 5.2.5.2.1: Simplify. Write each answer using positive exponents only. See Exam...
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 5.2.69: Perform each indicated operation. Write each answer in scientific n...
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 5.2.87: Solve.To convert from square inches to square meters, multiplyby 6....
 5.2.88: Solve.To convert from cubic inches to cubic meters, multiply by1.64...
 5.2.89: Simplify each expression. See Section 1.4.5y + 4y  18  y
 5.2.90: Simplify each expression. See Section 1.4.12m  14  15m  1
 5.2.91: Simplify each expression. See Section 1.4.3x  14x  22
 5.2.92: Simplify each expression. See Section 1.4.9y  15  6y2
 5.2.93: Simplify each expression. See Section 1.4.31z  42  213z + 12
 5.2.94: Simplify each expression. See Section 1.4.51x  32  412x  52
 5.2.95: Each side of the cube shown is 2x2y meters. Find its volume.
 5.2.96: The lot shown is in the shape of a parallelogram with base3x1y3 f...
 5.2.97: The density D of an object is equivalent to the quotient ofits mass...
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 5.2.99: Is there a number a such that a1 = a1 ? If so, give the value of a.
 5.2.100: Is there a number a such that a2 is a negative number? If so, give...
 5.2.101: Explain whether 0.4 * 105 is written in scientific notation.
 5.2.102: In your own words, explain why a0 = 1 (as long as a is not 0).
 5.2.103: The estimated population of the United States in April 2010 was 3.0...
 5.2.104: The estimated population of China at the end of 2010 was 1.34 * 109...
 5.2.105: In March 2011, the value of goods and services imported into the Un...
 5.2.106: In 2010, the population of the European Union was 4.92 * 108 people...
Solutions for Chapter 5.2: More Work with Exponents and Scientific Notation
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 5.2: More Work with Exponents and Scientific Notation
Get Full SolutionsThis textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046. Since 106 problems in chapter 5.2: More Work with Exponents and Scientific Notation have been answered, more than 62902 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.2: More Work with Exponents and Scientific Notation includes 106 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).