 90.1: What is the mean of 4.2, 4.8, and 5.1?
 90.2: The movie is 120 minutes long. If it begins at 7:15 p.m., when will...
 90.3: Fifteen of the 25 students in Room 20 are boys. What percent of the...
 90.4: This triangular prism has how many moreedges than vertices?
 90.5: The teacher cut a 12inch diameter circle from a sheet of construct...
 90.6: Write a description of a trapezoid
 90.7: Arrange these numbers in order from least to greatest:1, 2, 0, 4, 12
 90.8: Express the unknown factor as a mixed number:25n = 70
 90.9: Refer to the triangle to answer questions 911.What is the area of t...
 90.10: Refer to the triangle to answer questions 911.What is the perimeter...
 90.11: Refer to the triangle to answer questions 911.What is the ratio of ...
 90.12: Write 6.25 as a mixed number. Then subtract 58 from the mixed numbe...
 90.13: Ali was facing north. Then he turned to his left 180. Whatdirection...
 90.14: Write 28% as a reduced fraction.
 90.15: n12 2030
 90.16: 0.625 10
 90.17: 250.8
 90.18: 338 334
 90.19: 5 18 178
 90.20: 6 23 310 5 4
 90.21: One third of the two dozen knights were on horseback. How manyknigh...
 90.22: Weights totaling 38 ounces were placed on the left side ofthis scal...
 90.23: The cube at right is made up of smallercubes that each have a volum...
 90.24: Round fortyeight hundredths to the nearest tenth.
 90.25: 1144 1121
 90.26: The ratio of dogs to cats in the neighborhood is 6 to 5. What is th...
 90.27: 10 + 10 10 10 10
 90.28: The Thompsons drink a gallon of milk every two days. Thereare four ...
 90.29: Simplify: a. 10 cm + 100 mm (Write the answer in millimeters.) b. 3...
 90.30: On a coordinate plane draw a segment from point A (3, 1)to point B ...
Solutions for Chapter 90: Measuring Turns
Full solutions for Saxon Math, Course 1  1st Edition
ISBN: 9781591417835
Solutions for Chapter 90: Measuring Turns
Get Full SolutionsSaxon Math, Course 1 was written by and is associated to the ISBN: 9781591417835. Chapter 90: Measuring Turns includes 30 full stepbystep solutions. Since 30 problems in chapter 90: Measuring Turns have been answered, more than 33787 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Saxon Math, Course 1, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions.

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

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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.

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.

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

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

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.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

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 picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.