BEG+INTERMEDIATE ALG CNCT MATH ALEKS AC
BEG+INTERMEDIATE ALG CNCT MATH ALEKS AC
5th Edition
ISBN: 9781265677299
Author: Miller
Publisher: MCG CUSTOM
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Chapter 14, Problem 17CRE

For Exercises 14–17, factor completely.

w 3 + 9 w 2 4 w 36

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(1) Let F be a field, show that the vector space F,NEZ* be a finite dimension. (2) Let P2(x) be the vector space of polynomial of degree equal or less than two and M={a+bx+cx²/a,b,cЄ R,a+b=c),show that whether Mis hyperspace or not. (3) Let A and B be a subset of a vector space such that ACB, show that whether: (a) if A is convex then B is convex or not. (b) if B is convex then A is convex or not. (4) Let R be a field of real numbers and X=R, X is a vector space over R show that by definition the norms/II.II, and II.112 on X are equivalent where Ilxll₁ = max(lx,l, i=1,2,...,n) and llxll₂=(x²). oper (5) Let Ⓡ be a field of real numbers, Ⓡis a normed space under usual operations and norm, let E=(2,5,8), find int(E), b(E) and D(E). (6) Write the definition of bounded linear function between two normed spaces and write with prove the relation between continuous and bounded linear function between two normed spaces.
ind → 6 Q₁/(a) Let R be a field of real numbers and X-P(x)=(a+bx+cx²+dx/ a,b,c,dER},X is a vector space over R, show that is finite dimension. (b) Let be a bijective linear function from a finite dimension vector ✓ into a space Yand Sbe a basis for X, show that whether f(S) basis for or not. (c) Let be a vector space over a field F and A,B)affine subsets of X,show that whether aAn BB, aAU BB be affine subsets of X or not, a,ẞ EF. (12 Jal (answer only two) (6) Let M be a non-empty subset of a vector space X and tEX, show that M is a hyperspace of X iff t+M is a hyperplane of X and tЄt+M. (b) State Jahn-Banach theorem and write with prove an application of Hahn-
(b) Let A and B be two subset of a linear space X such that ACB, show that whether if A is affine set then B affine or need not and if B affine set then A affine set or need not. Qz/antonly be a-Show that every hyperspace of a vecor space X is hyperplane but the convers need not to be true. b- Let M be a finite dimension subspace of a Banach space X show that M is closed set. c-Show that every two norms on finite dimension vector space are equivant (1) Q/answer only two a-Write the definition of bounded set in: a normed space and write with prove an equivalent statement to a definition. b- Let f be a function from a normed space X into a normed space Y, show that f continuous iff f is bounded. c-Show that every finite dimension normed space is a Banach. Q/a- Let A and B two open sets in a normed space X, show that by definition AnB and AUB are open sets. (1 nood true

Chapter 14 Solutions

BEG+INTERMEDIATE ALG CNCT MATH ALEKS AC

