 8.4.8.1.280: A procedure used to convert from one unit of measurement to a diffe...
 8.4.8.1.281: A fraction in which the numerator and denominator contain different...
 8.4.8.1.282: The two unit fractions that relate seconds and minutes are and .
 8.4.8.1.283: The two unit fractions that relate feet and inches are and .
 8.4.8.1.284: The two unit fractions that relate meters and centimeters are and .
 8.4.8.1.285: The two unit fractions that relate liters and milliliters are and .
 8.4.8.1.286: a) When converting from kilograms to pounds, you would use the unit...
 8.4.8.1.287: a) When converting from centimeters to feet, you would use the unit...
 8.4.8.1.288: a) When converting from gallons to liters, you would use the unit f...
 8.4.8.1.289: a) When converting from square yards to square meters, you would us...
 8.4.8.1.290: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.291: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.292: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.293: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.294: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.295: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.296: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.297: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.298: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.299: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.300: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.301: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.302: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.303: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.304: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.305: In Exercises 1126, convert the quantity to the indicated units. Whe...
 8.4.8.1.306: In Exercises 2730, use the part of the scorecard that shows the dis...
 8.4.8.1.307: In Exercises 2730, use the part of the scorecard that shows the dis...
 8.4.8.1.308: In Exercises 2730, use the part of the scorecard that shows the dis...
 8.4.8.1.309: In Exercises 2730, use the part of the scorecard that shows the dis...
 8.4.8.1.310: Speed Limit The photo shows that the speed limit is 50 kph. Determi...
 8.4.8.1.311: How Far? Carol Ann Harles new car traveled 105 mi on 5 gal of gasol...
 8.4.8.1.312: Buying Carpet Victoria Montoya is buying outdoor carpet for her rec...
 8.4.8.1.313: Chicago to Atlanta The distance from Chicago, Illinois, to Atlanta,...
 8.4.8.1.314: The QEW Part of the Queen Elizabeth Way in Canada has a speed limit...
 8.4.8.1.315: Milliliters in a Glass A glass holds 8 fl oz. How many milliliters ...
 8.4.8.1.316: Poison Dart Frog A fullgrown strawberry poison dart frog has a wei...
 8.4.8.1.317: Swimming Pool A swimming pool holds 12,500 gal of water. What is th...
 8.4.8.1.318: Area of Tribal Park The Monument Valley Navajo Tribal Park has an a...
 8.4.8.1.319: Building a Basement A basement is to be 50 ft long, 30 ft wide, and...
 8.4.8.1.320: Cost of Rice If rice costs $1.10 per kilogram, determine the cost o...
 8.4.8.1.321: Weight Restriction The weight restriction on a road in Italy is 7.5...
 8.4.8.1.322: Capacity of a Tank Truck A tank truck holds 34.5 k/ of gasoline. Ho...
 8.4.8.1.323: Cost per Gram A 0.25oz bottle of Chanel perfume costs $80. What is...
 8.4.8.1.324: Cars Engine A specific cars engine has a capacity of 5.7 / of oil. ...
 8.4.8.1.325: Death Valley Elevation The lowest elevation in the United States is...
 8.4.8.1.326: Sign in Russia Using the White sign in the photo, determine the dis...
 8.4.8.1.327: A Precious Stone One gram is the same as 5 carats. David Erichs new...
 8.4.8.1.328: Square Meters to Square Feet One meter is about 3.3 ft. Use this in...
 8.4.8.1.329: Acres to Hectares One acre is about 0.4 hectare. a) Use this inform...
 8.4.8.1.330: Dosage for a Child The recommended dosage of the drug codeine for p...
 8.4.8.1.331: Dosage for a Man For each kilogram of a persons weight, 1.5 mg of t...
 8.4.8.1.332: Ampicillin The recommended dosage of the drug ampicillin for pediat...
 8.4.8.1.333: Medicine for a Dog For each kilogram of weight of a dog, 5 mg of th...
 8.4.8.1.334: Active Ingredients The label on the bottle of Triaminic expectorant...
 8.4.8.1.335: Stomach Ache Remedy The label on the bottle of Maximum Strength Pep...
 8.4.8.1.336: Gibraltar Gibraltar is a British territory that shares a 1.2kilome...
 8.4.8.1.337: Disney Magic The Disney Magic Cruise Ship is 964 feet long, has a w...
 8.4.8.1.338: Overseas Flight The photo of the monitor taken during an overseas f...
 8.4.8.1.339: Peppers Peppers in Rome, Italy, cost 2 euros (:) per kilogram. a) D...
 8.4.8.1.340: Saffron The photo shows Saffron for sale in Europe. a) Saffron cost...
 8.4.8.1.341: Unit Fractions On February 25, 2010, the conversion rate for the U....
 8.4.8.1.342: Unit Fractions An advertisement for Piaggio airplanes stated that t...
 8.4.8.1.343: Making Cookies Change all the measurements in the cookie recipe to ...
 8.4.8.1.344: Nursing Question The following question was selected from a nursing...
 8.4.8.1.345: How Much Beef Paul Gosse is planning a picnic and plans on purchasi...
 8.4.8.1.346: An Auto Engine The displacement of automobile engines is measured i...
 8.4.8.1.347: In Exercises 6875, try to solve the puzzle. What is1 millionth of a...
 8.4.8.1.348: In Exercises 6875, try to solve the puzzle. What is2000 pounds of C...
 8.4.8.1.349: In Exercises 6875, try to solve the puzzle. What is448 grams of cake?
 8.4.8.1.350: In Exercises 6875, try to solve the puzzle. What is 1000 aches?
 8.4.8.1.351: In Exercises 6875, try to solve the puzzle. What is 1 million bicyc...
 8.4.8.1.352: In Exercises 6875, try to solve the puzzle. What is 1 million phones?
 8.4.8.1.353: In Exercises 6875, try to solve the puzzle. What is 10 cards?
 8.4.8.1.354: In Exercises 6875, try to solve the puzzle. What is 2000 mockingbirds?
Solutions for Chapter 8.4: The Metric System
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 8.4: The Metric System
Get Full SolutionsThis textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Since 75 problems in chapter 8.4: The Metric System have been answered, more than 70703 students have viewed full stepbystep solutions from this chapter. Chapter 8.4: The Metric System includes 75 full stepbystep solutions. A Survey of Mathematics with Applications was written by and is associated to the ISBN: 9780321759665.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

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

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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

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.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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).

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.

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

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

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

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Solvable system Ax = b.
The right side b is in the column space of A.

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

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.