The Heart of Mathematics: An Invitation to Effective Thinking

4th Edition

ISBN: 9781118156599

Author: Edward B. Burger, Michael Starbird

Publisher: Wiley, John & Sons, Incorporated

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Chapter 4.3, Problem 27MS

Special K. As a student at the University of Ketchikan in Ketchikan, Alaska, you decide to create a new logo for the school’s dogsled team, the Special Ks. Your design involves a Golden Rectangle with its height of length l and its base of length 1. You block off a square as shown in the figure, and then draw a K using the diagonals of the square at the bottom and the smaller rectangle at the top. Find the area of the red square and the area of the black rectangle. Also find the length of the lower diagonal of the K. (You’ll need the Pythagorean Theorem from Section 4.1.)

Chapter 4.3, Problem 27MS, Special K. As a student at the University of Ketchikan in Ketchikan, Alaska, you decide to create a

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Chapter 4.3, Problem 26MS

Chapter 4.3, Problem 28MS

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1. Prove the following arguments using the rules of inference. Do not make use of conditional proof. (а) а → (ЪЛс) ¬C ..¬a (b) (pVq) → →r יור (c) (c^h) → j ¬j h (d) s→ d t d -d ..8A-t (e) (pVg) (rv¬s) Лѕ קר .'

The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = 1. Select all that apply: ☐ f(x) is not continuous at x = 1 because it is not defined at x = 1. ☐ f(x) is not continuous at x = 1 because lim f(x) does not exist. x+1 ☐ f(x) is not continuous at x = 1 because lim f(x) ‡ f(1). x+→1 ☐ f(x) is continuous at x = 1.

2. Consider the following argument: (a) Seabiscuit is a thoroughbred. Seabiscuit is very fast. Every very fast racehorse can win the race. .. Therefore, some thoroughbred racehorse can win the race. Let us define the following predicates, whose domain is racehorses: T(x) x is a thoroughbred F(x) x is very fast R(x) x can win the race : Write the above argument in logical symbols using these predicates. (b) Prove the argument using the rules of inference. Do not make use of conditional proof. (c) Rewrite the proof using full sentences, avoiding logical symbols. It does not need to mention the names of rules of inference, but a fellow CSE 16 student should be able to understand the logical reasoning.

Chapter 4 Solutions

The Heart of Mathematics: An Invitation to Effective Thinking

Ch. 4.1 - The main event. State the Pythagorean Theorem.Ch. 4.1 - Two out of three. If a right triangle has legs of...Ch. 4.1 - Hypotenuse hype. If a right triangle has legs of...Ch. 4.1 - Assesing area. Suppose you know the base of a...Ch. 4.1 - Squares all around. How does the figure below...Ch. 4.1 - Operating on the triangle. Using a straightedge,...Ch. 4.1 - Excite your friends about right triangles....Ch. 4.1 - Easy as 1,2,3? Can there be a right triangle with...Ch. 4.1 - Sky high (S). On a sunny, warm day, a student...Ch. 4.1 - Sand masting (H). The sailboat named Sand Bug has...

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