 7.7.1: Use Steps 2 and 3 of the sixstep method to set up the equation you...
 7.7.2: Use Steps 2 and 3 of the sixstep method to set up the equation you...
 7.7.3: Solve each problem. See Example 1.In a certain fraction, the denomi...
 7.7.4: Solve each problem. See Example 1.In a certain fraction, the denomi...
 7.7.5: Solve each problem. See Example 1.The numerator of a certain fracti...
 7.7.6: Solve each problem. See Example 1.The denominator of a certain frac...
 7.7.7: Solve each problem. See Example 1.Onethird of a number is 2 greate...
 7.7.8: Solve each problem. See Example 1.Oneseventh of a number is 6 grea...
 7.7.9: Solve each problem. See Example 1.A quantity, of it, of it, and of ...
 7.7.10: Solve each problem. See Example 1.A quantity, of it, of it, and of ...
 7.7.11: Solve each problem. See Example 5 in Section 2.7 (pages 143 and 144...
 7.7.12: Solve each problem. See Example 5 in Section 2.7 (pages 143 and 144...
 7.7.13: Solve each problem. See Example 5 in Section 2.7 (pages 143 and 144...
 7.7.14: Solve each problem. See Example 5 in Section 2.7 (pages 143 and 144...
 7.7.15: Solve each problem. See Example 5 in Section 2.7 (pages 143 and 144...
 7.7.16: Solve each problem. See Example 5 in Section 2.7 (pages 143 and 144...
 7.7.17: Solve each problem.Suppose Stephanie walks D miles at R mph in the ...
 7.7.18: Solve each problem.If a migrating hawk travels m mph in still air, ...
 7.7.19: Set up the equation you would use to solve each problem. Do not act...
 7.7.20: Set up the equation you would use to solve each problem. Do not act...
 7.7.21: Solve each problem. See Example 2.A boat can go 20 mi against a cur...
 7.7.22: Solve each problem. See Example 2.Vince Grosso can fly his plane 20...
 7.7.23: Solve each problem. See Example 2.The sanderling is a small shorebi...
 7.7.24: Solve each problem. See Example 2.Airplanes usually fly faster from...
 7.7.25: Solve each problem. See Example 2.An airplane maintaining a constan...
 7.7.26: Solve each problem. See Example 2.A river has a current of 4 km per...
 7.7.27: Solve each problem. See Example 2.Connie McNairs boat goes 12 mph. ...
 7.7.28: Solve each problem. See Example 2. Howie Sorkin can travel 8 mi ups...
 7.7.29: Solve each problem. See Example 2.The distance from Seattle, Washin...
 7.7.30: Solve each problem. See Example 2.Driving from Tulsa to Detroit, De...
 7.7.31: Solve each problem.If it takes Elayn 10 hr to do a job, what is her...
 7.7.32: Solve each problem.If it takes Clay 12 hr to do a job, how much of ...
 7.7.33: In Exercises 33 and 34, set up the equation you would use to solve ...
 7.7.34: In Exercises 33 and 34, set up the equation you would use to solve ...
 7.7.35: Solve each problem. See Example 3.Heather Schaefer, a high school m...
 7.7.36: Solve each problem. See Example 3.Zachary and Samuel are brothers w...
 7.7.37: Solve each problem. See Example 3.A pump can pump the water out of ...
 7.7.38: Solve each problem. See Example 3.Lou Viggianos copier can do a pri...
 7.7.39: Solve each problem. See Example 3.An experienced employee can enter...
 7.7.40: Solve each problem. See Example 3.One roofer can put a new roof on ...
 7.7.41: Solve each problem. See Example 3.One pipe can fill a swimming pool...
 7.7.42: Solve each problem. See Example 3.An inlet pipe can fill a swimming...
 7.7.43: Extend the concepts of Example 3 to solve each problemA coldwater ...
 7.7.44: Extend the concepts of Example 3 to solve each problemRefer to Exer...
 7.7.45: Solve each equation for k. See Section 2.2.200 = 15k
 7.7.46: Solve each equation for k. See Section 2.2.25 = 9k
 7.7.47: Solve each equation for k. See Section 2.2.180 = k20
 7.7.48: Solve each equation for k. See Section 2.2.92 = k2
 7.7.49: Solve each formula for k. See Section 2.5.y = kx
 7.7.50: Solve each formula for k. See Section 2.5.y = kx2
 7.7.51: Solve each formula for k. See Section 2.5.y = kx
 7.7.52: Solve each formula for k. See Section 2.5.y = kx2
Solutions for Chapter 7.7: Applications of Rational Expressions
Full solutions for Beginning Algebra  11th Edition
ISBN: 9780321673480
Solutions for Chapter 7.7: Applications of Rational Expressions
Get Full SolutionsThis textbook survival guide was created for the textbook: Beginning Algebra, edition: 11. Since 52 problems in chapter 7.7: Applications of Rational Expressions have been answered, more than 39698 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Beginning Algebra was written by and is associated to the ISBN: 9780321673480. Chapter 7.7: Applications of Rational Expressions includes 52 full stepbystep solutions.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

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.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

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).

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].

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

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

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.

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).

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)ยท(b  Ax) = o.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

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