 10.2.1: Find the volume of each solid in Exercises 16. All measurements are...
 10.2.2: Find the volume of each solid in Exercises 16. All measurements are...
 10.2.3: Find the volume of each solid in Exercises 16. All measurements are...
 10.2.4: Find the volume of each solid in Exercises 16. All measurements are...
 10.2.5: Find the volume of each solid in Exercises 16. All measurements are...
 10.2.6: Find the volume of each solid in Exercises 16. All measurements are...
 10.2.7: Use the information about the base and height of each solid to find...
 10.2.8: For Exercises 89, sketch and label each solid described, then find ...
 10.2.9: For Exercises 89, sketch and label each solid described, then find ...
 10.2.10: For Exercises 89, sketch and label each solid described, then find ...
 10.2.11: In Exercises 1113, express the volume of each solid with the help o...
 10.2.12: In Exercises 1113, express the volume of each solid with the help o...
 10.2.13: In Exercises 1113, express the volume of each solid with the help o...
 10.2.14: Application A cord of firewood is 128 cubic feet. Margaretta has th...
 10.2.15: Application A contractor needs to build a ramp, as shown at right, ...
 10.2.16: If an average rectangular block of limestone used to build the Grea...
 10.2.17: Although the Exxon Valdez oil spill (11 million gallons of oil) is ...
 10.2.18: When folded, a 12by12foot section of the AIDS Memorial Quilt req...
 10.2.19: For Exercises 19 and 20, draw and label each solid. Use dashed line...
 10.2.20: For Exercises 19 and 20, draw and label each solid. Use dashed line...
 10.2.21: For Exercises 21 and 22, identify each statement as true or false. ...
 10.2.22: For Exercises 21 and 22, identify each statement as true or false. ...
 10.2.23: The tower below is an unusual shape. Its neither a cylinder nor a c...
 10.2.24: Do research to find a photo or drawing of a chemical model of a cry...
 10.2.25: Six points are equally spaced around a circular track with a 20 m r...
 10.2.26: AS and AT are tangent to circle O at S and T, respectively. m SMO =...
Solutions for Chapter 10.2: Volume of Prisms and Cylinders
Full solutions for Discovering Geometry: An Investigative Approach  4th Edition
ISBN: 9781559538824
Solutions for Chapter 10.2: Volume of Prisms and Cylinders
Get Full SolutionsSince 26 problems in chapter 10.2: Volume of Prisms and Cylinders have been answered, more than 24733 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Discovering Geometry: An Investigative Approach was written by and is associated to the ISBN: 9781559538824. Chapter 10.2: Volume of Prisms and Cylinders includes 26 full stepbystep solutions. This textbook survival guide was created for the textbook: Discovering Geometry: An Investigative Approach, edition: 4.

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

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).

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.

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.

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

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

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.

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

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

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.