain the maximum profit,arrow_forward
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