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An 8-in.-diameter cylindrical duct and a 4 8-in. rectangular duct are to be joined as

Vector Mechanics for Engineers: Statics | 10th Edition | ISBN: 9780077402280 | Authors: Ferdinand Beer, E. Russell Johnston Jr., David Mazurek ISBN: 9780077402280 491

Solution for problem 5.112 Chapter 5

Vector Mechanics for Engineers: Statics | 10th Edition

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Vector Mechanics for Engineers: Statics | 10th Edition | ISBN: 9780077402280 | Authors: Ferdinand Beer, E. Russell Johnston Jr., David Mazurek

Vector Mechanics for Engineers: Statics | 10th Edition

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Problem 5.112

An 8-in.-diameter cylindrical duct and a 4 8-in. rectangular duct are to be joined as indicated. Knowing that the ducts were fabricated from the same sheet metal, which is of uniform thickness, locate the center of gravity of the assembly.

Step-by-Step Solution:
Step 1 of 3

Definition 1.1. Given two integers a and d with d non-zero, we say that d divides a (written d | a) if there is an integer c with a = cd. If no such integer exists, so d does not divide a, we write d - a. If d divides a, we say that d is a divisor of a. Proposition 1.2.1: Assume that a, b, and c are integers. If a | b and b | c, then a | c. Proposition 1.3. Assume that a, b, d, x, and y are integers. If d | a and d | b, then d | ax + by. Corollary 1.4. Assume that a, b, and d are integers. If d | a and d | b, then d | a + b and d | a − b. Proposition 1.4. Let a, b, c ∈ Z be integers. a) If a | b and b | c, then a | c. b) If a | b and b | a, then a = ±b. c) If a | b and a | c, then a | (b + c) and a | (b − c). Prime: A prime number is an integer p ≥ 2 whose only divisors are

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Chapter 5, Problem 5.112 is Solved
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Textbook: Vector Mechanics for Engineers: Statics
Edition: 10
Author: Ferdinand Beer, E. Russell Johnston Jr., David Mazurek
ISBN: 9780077402280

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An 8-in.-diameter cylindrical duct and a 4 8-in. rectangular duct are to be joined as