Ch. 14.1 - 11. Find the fifth term of . Ch. 14.1 - a. The expanded form of ( x + b ) 2 =...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 2–7, expand the binomials. Use...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For Exercises 8–13, rewrite each binomial of the...Ch. 14.1 - For a > 0 and b > 0 , what happens to the signs of...Ch. 14.1 - For Exercises 15–18, evaluate the expression. (See...Ch. 14.1 - For Exercises 15–18, evaluate the expression. (See...Ch. 14.1 - For Exercises 15–18, evaluate the expression. (See...Ch. 14.1 - For Exercises 15–18, evaluate the expression. (See...Ch. 14.1 - True or false: 0 ! ≠ 1 !Ch. 14.1 - True or false: n! is defined for negative...Ch. 14.1 - True or false: n ! = n for n = 1 and 2 .Ch. 14.1 - 22. Show that ! Ch. 14.1 - Show that 6 ! = 6 ⋅ 5 !Ch. 14.1 - Show that 8 ! = 8 ⋅ 7 !Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - For Exercises 25–32, evaluate the expression. (See...Ch. 14.1 - Prob. 33PECh. 14.1 - Prob. 34PECh. 14.1 - Prob. 35PECh. 14.1 - For Exercises 33–36, find the first three terms of...Ch. 14.1 - Prob. 37PECh. 14.1 - Prob. 38PECh. 14.1 - Prob. 39PECh. 14.1 - Prob. 40PECh. 14.1 - For Exercises 39–50, use the binomial theorem to...Ch. 14.1 - Prob. 42PECh. 14.1 - Prob. 43PECh. 14.1 - Prob. 44PECh. 14.1 - Prob. 45PECh. 14.1 - For Exercises 39–50, use the binomial theorem to...Ch. 14.1 - Prob. 47PECh. 14.1 - For Exercises 39–50, use the binomial theorem to...Ch. 14.1 - Prob. 49PECh. 14.1 - Prob. 50PECh. 14.1 - Prob. 51PECh. 14.1 - Prob. 52PECh. 14.1 - Prob. 53PECh. 14.1 - Prob. 54PECh. 14.1 - Prob. 55PECh. 14.1 - For Exercises 51–56, find the indicated term of...Ch. 14.2 - Prob. 1SPCh. 14.2 - Prob. 2SPCh. 14.2 - Prob. 3SPCh. 14.2 - Prob. 4SPCh. 14.2 - Prob. 5SPCh. 14.2 - Prob. 6SPCh. 14.2 - Prob. 7SPCh. 14.2 - Prob. 8SPCh. 14.2 - Prob. 9SPCh. 14.2 - Prob. 10SPCh. 14.2 - Prob. 11SPCh. 14.2 - Prob. 12SPCh. 14.2 - Prob. 1PECh. 14.2 - Prob. 2PECh. 14.2 - Prob. 3PECh. 14.2 - Prob. 4PECh. 14.2 - Prob. 5PECh. 14.2 - Prob. 6PECh. 14.2 - Prob. 7PECh. 14.2 - Prob. 8PECh. 14.2 - Prob. 9PECh. 14.2 - Prob. 10PECh. 14.2 - Prob. 11PECh. 14.2 - Prob. 12PECh. 14.2 - Prob. 13PECh. 14.2 - Prob. 14PECh. 14.2 - Prob. 15PECh. 14.2 - Prob. 16PECh. 14.2 - Prob. 17PECh. 14.2 - Prob. 18PECh. 14.2 - Prob. 19PECh. 14.2 - Prob. 20PECh. 14.2 - Prob. 21PECh. 14.2 - Prob. 22PECh. 14.2 - Prob. 23PECh. 14.2 - Prob. 24PECh. 14.2 - Prob. 25PECh. 14.2 - Prob. 26PECh. 14.2 - Prob. 27PECh. 14.2 - Prob. 28PECh. 14.2 - Prob. 29PECh. 14.2 - For Exercises 21–32, find a formula for the nth...Ch. 14.2 - Prob. 31PECh. 14.2 - Prob. 32PECh. 14.2 - Edmond borrowed $500. To pay off the loan, he...Ch. 14.2 - Prob. 34PECh. 14.2 - Prob. 35PECh. 14.2 - Prob. 36PECh. 14.2 - Prob. 37PECh. 14.2 - Prob. 38PECh. 14.2 - Prob. 39PECh. 14.2 - Prob. 40PECh. 14.2 - Prob. 41PECh. 14.2 - Prob. 42PECh. 14.2 - Prob. 43PECh. 14.2 - Prob. 44PECh. 14.2 - Prob. 45PECh. 14.2 - Prob. 46PECh. 14.2 - For Exercises 39–54, find the sums. (See Examples...Ch. 14.2 - Prob. 