(a) To determine To explain: What type of graph is represented by the equation y = 9 − ( x − 2 ) 2 . Explanation Formula used: The standard equation of the circle with center at ( h , k ) and radius r is ( x − h ) 2 + ( y − k ) 2 = r 2 . Calculation: Consider the given equation y = 9 − ( x − 2 ) 2 . Simplify the equation as follows, y = 9 − ( x − 2 ) 2 y 2 = 9 − ( x − 2 ) 2 ( x − 2 ) 2 + y 2 = 9 ( x (b) To determine To explain: What type of graph is represented by the equation y = − 9 − ( x − 2 ) 2 . (c) To determine To explain: Are the equations in parts (a) and (b) functions?

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 21.3, Problem 53E

(a)

To determine

To explain: What type of graph is represented by the equation y=9−(x−2)2.

(b)

To determine

To explain: What type of graph is represented by the equation y=−9−(x−2)2 .

(c)

To determine

To explain: Are the equations in parts (a) and (b) functions?

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Chapter 21.3, Problem 52E

Chapter 21.3, Problem 54E

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Example: For what odd primes p is 11 a quadratic residue modulo p? Solution: This is really asking "when is (11 | p) =1?" First, 11 = 3 (mod 4). To use LQR, consider two cases p = 1 or 3 (mod 4): p=1 We have 1 = (11 | p) = (p | 11), so p is a quadratic residue modulo 11. By brute force: 121, 224, 3² = 9, 4² = 5, 5² = 3 (mod 11) so the quadratic residues mod 11 are 1,3,4,5,9. Using CRT for p = 1 (mod 4) & p = 1,3,4,5,9 (mod 11). p = 1 (mod 4) & p = 1 (mod 11 gives p 1 (mod 44). p = 1 (mod 4) & p = 3 (mod 11) gives p25 (mod 44). p = 1 (mod 4) & p = 4 (mod 11) gives p=37 (mod 44). p = 1 (mod 4) & p = 5 (mod 11) gives p 5 (mod 44). p = 1 (mod 4) & p=9 (mod 11) gives p 9 (mod 44). So p =1,5,9,25,37 (mod 44).

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Chapter 21 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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