 9.683: In Exercises 16, use the figure shown to determine the following.AB...
 9.684: In Exercises 16, use the figure shown to determine the following.AB...
 9.685: In Exercises 16, use the figure shown to determine the following.BF...
 9.686: In Exercises 16, use the figure shown to determine the following.S ...
 9.687: In Exercises 16, use the figure shown to determine the following.gH...
 9.688: In Exercises 16, use the figure shown to determine the following.CF...
 9.689: mA = 35.4. Determine the measure of the complement of A.
 9.690: mB = 100.5. Determine the measure of the supplement B.
 9.691: In Exercises 912, use the similar triangles ABC and A B C shown to ...
 9.692: In Exercises 912, use the similar triangles ABC and A B C shown to ...
 9.693: In Exercises 912, use the similar triangles ABC and A B C shown to ...
 9.694: In Exercises 912, use the similar triangles ABC and A B C shown to ...
 9.695: In the following figure, l1 and l2 are parallel lines. Determine m1...
 9.696: Determine the sum of the measures of the interior angles of an octa...
 9.697: In Exercises 1518, determine (a) the area and (b) the perimeter of ...
 9.698: In Exercises 1518, determine (a) the area and (b) the perimeter of ...
 9.699: In Exercises 1518, determine (a) the area and (b) the perimeter of ...
 9.700: In Exercises 1518, determine (a) the area and (b) the perimeter of ...
 9.701: Determine (a) the area and (b) the circumference of the circle. Use...
 9.702: In Exercises 20 and 21, determine the shaded area. When appropriate...
 9.703: In Exercises 20 and 21, determine the shaded area. When appropriate...
 9.704: Cost of Kitchen Tile Determine the total cost of covering a 14ft b...
 9.705: In Exercises 2326, determine (a) the volume and (b) the surface are...
 9.706: In Exercises 2326, determine (a) the volume and (b) the surface are...
 9.707: In Exercises 2326, determine (a) the volume and (b) the surface are...
 9.708: In Exercises 2326, determine (a) the volume and (b) the surface are...
 9.709: In Exercises 27 and 28, determine the volume of the figure.
 9.710: In Exercises 27 and 28, determine the volume of the figure.
 9.711: In Exercises 29 and 30, determine the volume of the shaded area. Wh...
 9.712: In Exercises 29 and 30, determine the volume of the shaded area. Wh...
 9.713: Water Trough Steven Dale has a water trough whose ends are trapezoi...
 9.714: In Exercises 32 and 33, use the given triangle and reflection lines...
 9.715: In Exercises 32 and 33, use the given triangle and reflection lines...
 9.716: In Exercises 34 and 35, use translation vectors v and w to construc...
 9.717: In Exercises 34 and 35, use translation vectors v and w to construc...
 9.718: In Exercises 3638, use the given figure and rotation point P to con...
 9.719: In Exercises 3638, use the given figure and rotation point P to con...
 9.720: In Exercises 3638, use the given figure and rotation point P to con...
 9.721: In Exercises 39 and 40, use the given figure, translation vector v,...
 9.722: In Exercises 39 and 40, use the given figure, translation vector v,...
 9.723: In Exercises 41 and 42, use the following figure to answer the foll...
 9.724: In Exercises 41 and 42, use the following figure to answer the foll...
 9.725: In Exercises 43 and 44, use the following figure to answer the foll...
 9.726: In Exercises 43 and 44, use the following figure to answer the foll...
 9.727: Give an example of an object that has a) genus 0. b) genus 1. c) ge...
 9.728: Color the map by using a maximum of four colors so that no two regi...
 9.729: Determine whether point A is inside or outside the Jordan curve.
 9.730: State the fifth axiom of Euclidean, elliptical, and hyperbolic geom...
 9.731: Develop a fractal by beginning with a square and replacing each sid...
 9.732: Construct a Koch snowflake by beginning with an equilateral triangl...
 9.733: In Exercises 14, use the figure to describe the following sets of p...
 9.734: In Exercises 14, use the figure to describe the following sets of p...
 9.735: In Exercises 14, use the figure to describe the following sets of p...
 9.736: In Exercises 14, use the figure to describe the following sets of p...
 9.737: mA = 74.9. Determine the measure of the complement of A.
 9.738: mB = 10.4. Determine the measure of the supplement of B.
 9.739: In the figure, determine the measure of x.
 9.740: Determine the sum of the measures of the interior angles of a penta...
 9.741: Triangles ABC and ABC are similar figures. Determine the length of ...
 9.742: Right triangle ABC (see below) has one leg of length 12 in. and a h...
 9.743: Determine (a) the volume and (b) the surface area of a sphere of di...
 9.744: Determine the volume of the shaded area. Use the p key on your calc...
 9.745: Determine the volume of the pyramid. 7 ft 12 ft 4 ft
 9.746: Construct a reflection of rectangle ABCD, shown below, about line l...
 9.747: Construct a translation of quadrilateral ABCD, shown below, using t...
 9.748: Construct a 180 rotation of triangle ABC, shown below, about rotati...
 9.749: Construct a glide reflection of rectangle ABCD, shown below, using ...
 9.750: Use the figure below to answer the following questions. A B l D C P...
 9.751: What is a Mbius strip?
 9.752: What is a Mbius strip?
 9.753: Samantha Saraniti is thinking of buying a circular hot tub 12 ft in...
 9.754: David and Sandra Jessee are planning to build a ramp so that the fr...
Solutions for Chapter 9: Geometry
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 9: Geometry
Get Full SolutionsThis textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9. Chapter 9: Geometry includes 72 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. A Survey of Mathematics with Applications was written by and is associated to the ISBN: 9780321759665. Since 72 problems in chapter 9: Geometry have been answered, more than 74731 students have viewed full stepbystep solutions from this chapter.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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).

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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.

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.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

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.

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.

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

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.

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).

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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.

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

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

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).