48PECh. 14.2 - For Exercises 39–54, find the sums. (See Examples...Ch. 14.2 - Prob. 50PECh. 14.2 - Prob. 51PECh. 14.2 - Prob. 52PECh. 14.2 - Prob. 53PECh. 14.2 - For Exercises 39–54, find the sums. (See Examples...Ch. 14.2 - Prob. 55PECh. 14.2 - Prob. 56PECh. 14.2 - Prob. 57PECh. 14.2 - Prob. 58PECh. 14.2 - Prob. 59PECh. 14.2 - Prob. 60PECh. 14.2 - Prob. 61PECh. 14.2 - Prob. 62PECh. 14.2 - Prob. 63PECh. 14.2 - For Exercises 55–66, write the series in summation...Ch. 14.2 - Prob. 65PECh. 14.2 - Prob. 66PECh. 14.2 - Prob. 67PECh. 14.2 - Prob. 68PECh. 14.2 - Prob. 69PECh. 14.2 - Prob. 70PECh. 14.2 - 71. A famous sequence in mathematics is called the...Ch. 14.3 - Prob. 1SPCh. 14.3 - Prob. 2SPCh. 14.3 - Prob. 3SPCh. 14.3 - Prob. 4SPCh. 14.3 - Prob. 5SPCh. 14.3 - Prob. 1PECh. 14.3 - Prob. 2PECh. 14.3 - Prob. 3PECh. 14.3 - Prob. 4PECh. 14.3 - Prob. 5PECh. 14.3 - Prob. 6PECh. 14.3 - Prob. 7PECh. 14.3 - Prob. 8PECh. 14.3 - Prob. 9PECh. 14.3 - For Exercises 7–12, the first term of an...Ch. 14.3 - Prob. 11PECh. 14.3 - Prob. 12PECh. 14.3 - Prob. 13PECh. 14.3 - Prob. 14PECh. 14.3 - Prob. 15PECh. 14.3 - Prob. 16PECh. 14.3 - Prob. 17PECh. 14.3 - Prob. 18PECh. 14.3 - Prob. 19PECh. 14.3 - Prob. 20PECh. 14.3 - Prob. 21PECh. 14.3 - Prob. 22PECh. 14.3 - Prob. 23PECh. 14.3 - Prob. 24PECh. 14.3 - Prob. 25PECh. 14.3 - Prob. 26PECh. 14.3 - Prob. 27PECh. 14.3 - Prob. 28PECh. 14.3 - Prob. 29PECh. 14.3 - For Exercises 25–33, write the nth term of the...Ch. 14.3 - For Exercises 25–33, write the nth term of the...Ch. 14.3 - Prob. 32PECh. 14.3 - Prob. 33PECh. 14.3 - Prob. 34PECh. 14.3 - Prob. 35PECh. 14.3 - Prob. 36PECh. 14.3 - Prob. 37PECh. 14.3 - Prob. 38PECh. 14.3 - Prob. 39PECh. 14.3 - Prob. 40PECh. 14.3 - Prob. 41PECh. 14.3 - Prob. 42PECh. 14.3 - Prob. 43PECh. 14.3 - For Exercises 42–49, find the number of terms, n,...Ch. 14.3 - Prob. 45PECh. 14.3 - Prob. 46PECh. 14.3 - Prob. 47PECh. 14.3 - Prob. 48PECh. 14.3 - Prob. 49PECh. 14.3 - Prob. 50PECh. 14.3 - Prob. 51PECh. 14.3 - Prob. 52PECh. 14.3 - Prob. 53PECh. 14.3 - Prob. 54PECh. 14.3 - For Exercises 53–66, find the sum of the...Ch. 14.3 - Prob. 56PECh. 14.3 - Prob. 57PECh. 14.3 - Prob. 58PECh. 14.3 - For Exercises 53–66, find the sum of the...Ch. 14.3 - Prob. 60PECh. 14.3 - Prob. 61PECh. 14.3 - Prob. 62PECh. 14.3 - Prob. 63PECh. 14.3 - Prob. 64PECh. 14.3 - For Exercises 53–66, find the sum of the...Ch. 14.3 - Prob. 66PECh. 14.3 - Find the sum of the first 100 positive integers.Ch. 14.3 - Prob. 68PECh. 14.3 - Prob. 69PECh. 14.3 - A triangular array of dominoes has one domino in...Ch. 14.4 - Prob. 1SPCh. 14.4 - Prob. 2SPCh. 14.4 - Prob. 3SPCh. 14.4 - Prob. 4SPCh. 14.4 - Prob. 5SPCh. 14.4 - Prob. 6SPCh. 14.4 - Prob. 7SPCh. 14.4 - Prob. 8SPCh. 14.4 - 1. a. A ______________sequence is a sequence in...Ch. 14.4 - Prob. 2PECh. 14.4 - Prob. 3PECh. 14.4 - Prob. 4PECh. 14.4 - Prob. 5PECh. 14.4 - Prob. 6PECh. 14.4 - Prob. 7PECh. 14.4 - Prob. 8PECh. 14.4 - Prob. 9PECh. 14.4 - Prob. 10PECh. 14.4 - Prob. 11PECh. 14.4 - Prob. 12PECh. 14.4 - Prob. 13PECh. 14.4 - Prob. 14PECh. 14.4 - Prob. 15PECh. 14.4 - Prob. 16PECh. 14.4 - Prob. 17PECh. 14.4 - Prob. 18PECh. 14.4 - Prob. 19PECh. 14.4 - Prob. 20PECh. 14.4 - For Exercises 19–24, write the first five terms of...Ch. 14.4 - Prob. 22PECh. 14.4 - Prob. 23PECh. 14.4 - For Exercises 19–24, write the first five terms of...Ch. 14.4 - Prob. 25PECh. 14.4 - Prob. 26PECh. 14.4 - Prob. 27PECh. 14.4 - Prob. 28PECh. 14.4 - For Exercises 25–30, find the n th term of each...Ch. 14.4 - Prob. 30PECh. 14.4 - Prob. 31PECh. 14.4 - Prob. 32PECh. 14.4 - Prob. 33PECh. 14.4 - Prob. 34PECh. 14.4 - Prob. 35PECh. 14.4 - Prob. 36PECh. 14.4 - Prob. 37PECh. 14.4 - Prob. 38PECh. 14.4 - Prob. 39PECh. 14.4 - Prob. 40PECh. 14.4 - Prob. 41PECh. 14.4 - If the second and third terms of a geometric...Ch. 14.4 - 43. Explain the difference between a geometric...Ch. 14.4 - Prob. 44PECh. 14.4 - Prob. 45PECh. 14.4 - Prob. 46PECh. 14.4 - Prob. 47PECh. 14.4 - Prob. 48PECh. 14.4 - Prob. 49PECh. 14.4 - Prob. 50PECh. 14.4 - Prob. 51PECh. 14.4 - Prob. 52PECh. 14.4 - For Exercises 47–56, find the sum of the geometric...Ch. 14.4 - For Exercises 47–56, find the sum of the geometric...Ch. 14.4 - For Exercises 47–56, find the sum of the geometric...Ch. 14.4 - For Exercises 47–56, find the sum of the geometric...Ch. 14.4 - Prob. 57PECh. 14.4 - Prob. 58PECh. 14.4 - Prob. 59PECh. 14.4 - Prob. 60PECh. 14.4 - Prob. 61PECh. 14.4 - Prob. 62PECh. 14.4 - Prob. 63PECh. 14.4 - Prob. 64PECh. 14.4 - Prob. 65PECh. 14.4 - Prob. 66PECh. 14.4 - Prob. 67PECh. 14.4 - Prob. 68PECh. 14.4 - Prob. 69PECh. 14.4 - Prob. 70PECh. 14.4 - Prob. 71PECh. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14.4 - Prob. 2PRECh. 14.4 - Prob. 3PRECh. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14.4 - Prob. 5PRECh. 14.4 - Prob. 6PRECh. 14.4 - Prob. 7PRECh. 14.4 - Prob. 8PRECh. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14.4 - Prob. 10PRECh. 14.4 - Prob. 11PRECh. 14.4 - Prob. 12PRECh. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14.4 - Prob. 14PRECh. 14.4 - Prob. 15PRECh. 14.4 - Prob. 16PRECh. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14.4 - For Exercises 1–18, determine if the sequence is...Ch. 14 - Prob. 1RECh. 14 - Prob. 2RECh. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - Prob. 5RECh. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - 10. Find the middle term of the binomial...Ch. 14 - For Exercises 11–14, write the terms of the...Ch. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - Prob. 14RECh. 14 - Prob. 15RECh. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - For Exercises 19–20, find the sum of the...Ch. 14 - Prob. 20RECh. 14 - Prob. 21RECh. 14 - Prob. 22RECh. 14 - Prob. 23RECh. 14 - Prob. 24RECh. 14 - Prob. 25RECh. 14 - Prob. 26RECh. 14 - Prob. 27RECh. 14 - Prob. 28RECh. 14 - For Exercises 29–30, find the number of terms. 