Explanation The given system of equations is { x 2 − y 2 = 4 x y = 2 . The first equation can be write in terms y as follows. x 2 − y 2 = 4 y 2 = x 2 − 4 y = ± x 2 − 4 Write the above system equations in terms of y by denoting y 1 , y 2 , and y 3 as follows. { y 1 = x 2 − 4 y 2 = − x 2 − 4 y 3 = 2 x The solution of the above system is obtained by finding the intersection points of the above three functions. Plot the graph of the functions y 1 = x 2 − 4 , y 2 = − x 2 − 4 and y 3 = 2 x and obtain the solutions using TI-83 plus calculator as shown below in Screen shot

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 14, Problem 7PT

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To solve: The given system of equations graphically using graphing calculator.

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Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., 2 p-1 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. 23 The set T is the subset of these residues exceeding 2° So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1. how come?

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Chapter 14 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 14.1 - In Example 7, determine how many times the rocket...Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E

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