EBK MATHEMATICS FOR MACHINE TECHNOLOGY
7th Edition
ISBN: 9780100548169
Author: SMITH
Publisher: YUZU
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Chapter 77, Problem 4A
To determine
To find the length of the diagonal
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Question 1. Prove that the function f(x) = 2; f: (2,3] → R, is not uniformly
continuous on (2,3].
Consider the cones
K =
= {(x1, x2, x3) | € R³ :
X3
≥√√√2x² + 3x²
M =
= {(21,22,23)
(x1, x2, x3) Є R³: x3 >
+
2
3
Prove that M = K*.
Hint: Adapt the proof from the lecture notes for finding the dual of the Lorentz cone. Alternatively, prove the
formula (AL)* = (AT)-¹L*, for any cone LC R³ and any 3 × 3 nonsingular matrix A with real entries, where
AL = {Ax = R³ : x € L}, and apply it to the 3-dimensional Lorentz cone with an appropriately chosen matrix
A.
I am unable to solve part b.
Chapter 77 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 77 - Prob. 1ACh. 77 - Prob. 2ACh. 77 - Prob. 3ACh. 77 - Prob. 4ACh. 77 - Determine the arc dimension x in inches to 3...Ch. 77 - Prob. 6ACh. 77 - Prob. 7ACh. 77 - Prob. 8ACh. 77 - Prob. 9ACh. 77 - Prob. 10A
Ch. 77 - In each of Exercises 11 through 14, three Views of...Ch. 77 - Prob. 12ACh. 77 - Prob. 13ACh. 77 - In each of Exercises 11 through 14, three Views of...Ch. 77 - Prob. 15ACh. 77 - Prob. 16ACh. 77 - Prob. 17ACh. 77 - Prob. 18ACh. 77 - Prob. 19ACh. 77 - Prob. 20ACh. 77 - Prob. 21ACh. 77 - Prob. 22ACh. 77 - Prob. 23ACh. 77 - Prob. 24ACh. 77 - Prob. 25ACh. 77 - Prob. 26ACh. 77 - Prob. 27ACh. 77 - Prob. 28ACh. 77 - Prob. 29ACh. 77 - Prob. 30A
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- 12.42 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_forward11.9 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_forward
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