 12.1: The prism is called a right L_ prism.
 12.2: How many lateral faces are there?
 12.3: What kind of figure is each lateral face?
 12.4: Name two lateral edges and an altitude
 12.5: The length of an altitude is called the __2 . of the prism.
 12.6: Suppose the bases are regular hexagons with 4 cm edges.a. Find the ...
 12.7: Can a prism have lateral faces that are triangles?
 12.8: What is the minimum number of faces a prism can have?
 12.9: If two prisms have equal volumes, must they also have equal total a...
 12.10: a. Since 1 yd = 3 ft, 1 yd2 = _^ ft2 and 1 yd3 = ^_ ft3.b. Since 1 ...
 12.11: Exercises 712 refer to cubes with edges of length e. Complete the ...
 12.12: Exercises 712 refer to cubes with edges of length e. Complete the ...
 12.13: Find the lateral area of a right pentagonal prism with height 13 an...
 12.14: A right triangular prism has lateral area 120 cm2. If the base edge...
 12.15: If the edge of a cube is doubled, the total area is multiplied by :...
 12.16: If the length, width, and height of a rectangular solid are all tri...
 12.17: Equilateral triangle with side 8; h = 10
 12.18: Triangle with sides 9, 12, 15; h = 10
 12.19: Isosceles triangle with sides 13, 13, 10; h = 7
 12.20: Isosceles trapezoid with bases 10 and 4 and legs 5; h = 20
 12.21: Rhombus with diagonals 6 and 8; h = 9
 12.22: Regular hexagon with side 8; h = 12
 12.23: The container shown has the shape of a rectangularsolid. When a roc...
 12.24: A driveway 30 m long and 5 m wide is to be paved withblacktop 3 cm ...
 12.25: A brick with dimensions 20 cm, 10 cm, and 5 cm weighs 1.2 kg. Aseco...
 12.26: A drinking trough for horses is a right trapezoidal prism with dime...
 12.27: Find the weight, to the nearest kilogram, of the cement block shown...
 12.28: Find the weight, to the nearest 10 kg. of the steel Ibeam shown be...
 12.29: Find the volume and the total surface area of each solid in terms o...
 12.30: Find the volume and the total surface area of each solid in terms o...
 12.31: The length of a rectangular solid is twice the width, and the heigh...
 12.32: A right prism has square bases with edges that are three times as l...
 12.33: A diagonal of a box forms a 35 angle with a diagonal of the base, a...
 12.34: Refer to Exercise 33. Suppose another box has a base with dimension...
 12.35: A right prism has height x and bases that are equilateral triangles...
 12.36: A right prism has height h and bases that are regular hexagons with...
 12.37: A rectangular beam of wood 3 m long is cutinto six pieces, as shown...
 12.38: A rectangular beam of wood 3 m long is cutinto six pieces, as shown...
 12.39: All nine edges of a right triangular prism arecongruent. Find the l...
 12.40: If the length and width of a rectangular solidare each decreased by...
Solutions for Chapter 12: Prisms
Full solutions for Geometry  1st Edition
ISBN: 9780395977279
Solutions for Chapter 12: Prisms
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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).

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

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

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

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.

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

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.