3 ,...Ch. 14 - Prob. 30RECh. 14 - Prob. 31RECh. 14 - Prob. 32RECh. 14 - For Exercises 33–36, find the sum of the...Ch. 14 - Prob. 34RECh. 14 - Prob. 35RECh. 14 - Prob. 36RECh. 14 - For Exercises 37–38, find the common ratio. 5 , 15...Ch. 14 - Prob. 38RECh. 14 - Prob. 39RECh. 14 - Prob. 40RECh. 14 - Prob. 41RECh. 14 - Prob. 42RECh. 14 - Prob. 43RECh. 14 - Prob. 44RECh. 14 - Prob. 45RECh. 14 - Prob. 46RECh. 14 - Prob. 47RECh. 14 - Prob. 48RECh. 14 - Prob. 49RECh. 14 - Prob. 50RECh. 14 - Prob. 51RECh. 14 - Prob. 1TCh. 14 - Prob. 2TCh. 14 - Prob. 3TCh. 14 - Prob. 4TCh. 14 - Find the sixth term. ( a − c 3 ) 8Ch. 14 - Write the terms of the sequence. a n = − 3 n + 2 ;...Ch. 14 - 7. Find the sum. Ch. 14 - a. An 8-in. tomato seedling is planted on Sunday....Ch. 14 - Prob. 9TCh. 14 - Find the common difference. 3 ,   13 4 ,   7 2 ,  ...Ch. 14 - 11. Find the common ratio. Ch. 14 - Prob. 12TCh. 14 - Prob. 13TCh. 14 - Prob. 14TCh. 14 - Write an expression for the n th term of the...Ch. 14 - 16. Find the number of terms in the sequence. Ch. 14 - 17. Find the number of terms in the sequence. Ch. 14 - Prob. 18TCh. 14 - 19. Find the sum of the geometric series. Ch. 14 - Prob. 20TCh. 14 - Given a geometric series with a 6 = 9 and r = 3 ,...Ch. 14 - 22. Find the 18th term of the arithmetic sequence...Ch. 14 - Prob. 23TCh. 14 - Prob. 1CRECh. 14 - Prob. 2CRECh. 14 - Prob. 3CRECh. 14 - Prob. 4CRECh. 14 - Prob. 5CRECh. 14 - Prob. 6CRECh. 14 - Prob. 7CRECh. 14 - Prob. 8CRECh. 14 - Prob. 9CRECh. 14 - Prob. 10CRECh. 14 - Prob. 11CRECh. 14 - Prob. 12CRECh. 14 - Prob. 13CRECh. 14 - For Exercises 14–17, factor completely. 6 a 2 − 17...Ch. 14 - Prob. 15CRECh. 14 - Prob. 16CRECh. 14 - For Exercises 14–17, factor completely. w 3 + 9 w...Ch. 14 - Prob. 18CRECh. 14 - Prob. 19CRECh. 14 - Prob. 20CRECh. 14 - For Exercises 18–25, solve the equation. ( 5 y − 2...Ch. 14 - Prob. 22CRECh. 14 - Prob. 23CRECh. 14 - Prob. 24CRECh. 14 - Prob. 25CRECh. 14 - 26. Write the expression as a single logarithm. Ch. 14 - 27. Use a calculator to approximate the value of...Ch. 14 - For Exercises 28–32, solve the inequality. Write...Ch. 14 - For Exercises 28–32, solve the inequality. Write...Ch. 14 - Prob. 30CRECh. 14 - For Exercises 28–32, solve the inequality. Write...Ch. 14 - Prob. 32CRECh. 14 - Prob. 33CRECh. 14 - Prob. 34CRECh. 14 - For Exercises 33–35, graph the equation. 35. Ch. 14 - Graph the solution set. x 2 9 + y 2 25 ≤ 1Ch. 14 - 37. Given a. Determine the...Ch. 14 - Prob. 38CRECh. 14 - Write an equation of the line passing through the...Ch. 14 - Prob. 40CRECh. 14 - Prob. 41CRECh. 14 - Prob. 42CRECh. 14 - Prob. 43CRECh. 14 - Given the points ( 9 , − 4 ) and ( 3 , 0 ) , a....Ch. 14 - Prob. 45CRECh. 14 - The time t ( n ) (in minutes) required for a rat...Ch. 14 - The speed of a car varies inversely as the time to...Ch. 14 - Prob. 48CRECh. 14 - Prob. 49CRECh. 14 - 50. Against the wind, a plane can travel 4950 mi...
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