Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN: 9781305071742
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Cengage Learning
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Chapter 10.4, Problem 48E
To determine

To find:

The dimension of the rectangle.

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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.
+ Theorem: Let be a function from a topological space (X,T) on to a non-empty set y then is a quotient map iff vesy if f(B) is closed in X then & is >Y. ie Bclosed in bp closed in the quotient topology induced by f iff (B) is closed in x- التاريخ Acy الموضوع : Theorem:- IP & and I are topological space and fix sy is continuous او function and either open or closed then the topology Cony is the quatient topology p proof: Theorem: Lety have the quotient topology induced by map f of X onto y. The-x: then an arbirary map g:y 7 is continuous 7. iff gof: x > z is "g of continuous Continuous function f

Chapter 10 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - SKILLS 1314 Graphical MethodTwo equations and...Ch. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Prob. 16ECh. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - SKILLS 1520 Number of Solutions Determined...Ch. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - 2150 Solving a System of Equations Solve the...Ch. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - 2150 Solving a System of Equations Solve the...Ch. 10.1 - 2150 Solving a System of Equations Solve the...Ch. 10.1 - Prob. 33ECh. 10.1 - Prob. 34ECh. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - 21-50Solving a system of linear equationsSolve the...Ch. 10.1 - 21-50Solving a system of linear equationsSolve the...Ch. 10.1 - Prob. 39ECh. 10.1 - Prob. 40ECh. 10.1 - Prob. 41ECh. 10.1 - Prob. 42ECh. 10.1 - 21-50Solving a system of linear equationsSolve the...Ch. 10.1 - Prob. 44ECh. 10.1 - Prob. 45ECh. 10.1 - Prob. 46ECh. 10.1 - Prob. 47ECh. 10.1 - Prob. 48ECh. 10.1 - 2150 Solving a System of Equations Solve the...Ch. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Prob. 52ECh. 10.1 - Prob. 53ECh. 10.1 - Prob. 54ECh. 10.1 - SKILLS Plus 55-58 Solving a General System of...Ch. 10.1 - Prob. 56ECh. 10.1 - Prob. 57ECh. 10.1 - Prob. 58ECh. 10.1 - Prob. 59ECh. 10.1 - Prob. 60ECh. 10.1 - APPLICATIONS Value of Coins A man has 14 coins in...Ch. 10.1 - Prob. 62ECh. 10.1 - Prob. 63ECh. 10.1 - Prob. 64ECh. 10.1 - Prob. 65ECh. 10.1 - Prob. 66ECh. 10.1 - Nutrition A researcher performs an experiment to...Ch. 10.1 - Prob. 68ECh. 10.1 - Prob. 69ECh. 10.1 - Mixture problem A biologist has two brine...Ch. 10.1 - Prob. 71ECh. 10.1 - Prob. 72ECh. 10.1 - APPLICATIONS Distance, Speed, and Time John and...Ch. 10.1 - Prob. 74ECh. 10.1 - Prob. 75ECh. 10.1 - Prob. 76ECh. 10.1 - Prob. 77ECh. 10.2 - 1-2these exercises refer to the following system:...Ch. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - SKILLS 7-12Triangular SystemsUse back-substitution...Ch. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - SKILLS 13-16Eliminating a VariablePerform an...Ch. