 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 16386 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.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

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.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

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

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

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

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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).

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.
I don't want to reset my password
Need help? Contact support
Having trouble accessing your account? Let us help you, contact support at +1(510) 9441054 or support@studysoup.com
Forgot password? Reset it here