 10.7.1: The function f1x2 = 3 sin14x2 has amplitude and period . (pp. 402404)
 10.7.2: Let x = f1t2 and y = g1t2, where f and g are two functions whose co...
 10.7.3: The parametric equations x = 2 sin t, y = 3 cos t define a(n) .
 10.7.4: f a circle rolls along a horizontal line without slippage, a fixed ...
 10.7.5: True or False Parametric equations defining a curve are unique
 10.7.6: True or False Curves defined using parametric equations have an ori...
 10.7.7: In 726, graph the curve whose parametric equations are given and sh...
 10.7.8: In 726, graph the curve whose parametric equations are given and sh...
 10.7.9: In 726, graph the curve whose parametric equations are given and sh...
 10.7.10: In 726, graph the curve whose parametric equations are given and sh...
 10.7.11: In 726, graph the curve whose parametric equations are given and sh...
 10.7.12: In 726, graph the curve whose parametric equations are given and sh...
 10.7.13: In 726, graph the curve whose parametric equations are given and sh...
 10.7.14: In 726, graph the curve whose parametric equations are given and sh...
 10.7.15: In 726, graph the curve whose parametric equations are given and sh...
 10.7.16: In 726, graph the curve whose parametric equations are given and sh...
 10.7.17: In 726, graph the curve whose parametric equations are given and sh...
 10.7.18: In 726, graph the curve whose parametric equations are given and sh...
 10.7.19: In 726, graph the curve whose parametric equations are given and sh...
 10.7.20: In 726, graph the curve whose parametric equations are given and sh...
 10.7.21: In 726, graph the curve whose parametric equations are given and sh...
 10.7.22: In 726, graph the curve whose parametric equations are given and sh...
 10.7.23: In 726, graph the curve whose parametric equations are given and sh...
 10.7.24: In 726, graph the curve whose parametric equations are given and sh...
 10.7.25: In 726, graph the curve whose parametric equations are given and sh...
 10.7.26: In 726, graph the curve whose parametric equations are given and sh...
 10.7.27: In 2734, find two different parametric equations for each rectangul...
 10.7.28: In 2734, find two different parametric equations for each rectangul...
 10.7.29: In 2734, find two different parametric equations for each rectangul...
 10.7.30: In 2734, find two different parametric equations for each rectangul...
 10.7.31: In 2734, find two different parametric equations for each rectangul...
 10.7.32: In 2734, find two different parametric equations for each rectangul...
 10.7.33: In 2734, find two different parametric equations for each rectangul...
 10.7.34: In 2734, find two different parametric equations for each rectangul...
 10.7.35: In 3538, find parametric equations that define the curve shown.
 10.7.36: In 3538, find parametric equations that define the curve shown.
 10.7.37: In 3538, find parametric equations that define the curve shown.
 10.7.38: In 3538, find parametric equations that define the curve shown.
 10.7.39: The motion begins at 12, 02, is clockwise, and requires 2 seconds f...
 10.7.40: The motion begins at 10, 32, is counterclockwise, and requires 1 se...
 10.7.41: The motion begins at 10, 32, is clockwise, and requires 1 second fo...
 10.7.42: The motion begins at 12, 02, is counterclockwise, and requires 3 se...
 10.7.43: In 43 and 44, the parametric equations of four curves are given. Gr...
 10.7.44: In 43 and 44, the parametric equations of four curves are given. Gr...
 10.7.45: In 45 48, use a graphing utility to graph the curve defined by the ...
 10.7.46: In 45 48, use a graphing utility to graph the curve defined by the ...
 10.7.47: In 45 48, use a graphing utility to graph the curve defined by the ...
 10.7.48: In 45 48, use a graphing utility to graph the curve defined by the ...
 10.7.49: Bob throws a ball straight up with an initial speed of 50 feet per ...
 10.7.50: Alice throws a ball straight up with an initial speed of 40 feet pe...
 10.7.51: Bills train leaves at 8:06 am and accelerates at the rate of 2 mete...
 10.7.52: Jodis bus leaves at 5:30 pm and accelerates at the rate of 3 meters...
 10.7.53: Ichiro throws a baseball with an initial speed of 145 feet per seco...
 10.7.54: Mark Texeira hit a baseball with an initial speed of 125 feet per s...
 10.7.55: Suppose that Adam hits a golf ball off a cliff 300 meters high with...
 10.7.56: Suppose that Karla hits a golf ball off a cliff 300 meters high wit...
 10.7.57: A Toyota Camry (traveling east at 40 mph) and a Chevy Impala (trave...
 10.7.58: A Cessna (heading south at 120 mph) and a Boeing 747 (heading west ...
 10.7.59: The left field wall at Fenway Park is 310 feet from home plate; the...
 10.7.60: The position of a projectile fired with an initial velocity y0 feet...
 10.7.61: Show that the parametric equations for a line passing through the p...
 10.7.62: Hypocycloid The hypocycloid is a curve defined by the parametric eq...
 10.7.63: In 62, we graphed the hypocycloid. Now graph the rectangular equati...
 10.7.64: Look up the curves called hypocycloid and epicycloid. Write a repor...
Solutions for Chapter 10.7: Plane Curves and Parametric Equations
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 10.7: Plane Curves and Parametric Equations
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Since 64 problems in chapter 10.7: Plane Curves and Parametric Equations have been answered, more than 59084 students have viewed full stepbystep solutions from this chapter. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. Chapter 10.7: Plane Curves and Parametric Equations includes 64 full stepbystep solutions.

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).

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).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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].

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

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

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.

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.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

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