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - SKILLS 17-38Solving a System of Equations in Three...Ch. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - SKILLS 17-38Solving a System of Equations in Three...Ch. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - SKILLS 17-38Solving a System of Equations in Three...Ch. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - SKILLS 17-38Solving a System of Equations in Three...Ch. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - SKILLS 17-38Solving a System of Equations in Three...Ch. 10.2 - Prob. 38ECh. 10.2 - APPLICATIONS Financial PlanningMark has 100,000 to...Ch. 10.2 - Prob. 40ECh. 10.2 - APPLICATIONS AgricultureA farmer has 1200 acres of...Ch. 10.2 - Gas Station A gas station sells three types of...Ch. 10.2 - Nutrition A biologist is performing an experiment...Ch. 10.2 - Prob. 44ECh. 10.2 - APPLICATIONS Juice Blends The Juice Company offers...Ch. 10.2 - Prob. 46ECh. 10.2 - APPLICATIONS Stock Portfolio An investor owns...Ch. 10.2 - Electricity By using Kirchhoffs Laws, it can be...Ch. 10.2 - Prob. 49ECh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.4 - CONCEPTS 1-2The system of equations {2yx2=0yx=4 is...Ch. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - SKILLS 3-8Substitution MethodUse the substitution...Ch. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - SKILLS 9-14Elimination MethodUse the elimination...Ch. 10.4 - SKILLS 9-14Elimination MethodUse the elimination...Ch. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - SKILLS 15-18Finding Intersection Points...Ch. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - SKILLS 19-32Solving Nonlinear SystemsFind all...Ch. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - SKILLS 19-32Solving Nonlinear SystemsFind all...Ch. 10.4 - SKILLS 19-32Solving Nonlinear SystemsFind all...Ch. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - SKILLS 19-32Solving Nonlinear SystemsFind all...Ch. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - SKILLS 33-40Graphical MethodUse the graphical...Ch. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - SKILLS Plus 41-44Some Tricker SystemsFollow the...Ch. 10.4 - Prob. 44ECh. 10.4 - Prob. 45ECh. 10.4 - Prob. 46ECh. 10.4 - Prob. 47ECh. 10.4 - Prob. 48ECh. 10.4 - APPLICATIONS Flight of a RocketA hill is inclined...Ch. 10.4 - Prob. 50ECh. 10.4 - Global Positioning System GPS The Global...Ch. 10.4 - Prob. 52ECh. 10.5 - Prob. 1ECh. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - Prob. 9ECh. 10.5 - Prob. 10ECh. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Prob. 13ECh. 10.5 - Prob. 14ECh. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - Prob. 32ECh. 10.5 - Prob. 33ECh. 10.5 - Prob. 34ECh. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Prob. 37ECh. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - Prob. 40ECh. 10.5 - Prob. 41ECh. 10.5 - Prob. 42ECh. 10.5 - Prob. 43ECh. 10.5 - Prob. 44ECh. 10.5 - Prob. 45ECh. