 7.3.1: In Exercises 16, match the equation with one of thegraphs (a)(f), w...
 7.3.2: In Exercises 16, match the equation with one of thegraphs (a)(f), w...
 7.3.3: In Exercises 16, match the equation with one of thegraphs (a)(f), w...
 7.3.4: In Exercises 16, match the equation with one of thegraphs (a)(f), w...
 7.3.5: In Exercises 16, match the equation with one of thegraphs (a)(f), w...
 7.3.6: In Exercises 16, match the equation with one of thegraphs (a)(f), w...
 7.3.7: Find an equation of a hyperbola satisfying the givenconditions. Ver...
 7.3.8: Find an equation of a hyperbola satisfying the givenconditions. Ver...
 7.3.9: Find an equation of a hyperbola satisfying the givenconditions. Asy...
 7.3.10: Find an equation of a hyperbola satisfying the givenconditions. Asy...
 7.3.11: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.12: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.13: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.14: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.15: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.16: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.17: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.18: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.19: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.20: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.21: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.22: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.23: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.24: Find the center, the vertices, the foci, and theasymptotes. Then dr...
 7.3.25: Find the center, the vertices, the foci, and the asymptotesof the h...
 7.3.26: Find the center, the vertices, the foci, and the asymptotesof the h...
 7.3.27: Find the center, the vertices, the foci, and the asymptotesof the h...
 7.3.28: Find the center, the vertices, the foci, and the asymptotesof the h...
 7.3.29: Find the center, the vertices, the foci, and the asymptotesof the h...
 7.3.30: Find the center, the vertices, the foci, and the asymptotesof the h...
 7.3.31: Find the center, the vertices, the foci, and the asymptotesof the h...
 7.3.32: Find the center, the vertices, the foci, and the asymptotesof the h...
 7.3.33: Find the center, the vertices, the foci, and the asymptotesof the h...
 7.3.34: Find the center, the vertices, the foci, and the asymptotesof the h...
 7.3.35: The eccentricity of a hyperbola is defined as e = c>a.For a hyperbo...
 7.3.36: Which hyperbola has the larger eccentricity?(Assume that the coordi...
 7.3.37: Find an equation of a hyperbola with vertices13, 72 and 13, 72 and...
 7.3.38: Find an equation of a hyperbola with vertices11, 32 and 11, 72 an...
 7.3.39: Nuclear Cooling Tower. A cross section of a nuclearcooling tower is...
 7.3.40: Hyperbolic Mirror. Certain telescopes containboth a parabolic mirro...
 7.3.41: In Exercises 4144, given the function:a) Determine whether it is on...
 7.3.42: In Exercises 4144, given the function:a) Determine whether it is on...
 7.3.43: In Exercises 4144, given the function:a) Determine whether it is on...
 7.3.44: In Exercises 4144, given the function:a) Determine whether it is on...
 7.3.45: Solve x + y = 5,x  y = 7
 7.3.46: Solve 3x  2y = 5,5x + 2y = 3
 7.3.47: Solve 2x  3y = 7,3x + 5y = 1
 7.3.48: Solve 3x + 2y = 1,2x + 3y = 6
 7.3.49: Find an equation of a hyperbola satisfying the givenconditions. Ver...
 7.3.50: Find an equation of a hyperbola satisfying the givenconditions. Ver...
 7.3.51: Use a graphing calculator to find the center, the vertices,and the ...
 7.3.52: Use a graphing calculator to find the center, the vertices,and the ...
 7.3.53: Navigation. Two radio transmitters positioned300 mi apart along the...
Solutions for Chapter 7.3: The Hyperbola
Full solutions for College Algebra: Graphs and Models  5th Edition
ISBN: 9780321783950
Solutions for Chapter 7.3: The Hyperbola
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra: Graphs and Models, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Since 53 problems in chapter 7.3: The Hyperbola have been answered, more than 29552 students have viewed full stepbystep solutions from this chapter. College Algebra: Graphs and Models was written by and is associated to the ISBN: 9780321783950. Chapter 7.3: The Hyperbola includes 53 full stepbystep solutions.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

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!

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

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

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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.

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

Iterative method.
A sequence of steps intended to approach the desired solution.

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

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.

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)·(b  Ax) = o.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

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

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

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.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

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

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.