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 PL, Problem 3P
Cutting up a Wire A piece of wire is bent as shown in the figure. You can see that one cut through the wire produces four pieces and two parallel cuts produce seven pieces. How many pieces will be produced by 142 parallel cuts? Write a formula for the number of pieces produced by n parallel cuts.
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Chapter PL Solutions
Algebra and Trigonometry (MindTap Course List)
Ch. PL - PROBLEMS Distance, Time, and Speed An old car has...Ch. PL - Comparing Discounts Which price is better for the...Ch. PL - Cutting up a Wire A piece of wire is bent as shown...Ch. PL - Amoeba Propagation An amoeba propagates by simple...Ch. PL - Batting Averages Player A has a higher batting...Ch. PL - Coffee and Cream A spoonful of cream is taken from...Ch. PL - Wrapping the World A ribbon is tied tightly around...Ch. PL - Prob. 8P
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- 1.2.7. (-) Prove that a bipartite graph has a unique bipartition (except for interchang- ing the two partite sets) if and only if it is connected.arrow_forwardSx. KG A3 is collection of Countin uous function on a to Polgical Which separates Points Srem closed set then the toplogy onx is the weak toplogy induced by the map fx. Prove that using dief speParts Point If B closed and x&B in X then for some xеA fx(x) € fa(B). If (π Xx, prodect) is prodect space KEA S Prove s. BxXx (πh Bx) ≤ πTx B x Prove is an A is finte = (πT. Bx) = πT. Bå KEA XEAarrow_forwardShow that is exist homomor Pick to Subspace Product. to plogy. Prove that Pen Projection map TTB: TTX XB is countiunals and open map but hot closed map.arrow_forward
- @when ever one Point sets in x are closed a collection of functions which separates Points from closed set will separates Point. 18 (prod) is product topological space then VaeA (xx, Tx) is homeomorphic to sul space of the Product space (Txa, prod). KeA © The Bin Projection map B: Tx XP is continuous and open but heed hot to be closed. A collection (SEA) of continuos function oha topolgical Space X se partes Points from closed sets inx iff the set (v) for KEA and Vopen set in Xx from a base for top on x.arrow_forwardSimply:(p/(x-a))-(p/(x+a))arrow_forwardQ1lal 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 -…arrow_forward
- 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.arrow_forward+ 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 farrow_forwardFor the problem below, what are the possible solutions for x? Select all that apply. 2 x²+8x +11 = 0 x2+8x+16 = (x+4)² = 5 1116arrow_forward
- For the problem below, what are the possible solutions for x? Select all that apply. x² + 12x - 62 = 0 x² + 12x + 36 = 62 + 36 (x+6)² = 98arrow_forwardSelect the polynomials below that can be solved using Completing the Square as written. 6m² +12m 8 = 0 Oh²-22x 7 x²+4x-10= 0 x² + 11x 11x 4 = 0arrow_forwardProve that the usual toplogy is firast countble or hot and second countble. ①let cofinte toplogy onx show that Sivast countble or hot and second firast. 3) let (x,d) be matricspace show that is first and second countble. 6 Show that Indiscret toplogy is firstand Second op countble or not.arrow_forward
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