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.5 - Prob. 50ECh. 10.5 - Prob. 51ECh. 10.5 - Prob. 52ECh. 10.5 - Prob. 53ECh. 10.5 - Prob. 54ECh. 10.5 - Prob. 55ECh. 10.5 - Prob. 56ECh. 10.5 - Prob. 57ECh. 10.5 - Prob. 58ECh. 10.5 - Prob. 59ECh. 10.5 - Prob. 60ECh. 10.5 - Prob. 61ECh. 10.5 - Prob. 62ECh. 10.5 - Prob. 63ECh. 10.5 - Prob. 64ECh. 10.5 - Prob. 65ECh. 10.5 - Prob. 66ECh. 10.5 - Prob. 67ECh. 10.5 - Prob. 68ECh. 10.5 - Prob. 69ECh. 10.5 - Prob. 70ECh. 10.5 - Prob. 71ECh. 10.5 - Prob. 72ECh. 10.5 - APPLICATIONS Coffee BlendsA coffee merchant sells...Ch. 10.5 - Prob. 74ECh. 10.5 - Prob. 75ECh. 10.CR - Prob. 1CCCh. 10.CR - Prob. 2CCCh. 10.CR - What is a system of linear equations in the...Ch. 10.CR - For a system of two linear equations in two...Ch. 10.CR - What operations can be performed on a linear...Ch. 10.CR - aExplain how Gaussian elimination works. bUse...Ch. 10.CR - Prob. 7CCCh. 10.CR - Prob. 8CCCh. 10.CR - Prob. 9CCCh. 10.CR - Prob. 1ECh. 10.CR - Prob. 2ECh. 10.CR - Prob. 3ECh. 10.CR - Prob. 4ECh. 10.CR - Prob. 5ECh. 10.CR - Prob. 6ECh. 10.CR - Prob. 7ECh. 10.CR - Prob. 8ECh. 10.CR - Prob. 9ECh. 10.CR - Prob. 10ECh. 10.CR - Prob. 11ECh. 10.CR - Prob. 12ECh. 10.CR - Prob. 13ECh. 10.CR - Prob. 14ECh. 10.CR - Prob. 15ECh. 10.CR - Prob. 16ECh. 10.CR - Prob. 17ECh. 10.CR - Prob. 18ECh. 10.CR - Prob. 19ECh. 10.CR - Prob. 20ECh. 10.CR - Prob. 21ECh. 10.CR - Prob. 22ECh. 10.CR - Prob. 23ECh. 10.CR - Prob. 24ECh. 10.CR - Prob. 25ECh. 10.CR - Prob. 26ECh. 10.CR - Prob. 27ECh. 10.CR - Prob. 28ECh. 10.CR - Prob. 29ECh. 10.CR - Prob. 30ECh. 10.CR - Prob. 31ECh. 10.CR - Prob. 32ECh. 10.CR - Prob. 33ECh. 10.CR - Prob. 34ECh. 10.CR - Prob. 35ECh. 10.CR - Prob. 36ECh. 10.CR - Prob. 37ECh. 10.CR - Prob. 38ECh. 10.CR - Prob. 39ECh. 10.CR - Prob. 40ECh. 10.CR - Prob. 41ECh. 10.CR - Prob. 42ECh. 10.CR - Prob. 43ECh. 10.CR - Prob. 44ECh. 10.CR - Prob. 45ECh. 10.CR - Prob. 46ECh. 10.CR - Prob. 47ECh. 10.CR - Prob. 48ECh. 10.CR - Prob. 49ECh. 10.CR - Prob. 50ECh. 10.CR - Prob. 51ECh. 10.CR - Prob. 52ECh. 10.CR - Prob. 53ECh. 10.CR - Prob. 54ECh. 10.CR - Prob. 55ECh. 10.CR - Prob. 56ECh. 10.CR - Prob. 57ECh. 10.CR - Prob. 58ECh. 10.CT - Prob. 1CTCh. 10.CT - Prob. 2CTCh. 10.CT - Prob. 3CTCh. 10.CT - Prob. 4CTCh. 10.CT - Prob. 5CTCh. 10.CT - Prob. 6CTCh. 10.CT - Prob. 7CTCh. 10.CT - Prob. 8CTCh. 10.CT - In 212h an airplane travels 600km against the...Ch. 10.CT - Prob. 10CTCh. 10.CT - Prob. 11CTCh. 10.CT - Prob. 12CTCh. 10.CT - Prob. 13CTCh. 10.CT - Prob. 14CTCh. 10.CT - Prob. 15CTCh. 10.CT - Prob. 16CTCh. 10.FOM - PROBLEMS 1-4Find the maximum and minimum values of...Ch. 10.FOM - 1-4 Find the maximum and the minimum values of the...Ch. 10.FOM - 1-4 Find the maximum and minimum values of the...Ch. 10.FOM - Prob. 4PCh. 10.FOM - Making FurnitureA furniture manufacturer makes...Ch. 10.FOM - A Housing DevelopmentA housing contractor has...Ch. 10.FOM - Prob. 7PCh. 10.FOM - Manufacturing Calculators A manufacturer of...Ch. 10.FOM - Shipping TelevisionsAn electronics discount chain...Ch. 10.FOM - Prob. 10PCh. 10.FOM - Prob. 11PCh. 10.FOM - Prob. 12PCh. 10.FOM - Investing in BondsA woman wishes to invest 12,000...Ch. 10.FOM - Prob. 14PCh. 10.FOM - Business StrategyA small software company...Ch. 10.FOM - Feasible RegionAll parts of this problem refer to...
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