Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 6, Problem 15A

Four studs of the following lengths in inches are to be machined from bar stock: 1 3 ' ' 4 , 1 7 ' ' 8 , 2 5 ' ' 16 and 1 11 ' ' 32 . Allow 1 8 inch waste for each cut and 1 32 inch on each end of each stud for facing. What is the shortest length of bar stock required so that only three cuts are needed?

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3. Solve the Heat Equation with Initial and Boundary Conditions Turn to page 71 for the heat equation problem. Solve the partial differential equation using Fourier series or another suitable method, given the initial and boundary conditions. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Provide all derivations and intermediate steps.
2. Classify the Stability of Fixed Points in a Dynamical System The dynamical system problem is located on page 60 of the file. Identify the fixed points and classify their stability using linearization and eigenvalues. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Provide a detailed explanation of your analysis.
Evaluate the Z-Transform of the Sequence The Z-transform problem is provided on page 70. Compute the Z-transform of the given sequence and determine the region of convergence. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Show all steps and provide detailed reasoning.
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