 7.6.1: Solve. See Examples 1 and 2.22x = 4
 7.6.2: Solve. See Examples 1 and 2.23x = 3
 7.6.3: Solve. See Examples 1 and 2.2x  3 = 2
 7.6.4: Solve. See Examples 1 and 2.2x + 1 = 5
 7.6.5: Solve. See Examples 1 and 2.22x = 4
 7.6.6: Solve. See Examples 1 and 2.25x = 5
 7.6.7: Solve. See Examples 1 and 2.24x  3  5 = 0
 7.6.8: Solve. See Examples 1 and 2.2x  3  1 = 0
 7.6.9: Solve. See Examples 1 and 2.22x  3  2 = 1
 7.6.10: Solve. See Examples 1 and 2.23x + 3  4 = 8
 7.6.11: Solve. See Example 3.23 6x = 3
 7.6.12: Solve. See Example 3.23 4x = 2
 7.6.13: Solve. See Example 3.23 x  2  3 = 0
 7.6.14: Solve. See Example 3.23 2x  6  4 = 0
 7.6.15: Solve. See Examples 4 and 5213  x = x  1
 7.6.16: Solve. See Examples 4 and 522x  3 = 3  x
 7.6.17: Solve. See Examples 4 and 5 x  24  3x = 8
 7.6.18: Solve. See Examples 4 and 52x + 2x + 1 = 8
 7.6.19: Solve. See Examples 4 and 52y + 5 = 2  2y  4
 7.6.20: Solve. See Examples 4 and 52x + 3 + 2x  5 = 3
 7.6.21: Solve. See Examples 4 and 52x  3 + 2x + 2 = 5
 7.6.22: Solve. See Examples 4 and 522x  4  23x + 4 = 2
 7.6.23: Solve. See Examples 1 through 523x  2 = 5
 7.6.24: Solve. See Examples 1 through 525x  4 = 9
 7.6.25: Solve. See Examples 1 through 5 22x + 4 = 6
 7.6.26: Solve. See Examples 1 through 5  23x + 9 = 12
 7.6.27: Solve. See Examples 1 through 523x + 1 + 2 = 0
 7.6.28: Solve. See Examples 1 through 523x + 1  2 = 0
 7.6.29: Solve. See Examples 1 through 524 4x + 1  2 = 0
 7.6.30: Solve. See Examples 1 through 524 2x  9  3 = 0
 7.6.31: Solve. See Examples 1 through 524x  3 = 7
 7.6.32: Solve. See Examples 1 through 523x + 9 = 6
 7.6.33: Solve. See Examples 1 through 523 6x  3  3 = 0
 7.6.34: Solve. See Examples 1 through 523 3x + 4 = 7
 7.6.35: Solve. See Examples 1 through 523 2x  3  2 = 5
 7.6.36: Solve. See Examples 1 through 5 23 x  4  5 = 7
 7.6.37: Solve. See Examples 1 through 52x + 4 = 22x  5
 7.6.38: Solve. See Examples 1 through 523y + 6 = 27y  6
 7.6.39: Solve. See Examples 1 through 5x  21  x = 5
 7.6.40: Solve. See Examples 1 through 5x  2x  2 = 4
 7.6.41: Solve. See Examples 1 through 523 6x  1 = 23 2x  5
 7.6.42: Solve. See Examples 1 through 523 4x  3 = 23 x  15
 7.6.43: Solve. See Examples 1 through 525x  1  2x + 2 = 3
 7.6.44: Solve. See Examples 1 through 522x  1  4 =  2x  4
 7.6.45: Solve. See Examples 1 through 522x  1 = 21  2x
 7.6.46: Solve. See Examples 1 through 527x  4 = 24  7x
 7.6.47: Solve. See Examples 1 through 523x + 4  1 = 22x + 1
 7.6.48: Solve. See Examples 1 through 52x  2 + 3 = 24x + 1
 7.6.49: Solve. See Examples 1 through 52y + 3  2y  3 = 1
 7.6.50: Solve. See Examples 1 through 5 2x + 1  2x  1 = 2
 7.6.51: Find the length of the unknown side of each triangle. See Example 6...
 7.6.52: Find the length of the unknown side of each triangle. See Example 6...
 7.6.53: Find the length of the unknown side of each triangle. See Example 6.m3
 7.6.54: Find the length of the unknown side of each triangle. See Example 6...
 7.6.55: Find the length of the unknown side of each triangle. Give the exac...
 7.6.56: Find the length of the unknown side of each triangle. Give the exac...
 7.6.57: Find the length of the unknown side of each triangle. Give the exac...
 7.6.58: Find the length of the unknown side of each triangle. Give the exac...
 7.6.59: Solve. Give exact answers and twodecimalplace approximations wher...
 7.6.60: Solve. Give exact answers and twodecimalplace approximations wher...
 7.6.61: A spotlight is mounted on the eaves of a house 12 feet above the gr...
 7.6.62: A wire is to be attached to support a telephone pole. Because of su...
 7.6.63: The radius of the moon is 1080 miles. Use the formula forthe radius...
 7.6.64: Police departments find it very useful to be able to approximate th...
 7.6.65: The formula v = 22gh gives the velocity v, in feet per second, of a...
