 49.1: Is the set of points on a circle a function? Explain why or why not.
 49.2: Explain why (x 2 h)2 1 (y 2 k)2 5 24 is not the equation of a circle.
 49.3: In 310, the coordinates of point P on the circle with center at C a...
 49.4: In 310, the coordinates of point P on the circle with center at C a...
 49.5: In 310, the coordinates of point P on the circle with center at C a...
 49.6: In 310, the coordinates of point P on the circle with center at C a...
 49.7: In 310, the coordinates of point P on the circle with center at C a...
 49.8: In 310, the coordinates of point P on the circle with center at C a...
 49.9: In 310, the coordinates of point P on the circle with center at C a...
 49.10: In 310, the coordinates of point P on the circle with center at C a...
 49.11: In 1119, write the equation of each circle
 49.12: In 1119, write the equation of each circle
 49.13: In 1119, write the equation of each circle
 49.14: In 1119, write the equation of each circle
 49.15: In 1119, write the equation of each circle
 49.16: In 1119, write the equation of each circle
 49.17: In 1119, write the equation of each circle
 49.18: In 1119, write the equation of each circle
 49.19: In 1119, write the equation of each circle
 49.20: In 2027: a. Write each equation in centerradius form. b. Find the ...
 49.21: In 2027: a. Write each equation in centerradius form. b. Find the ...
 49.22: In 2027: a. Write each equation in centerradius form. b. Find the ...
 49.23: In 2027: a. Write each equation in centerradius form. b. Find the ...
 49.24: In 2027: a. Write each equation in centerradius form. b. Find the ...
 49.25: In 2027: a. Write each equation in centerradius form. b. Find the ...
 49.26: In 2027: a. Write each equation in centerradius form. b. Find the ...
 49.27: In 2027: a. Write each equation in centerradius form. b. Find the ...
 49.28: An architect is planning the entryway into a courtyard as an arch i...
 49.29: What is the measure of a side of a square that can be drawn with it...
 49.30: What are dimensions of a rectangle whose length is twice the width ...
 49.31: Airplane passengers have been surprised to look down over farmland ...
Solutions for Chapter 49: Circles
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 49: Circles
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. Since 31 problems in chapter 49: Circles have been answered, more than 28644 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Chapter 49: Circles includes 31 full stepbystep solutions.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

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 .

Outer product uv T
= column times row = rank one matrix.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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

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

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

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

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.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·