 43.1: The bike cost $120. The salestax rate was 8%. What was thetotal co...
 43.2: If one hundred fifty knights could sit at the Round Table andonly o...
 43.3: During the 1996 Summer Olympics in Atlanta, Georgia, the Americanat...
 43.4: In problems 4 and 5, multiply by a fraction equal to 1 to complete ...
 43.5: In problems 4 and 5, multiply by a fraction equal to 1 to complete ...
 43.6: Find each unknown number. Remember to check your work.23n 1
 43.7: Find each unknown number. Remember to check your work.6 w 145
 43.8: Find each unknown number. Remember to check your work.m 414 634
 43.9: Find each unknown number. Remember to check your work.c 2.45 = 3
 43.10: Find each unknown number. Remember to check your work.12 d = 1.43
 43.11: Find each unknown number. Remember to check your work.58 15
 43.12: Find each unknown number. Remember to check your work.34 5
 43.13: Find each unknown number. Remember to check your work.378 138
 43.14: Which of these numbers is not a prime number? A 23 B 33 C 43
 43.15: Compare: 2222 22
 43.16: In football a loss of yardage is often expressed as a negative numb...
 43.17: Write the decimal number for nine and twelve hundredths.
 43.18: Round 67,492,384 to the nearest million.
 43.19: 0.37 102
 43.20: 0.6 0.4 0.2
 43.21: The perimeter of a square room is 80 feet. The area of the room is ...
 43.22: Divide 100 by 16 and write the answer as a mixed number. Reduce the...
 43.23: a. Instead of dividing 100 by 16, Sandy divided the dividendand div...
 43.24: What is the least common multiple (LCM) of 4, 6, and 8?
 43.25: What are the next three numbers in this sequence?22 22 22116,18, 31...
 43.26: Find the length of the segment below to the nearest eighth of an inch.
 43.27: What mixed number is indicated on the number line below?
 43.28: Write 12 and 15 as fractions with denominators of 10. Then add ther...
 43.29: Forty percent of the 20 seats on the bus were occupied. Write40% as...
 43.30: Describe each angle in the figure as acute,right, or obtuse. a. ang...
Solutions for Chapter 43: Equivalent Division Problems Finding Unknowns in Fraction and Decimal Problems
Full solutions for Saxon Math, Course 1  1st Edition
ISBN: 9781591417835
Solutions for Chapter 43: Equivalent Division Problems Finding Unknowns in Fraction and Decimal Problems
Get Full SolutionsSince 30 problems in chapter 43: Equivalent Division Problems Finding Unknowns in Fraction and Decimal Problems have been answered, more than 33638 students have viewed full stepbystep solutions from this chapter. Saxon Math, Course 1 was written by and is associated to the ISBN: 9781591417835. Chapter 43: Equivalent Division Problems Finding Unknowns in Fraction and Decimal Problems includes 30 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Saxon Math, Course 1, edition: 1.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

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).

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

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

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

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.

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.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

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.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

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.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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

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.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.