 9.4.9.1.263: A measure of the capacity of a threedimensional figure is called t...
 9.4.9.1.264: The sum of the areas of the surfaces of a threedimensional figure ...
 9.4.9.1.265: A regular polyhedron, whose faces are all regular polygons of the s...
 9.4.9.1.266: A polyhedron whose bases are congruent polygons and whose sides are...
 9.4.9.1.267: A prism whose sides are rectangles is called a prism.
 9.4.9.1.268: Eulers polyhedron formula states that, for any polyhedron, the numb...
 9.4.9.1.269: In Exercises 716, determine (a) the volume and (b) the surface area...
 9.4.9.1.270: In Exercises 716, determine (a) the volume and (b) the surface area...
 9.4.9.1.271: In Exercises 716, determine (a) the volume and (b) the surface area...
 9.4.9.1.272: In Exercises 716, determine (a) the volume and (b) the surface area...
 9.4.9.1.273: In Exercises 716, determine (a) the volume and (b) the surface area...
 9.4.9.1.274: In Exercises 716, determine (a) the volume and (b) the surface area...
 9.4.9.1.275: In Exercises 716, determine (a) the volume and (b) the surface area...
 9.4.9.1.276: In Exercises 716, determine (a) the volume and (b) the surface area...
 9.4.9.1.277: In Exercises 716, determine (a) the volume and (b) the surface area...
 9.4.9.1.278: In Exercises 716, determine (a) the volume and (b) the surface area...
 9.4.9.1.279: In Exercises 1720, determine the volume of the threedimensional fig...
 9.4.9.1.280: In Exercises 1720, determine the volume of the threedimensional fig...
 9.4.9.1.281: In Exercises 1720, determine the volume of the threedimensional fig...
 9.4.9.1.282: In Exercises 1720, determine the volume of the threedimensional fig...
 9.4.9.1.283: In Exercises 2128, determine the volume of the shaded region. When ...
 9.4.9.1.284: In Exercises 2128, determine the volume of the shaded region. When ...
 9.4.9.1.285: In Exercises 2128, determine the volume of the shaded region. When ...
 9.4.9.1.286: In Exercises 2128, determine the volume of the shaded region. When ...
 9.4.9.1.287: In Exercises 2128, determine the volume of the shaded region. When ...
 9.4.9.1.288: In Exercises 2128, determine the volume of the shaded region. When ...
 9.4.9.1.289: In Exercises 2128, determine the volume of the shaded region. When ...
 9.4.9.1.290: In Exercises 2128, determine the volume of the shaded region. When ...
 9.4.9.1.291: In Exercises 2932, use the fact that 1 yd3 equals 27 ft 3 to make t...
 9.4.9.1.292: In Exercises 2932, use the fact that 1 yd3 equals 27 ft 3 to make t...
 9.4.9.1.293: In Exercises 2932, use the fact that 1 yd3 equals 27 ft 3 to make t...
 9.4.9.1.294: In Exercises 2932, use the fact that 1 yd3 equals 27 ft 3 to make t...
 9.4.9.1.295: In Exercises 3336, use the fact that 1 m 3 equals 1,000,000 cm3 to ...
 9.4.9.1.296: In Exercises 3336, use the fact that 1 m 3 equals 1,000,000 cm3 to ...
 9.4.9.1.297: In Exercises 3336, use the fact that 1 m 3 equals 1,000,000 cm3 to ...
 9.4.9.1.298: In Exercises 3336, use the fact that 1 m 3 equals 1,000,000 cm3 to ...
 9.4.9.1.299: Playground Mulch Bob Malena is building a backyard playground for h...
 9.4.9.1.300: Volume of a Freezer The dimensions of the interior of an upright fr...
 9.4.9.1.301: CD Case A compact disc case is a rectangular solid that is 142 mm l...
 9.4.9.1.302: Globe Surface Area The Everest model globe has a diameter of 20 in....
 9.4.9.1.303: Volume of a Bread Pan A bread pan is 12 in. * 4 in. * 3 in. How man...
 9.4.9.1.304: IceCream Comparison The Louisburg Creamery packages its homemade i...
 9.4.9.1.305: A Fish Tank a) How many cubic centimeters of water will a rectangul...
 9.4.9.1.306: The Pyramid of Cheops The Pyramid of Cheops in Egypt has a square b...
 9.4.9.1.307: Engine Capacity The engine in a 1957 Chevrolet Corvette has eight c...
 9.4.9.1.308: Rose Garden Topsoil Marisa Raffaele wishes to plant a rose garden i...
 9.4.9.1.309: Pool Toys A Wacky Noodle Pool Toy, frequently referred to as a nood...
 9.4.9.1.310: Comparing Cake Pans When baking a cake, you can choose between a ro...
 9.4.9.1.311: Cake Icing A bag used to apply icing to a cake is in the shape of a...
 9.4.9.1.312: Flower Box The flower box shown below is 4 ft long, and its ends ar...
 9.4.9.1.313: In Exercises 5156, find the missing value indicated by the question...
 9.4.9.1.314: In Exercises 5156, find the missing value indicated by the question...
 9.4.9.1.315: In Exercises 5156, find the missing value indicated by the question...
 9.4.9.1.316: In Exercises 5156, find the missing value indicated by the question...
 9.4.9.1.317: In Exercises 5156, find the missing value indicated by the question...
 9.4.9.1.318: In Exercises 5156, find the missing value indicated by the question...
 9.4.9.1.319: Earth and Moon Comparisons The diameter of Earth is approximately 1...
 9.4.9.1.320: Packing Orange Juice A box is packed with six cans of orange juice....
 9.4.9.1.321: Doubling the Edges of a Cube In this exercise, we will explore what...
 9.4.9.1.322: Doubling the Radius of a Sphere In this exercise, we will explore w...
 9.4.9.1.323: a) Explain how to demonstrate, using the cube shown below, that (a ...
 9.4.9.1.324: More Pool Toys Wacky Noodle Pool Toys (see Exercise 47) come in man...
 9.4.9.1.325: AirConditioner Selection Calculate the volume of the room in which...
 9.4.9.1.326: Pappus of Alexandria (ca. A.D. 350) was the last of the wellknown ...
 9.4.9.1.327: Platonic Solids Construct cardboard models of one or more of the pl...
Solutions for Chapter 9.4: Geometry
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 9.4: Geometry
Get Full SolutionsChapter 9.4: Geometry includes 65 full stepbystep solutions. Since 65 problems in chapter 9.4: Geometry have been answered, more than 74361 students have viewed full stepbystep solutions from this chapter. 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. This textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9.

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.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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.

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 .

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

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

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 •

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).

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

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