Explanation The given equations are as follows: 2 x 2 − y 2 = 8 … … ( 1 ) 4 x 2 + y 2 = 16 … … ( 2 ) Now, add equation (1) in equation (2), to eliminate the variable y as follows: 2 x 2 − y 2 = 8 4 x 2 + y 2 = 16 _ 6 x 2 = 24 Simplify the obtained equation as follows: 6 x 2 = 24 x 2 = 4 ( Divide by 4 ) x = ± 2 ( Square root ) x = 2 or − 2 Therefore, the two values of x are x = − 2 and x = 2 . Now, substitute − 2 for x in one of the given equation and obtain the value for y . Replace x by − 2 in the equation (1)

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ISBN: 9780134696522

Author: HORNSBY, John, Lial, Margaret L., Rockswold, Gary K.

Publisher: Pearson Education, Inc.,

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Chapter 8, Problem 53RE

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To solve: The system of nonlinear equations 2x2−y2=8 and 4x2+y2=16.

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Chapter 8, Problem 52RE

Chapter 8, Problem 54RE

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Simply:(p/(x-a))-(p/(x+a))

Q1lal Let X be an arbitrary infinite set and let r the family of all subsets F of X which do not contain a particular point x, EX and the complements F of all finite subsets F of X show that (X.r) is a topology. bl The nbhd system N(x) at x in a topological space X has the following properties NO- N(x) for any xX N1- If N EN(x) then x€N N2- If NEN(x), NCM then MeN(x) N3- If NEN(x), MEN(x) then NOMEN(x) N4- If N = N(x) then 3M = N(x) such that MCN then MeN(y) for any уем Show that there exist a unique topology τ on X. Q2\a\let (X,r) be the topology space and BST show that ẞ is base for a topology on X iff for any G open set xEG then there exist A Eẞ such that x E ACG. b\Let ẞ is a collection of open sets in X show that is base for a topology on X iff for each xex the collection B, (BEB\xEB) is is a nbhd base at x. - Q31 Choose only two: al Let A be a subspace of a space X show that FCA is closed iff F KOA, K is closed set in X. الرياضيات b\ Let X and Y be two topological space and f:X -…

Q1\ Let X be a topological space and let Int be the interior operation defined on P(X) such that 1₁.Int(X) = X 12. Int (A) CA for each A = P(X) 13. Int (int (A) = Int (A) for each A = P(X) 14. Int (An B) = Int(A) n Int (B) for each A, B = P(X) 15. A is open iff Int (A) = A Show that there exist a unique topology T on X. Q2\ Let X be a topological space and suppose that a nbhd base has been fixed at each x E X and A SCX show that A open iff A contains a basic nbdh of each its point Q3\ Let X be a topological space and and A CX show that A closed set iff every limit point of A is in A. A'S A ACA Q4\ If ẞ is a collection of open sets in X show that ẞ is a base for a topology on X iff for each x E X then ẞx = {BE B|x E B} is a nbhd base at x. Q5\ If A subspace of a topological space X, if x Є A show that V is nbhd of x in A iff V = Un A where U is nbdh of x in X.

Chapter 8 Solutions

Graphical Approach To College Algebra

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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Orbit of the Comet Swift-Tuttle Comet Swift–Tuttle...Ch. 8 - Prob. 61RE Ch. 8 - Prob. 62RE Ch. 8 - Prob. 63RE Ch. 8 - Prob. 64RE Ch. 8 - Prob. 1T Ch. 8 - Prob. 2T Ch. 8 - Prob. 3T Ch. 8 - Prob. 4T Ch. 8 - Prob. 5T Ch. 8 - Prob. 6T Ch. 8 - Prob. 7T Ch. 8 - Prob. 8T Ch. 8 - Graph each relation by hand. Identify the graph,...Ch. 8 - Prob. 10T Ch. 8 - Prob. 11T Ch. 8 - Prob. 12T Ch. 8 - Prob. 13T Ch. 8 - Prob. 14T Ch. 8 - Prob. 15T Ch. 8 - Prob. 16T

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The system of nonlinear equations 2 x 2 − y 2 = 8 and 4 x 2 + y 2 = 16 .

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To solve: The system of nonlinear equations 2x2−y2=8 and 4x2+y2=16.

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Chapter 8 Solutions