 Chapter 6.1: If f(x) = x2 + 2x  3 x2  4 , find the following function values. ...
 Chapter 6.2: f(x) = x  6 (x  3)(x + 4)
 Chapter 6.3: f(x) = x + 2 x2 + x  2
 Chapter 6.4: 5x3  35x 15x2
 Chapter 6.5: x2 + 6x  7 x2  49
 Chapter 6.6: 6x2 + 7x + 2 2x2  9x  5
 Chapter 6.7: x2 + 4 x2  4
 Chapter 6.8: x3  8 x2  4
 Chapter 6.9: 5x2  5 3x + 12 # x + 4 x  1
 Chapter 6.10: 2x + 5 4x2 + 8x  5 # 4x2  4x + 1 x + 1
 Chapter 6.11: x2  9x + 14 x3 + 2x2 # x2  4 x2  4x + 4
 Chapter 6.12: 1 x2 + 8x + 15 , 3 x + 5
 Chapter 6.13: x2 + 16x + 64 2x2  128 , x2 + 10x + 16 x2  6x  16
 Chapter 6.14: y2  16 y3  64 , y2  3y  18 y2 + 5y + 6
 Chapter 6.15: x2  4x + 4  y2 2x2  11x + 15 # x4y x  2 + y , x3y  2x2y  x2y2...
 Chapter 6.16: Deer are placed into a newly acquired habitat. The deer population ...
 Chapter 6.17: 4x + 1 3x  1 + 8x  5 3x  1
 Chapter 6.18: 2x  7 x2  9  x  4 x2  9
 Chapter 6.19: 4x2  11x + 4 x  3  x2  4x + 10 x  3
 Chapter 6.20: 7 9x3 and 5 12x
 Chapter 6.21: x + 7 x2 + 2x  35 and x x2 + 9x + 14
 Chapter 6.22: 1 x + 2 x  5
 Chapter 6.23: 2 x2  5x + 6 + 3 x2  x  6
 Chapter 6.24: x  3 x2  8x + 15 + x + 2 x2  x  6
 Chapter 6.25: 3x2 9x2  16  x 3x + 4
 Chapter 6.26: y y2 + 5y + 6  2 y2 + 3y + 2
 Chapter 6.27: x x + 3 + x x  3  9 x2  9
 Chapter 6.28: 3x2 x  y + 3y2 y  x
 Chapter 6.29: 3 x  3 8 x  8
 Chapter 6.30: 5 x + 1 1  25 x2
 Chapter 6.31: 3  1 x + 3 3 + 1 x + 3
 Chapter 6.32: 4 x + 3 2 x  2  1 x2 + x  6
 Chapter 6.33: 2 x2  x  6 + 1 x2  4x + 3 3 x2 + x  2  2 x2 + 5x + 6
 Chapter 6.34: x 2 + x 1 x 2  x 1
 Chapter 6.35: (15x3  30x2 + 10x  2) , (5x2 )
 Chapter 6.36: (36x4y3 + 12x2y3  60x2y2 ) , (6xy2 )
 Chapter 6.37: (6x2  5x + 5) , (2x + 3)
 Chapter 6.38: (10x3  26x2 + 17x  13) , (5x  3)
 Chapter 6.39: (x6 + 3x5  2x4 + x2  3x + 2) , (x  2)
 Chapter 6.40: (4x4 + 6x3 + 3x  1) , (2x2 + 1)
 Chapter 6.41: (4x3  3x2  2x + 1) , (x + 1)
 Chapter 6.42: (3x4  2x2  10x  20) , (x  2)
 Chapter 6.43: (x4 + 16) , (x + 4)
 Chapter 6.44: f(x) = 2x3  5x2 + 4x  1; f(2)
 Chapter 6.45: f(x) = 3x4 + 7x3 + 8x2 + 2x + 4; f 11 3 2
 Chapter 6.46: 2x3  x2  8x + 4 = 0; 2
 Chapter 6.47: x4  x3  7x2 + x + 6 = 0; 4
 Chapter 6.48: Use synthetic division to show that 1 2 is a solution of 6x3 + x2 ...
 Chapter 6.49: 3 x + 1 3 = 5 x
 Chapter 6.50: 5 3x + 4 = 3 2x  8
 Chapter 6.51: 1 x  5  3 x + 5 = 6 x2  25
 Chapter 6.52: x + 5 x + 1  x x + 2 = 4x + 1 x2 + 3x + 2
 Chapter 6.53: 2 3  5 3x = 1 x2
 Chapter 6.54: 2 x  1 = 1 4 + 7 x + 2
 Chapter 6.55: 2x + 7 x + 5  x  8 x  4 = x + 18 x2 + x  20
 Chapter 6.56: The function f(x) = 4x 100  x models the cost, f(x), in millions o...
 Chapter 6.57: P = R  C n for C
 Chapter 6.58: P1V1 T1 = P2V2 T2 for T1
 Chapter 6.59: T = A  P Pr for P
 Chapter 6.60: 1 R = 1 R1 + 1 R2 for R
 Chapter 6.61: I = nE R + nr for n
 Chapter 6.62: A company is planning to manufacture affordable graphing calculator...
 Chapter 6.63: After riding at a steady rate for 60 miles, a bicyclist had a flat ...
 Chapter 6.64: The current of a river moves at 3 miles per hour. It takes a boat a...
 Chapter 6.65: Working alone, two people can clean their house in 3 hours and 6 ho...
 Chapter 6.66: Working together, two crews can clear snow from the citys streets i...
 Chapter 6.67: An inlet faucet can fill a small pond in 60 minutes. The pond can b...
 Chapter 6.68: A companys profit varies directly as the number of products it sell...
 Chapter 6.69: The distance that a body falls from rest varies directly as the squ...
 Chapter 6.70: The pitch of a musical tone varies inversely as its wavelength. A t...
 Chapter 6.71: The loudness of a stereo speaker, measured in decibels, varies inve...
 Chapter 6.72: The time required to assemble computers varies directly as the numb...
 Chapter 6.73: The volume of a pyramid varies jointly as its height and the area o...
Solutions for Chapter Chapter 6: Rational Expressions, Functions, and Equations
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter Chapter 6: Rational Expressions, Functions, and Equations
Get Full SolutionsChapter Chapter 6: Rational Expressions, Functions, and Equations includes 73 full stepbystep solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. Since 73 problems in chapter Chapter 6: Rational Expressions, Functions, and Equations have been answered, more than 31981 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6.

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.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Iterative method.
A sequence of steps intended to approach the desired solution.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

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

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).