 7.6.66: Two tractors are pulling a tree stump from a field. If twoforces A ...
 7.6.67: In psychology, it has been suggested that the number S of nonsense ...
 7.6.68: In psychology, it has been suggested that the number S of nonsense ...
 7.6.69: The period of a pendulum is the time it takes for the pendulum toma...
 7.6.70: The period of a pendulum is the time it takes for the pendulum toma...
 7.6.71: The period of a pendulum is the time it takes for the pendulum toma...
 7.6.72: The period of a pendulum is the time it takes for the pendulum toma...
 7.6.73: The period of a pendulum is the time it takes for the pendulum toma...
 7.6.74: The period of a pendulum is the time it takes for the pendulum toma...
 7.6.75: If the three lengths of the sides of a triangle are known, Heronsfo...
 7.6.76: If the three lengths of the sides of a triangle are known, Heronsfo...
 7.6.77: Describe when Herons formula might be useful.
 7.6.78: In your own words, explain why you think s in Herons formula is cal...
 7.6.79: The maximum distance D(h) in kilometers that a person can see from ...
 7.6.80: The maximum distance D(h) in kilometers that a person can see from ...
 7.6.81: Use the vertical line test to determine whether each graph represen...
 7.6.82: Use the vertical line test to determine whether each graph represen...
 7.6.83: Use the vertical line test to determine whether each graph represen...
 7.6.84: Use the vertical line test to determine whether each graph represen...
 7.6.85: Use the vertical line test to determine whether each graph represen...
 7.6.86: Use the vertical line test to determine whether each graph represen...
 7.6.87: Simplify. See Section 6.3x62x3+12
 7.6.88: Simplify. See Section 6.31y+45 320
 7.6.89: Simplify. See Section 6.3z5+110z20  z5
 7.6.90: Simplify. See Section 6.31y+1x1y  1x
 7.6.91: Find the error in each solution and correct. See the second Concept...
 7.6.92: Find the error in each solution and correct. See the second Concept...
 7.6.93: Solve: 21x + 3 + 1x = 13
 7.6.94: The cost C(x) in dollars per day to operate a small delivery servic...
 7.6.95: Consider the equations 22x = 4 and 23 2x = 4.a. Explain the differe...
 7.6.96: Explain why proposed solutions of radical equations mustbe checked....
 7.6.97: In this problem, we have four possible solutions: 0, 3, 4, and 1.A...
 7.6.98: In this problem, we have four possible solutions: 0, 3, 4, and 1.A...
 7.6.99: In this problem, we have four possible solutions: 0, 3, 4, and 1.A...
 7.6.100: In this problem, we have four possible solutions: 0, 3, 4, and 1.A...
Solutions for Chapter 7.6: Radical Equations and Problem Solving
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 7.6: Radical Equations and Problem Solving
Get Full SolutionsThis textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. Chapter 7.6: Radical Equations and Problem Solving includes 100 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 100 problems in chapter 7.6: Radical Equations and Problem Solving have been answered, more than 59560 students have viewed full stepbystep solutions from this chapter. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046.

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).

Column space C (A) =
space of all combinations of the columns of A.

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.

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

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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

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

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

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.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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.

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

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.