 5.4.1: Solve the inequality 3  4x 7 5 . Graph the solution set.
 5.4.2: Solve the inequality x2  5x 24 . Graph the solution set.
 5.4.3: True or False A test number for the interval 2 6 x 6 5 could be 4.
 5.4.4: True or False The graph of is above the xaxis for or ,so the solut...
 5.4.5: In 58, use the graph of the function f to solve the inequality.(a) ...
 5.4.6: In 58, use the graph of the function f to solve the inequality.a) (...
 5.4.7: In 58, use the graph of the function f to solve the inequality.(a) ...
 5.4.8: In 58, use the graph of the function f to solve the inequality.(a) ...
 5.4.9: In 914,solve the inequality by using the graph of the function. [Hi...
 5.4.10: In 914,solve the inequality by using the graph of the function. [Hi...
 5.4.11: In 914,solve the inequality by using the graph of the function. [Hi...
 5.4.12: In 914,solve the inequality by using the graph of the function. [Hi...
 5.4.13: In 914,solve the inequality by using the graph of the function. [Hi...
 5.4.14: In 914,solve the inequality by using the graph of the function. [Hi...
 5.4.15: In 1518,solve the inequality by using the graph of the function. [H...
 5.4.16: In 1518,solve the inequality by using the graph of the function. [H...
 5.4.17: In 1518,solve the inequality by using the graph of the function. [H...
 5.4.18: In 1518,solve the inequality by using the graph of the function. [H...
 5.4.19: In 1948,solve each inequality algebraically. 1x  5221x + 22 6 0
 5.4.20: In 1948,solve each inequality algebraically. 1x  521x + 222 7 0
 5.4.21: In 1948,solve each inequality algebraically. x3  4x2 7 0
 5.4.22: In 1948,solve each inequality algebraically. x3 + 8x2 6 0
 5.4.23: In 1948,solve each inequality algebraically. 2x3 7 8x2
 5.4.24: In 1948,solve each inequality algebraically. 3x3 6 15x2
 5.4.25: In 1948,solve each inequality algebraically. 1x  121x  221x  32 0
 5.4.26: In 1948,solve each inequality algebraically. 1x + 121x + 221x + 32 0
 5.4.27: In 1948,solve each inequality algebraically. x3  2x2  3x 7 0
 5.4.28: In 1948,solve each inequality algebraically. x3 + 2x2  3x 7 0
 5.4.29: In 1948,solve each inequality algebraically.x4 7 x2
 5.4.30: In 1948,solve each inequality algebraically. x4 6 9x2
 5.4.31: In 1948,solve each inequality algebraically. x4 7 1
 5.4.32: In 1948,solve each inequality algebraically. x3 7 1
 5.4.33: In 1948,solve each inequality algebraically. x + 1x  17 0
 5.4.34: In 1948,solve each inequality algebraically. x  3x + 17 0
 5.4.35: In 1948,solve each inequality algebraically. 1x  121x + 12x 0
 5.4.36: In 1948,solve each inequality algebraically. 1x  321x + 22x  1 0
 5.4.37: In 1948,solve each inequality algebraically. 1x  222x2  1 0
 5.4.38: In 1948,solve each inequality algebraically. 1x + 522x2  4 0
 5.4.39: In 1948,solve each inequality algebraically. x + 4x  2 1
 5.4.40: In 1948,solve each inequality algebraically. x + 2x  4 1
 5.4.41: In 1948,solve each inequality algebraically. 3x  5x + 2 2
 5.4.42: In 1948,solve each inequality algebraically. x  42x + 4 1
 5.4.43: In 1948,solve each inequality algebraically. 1x  2623x  9
 5.4.44: In 1948,solve each inequality algebraically. 5x  373x + 1
 5.4.45: In 1948,solve each inequality algebraically. x213 + x21x + 421x + 5...
 5.4.46: In 1948,solve each inequality algebraically. x1x2 + 121x  221x  1...
 5.4.47: In 1948,solve each inequality algebraically. 13  x2312x + 12x3  16 0
 5.4.48: In 1948,solve each inequality algebraically. 12  x2313x  22x3 + 16 0
 5.4.49: In 4960,solve each inequality algebraically. 1x + 121x  321x  52 7 0
 5.4.50: In 4960,solve each inequality algebraically. 12x  121x + 221x + 52...
 5.4.51: In 4960,solve each inequality algebraically. 7x  4 2x2
 5.4.52: In 4960,solve each inequality algebraically. x2 + 3x 10
 5.4.53: In 4960,solve each inequality algebraically. x + 1x  3 2
 5.4.54: In 4960,solve each inequality algebraically. x  1x + 2 2
 5.4.55: In 4960,solve each inequality algebraically. 31x2  22 6 21x  122 ...
 5.4.56: In 4960,solve each inequality algebraically. 1x  321x + 22 6 x2 + ...
 5.4.57: In 4960,solve each inequality algebraically. 6x  5 66x
 5.4.58: In 4960,solve each inequality algebraically. x +12x 6 7
 5.4.59: In 4960,solve each inequality algebraically. x3  9x 0
 5.4.60: In 4960,solve each inequality algebraically. x3  x 0
 5.4.61: For what positive numbers will the cube of a number exceed four tim...
 5.4.62: For what positive numbers will the cube of a number be less than th...
 5.4.63: What is the domain of the functionf1x2 = 2x4  16?
 5.4.64: What is the domain of the functionf1x2 = 2x3  3x2?
 5.4.65: What is the domain of the functionf1x2 = A x  2 x + 4?
 5.4.66: What is the domain of the functionf1x2 = A x  1 x + 4?
 5.4.67: In 6770, determine where the graph of f is below the graph of g by ...
 5.4.68: In 6770, determine where the graph of f is below the graph of g by ...
 5.4.69: In 6770, determine where the graph of f is below the graph of g by ...
 5.4.70: In 6770, determine where the graph of f is below the graph of g by ...
 5.4.71: Average Cost Suppose that the daily cost C of manufacturing bicycle...
 5.4.72: Average Cost See 71.Suppose that the government imposes a $1000 per...
 5.4.73: Bungee Jumping Originating on Pentecost Island in the Pacific, the ...
 5.4.74: Gravitational Force According to Newtons Law of universal gravitati...
 5.4.75: Field Trip Mrs. West has decided to take her fifth grade class to a...
 5.4.76: Make up an inequality that has no solution. Make up one that has ex...
 5.4.77: The inequality has no solution. Explain why
 5.4.78: A student attempted to solve the inequality by multiplying both sid...
 5.4.79: Write a rational inequality whose solution set is {x3 6 x 5}.
Solutions for Chapter 5.4: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 5.4
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. Chapter 5.4 includes 79 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. Since 79 problems in chapter 5.4 have been answered, more than 57279 students have viewed full stepbystep solutions from this chapter.

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

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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

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

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = 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.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

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

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

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.