 11.7.1: The function f1x2 = 3 sin14x2 has amplitude and period
 11.7.2: Let and where and are two functions whose common domain is some int...
 11.7.3: The parametric equations define a(n)
 11.7.4: If a circle rolls along a horizontal line without slippage, a fixed...
 11.7.5: True or False Parametric equations defining a curve are unique.
 11.7.6: True or False Curves defined using parametric equations have an ori...
 11.7.7: In 726, graph the curve whose parametric equations are given and sh...
 11.7.8: In 726, graph the curve whose parametric equations are given and sh...
 11.7.9: In 726, graph the curve whose parametric equations are given and sh...
 11.7.10: In 726, graph the curve whose parametric equations are given and sh...
 11.7.11: In 726, graph the curve whose parametric equations are given and sh...
 11.7.12: In 726, graph the curve whose parametric equations are given and sh...
 11.7.13: In 726, graph the curve whose parametric equations are given and sh...
 11.7.14: In 726, graph the curve whose parametric equations are given and sh...
 11.7.15: In 726, graph the curve whose parametric equations are given and sh...
 11.7.16: In 726, graph the curve whose parametric equations are given and sh...
 11.7.17: In 726, graph the curve whose parametric equations are given and sh...
 11.7.18: In 726, graph the curve whose parametric equations are given and sh...
 11.7.19: In 726, graph the curve whose parametric equations are given and sh...
 11.7.20: In 726, graph the curve whose parametric equations are given and sh...
 11.7.21: In 726, graph the curve whose parametric equations are given and sh...
 11.7.22: In 726, graph the curve whose parametric equations are given and sh...
 11.7.23: In 726, graph the curve whose parametric equations are given and sh...
 11.7.24: In 726, graph the curve whose parametric equations are given and sh...
 11.7.25: In 726, graph the curve whose parametric equations are given and sh...
 11.7.26: In 726, graph the curve whose parametric equations are given and sh...
 11.7.27: In 2734, find two different parametric equations for each rectangul...
 11.7.28: In 2734, find two different parametric equations for each rectangul...
 11.7.29: In 2734, find two different parametric equations for each rectangul...
 11.7.30: In 2734, find two different parametric equations for each rectangul...
 11.7.31: In 2734, find two different parametric equations for each rectangul...
 11.7.32: In 2734, find two different parametric equations for each rectangul...
 11.7.33: In 2734, find two different parametric equations for each rectangul...
 11.7.34: In 2734, find two different parametric equations for each rectangul...
 11.7.35: n 3538, find parametric equations that define the curve shown.
 11.7.36: n 3538, find parametric equations that define the curve shown.
 11.7.37: n 3538, find parametric equations that define the curve shown.
 11.7.38: n 3538, find parametric equations that define the curve shown.
 11.7.39: In 3942, find parametric equations for an object that moves along t...
 11.7.40: In 3942, find parametric equations for an object that moves along t...
 11.7.41: In 3942, find parametric equations for an object that moves along t...
 11.7.42: In 3942, find parametric equations for an object that moves along t...
 11.7.43: In 43 and 44, the parametric equations of four curves are given. Gr...
 11.7.44: In 43 and 44, the parametric equations of four curves are given. Gr...
 11.7.45: In 4548, use a graphing utility to graph the curve defined by the g...
 11.7.46: In 4548, use a graphing utility to graph the curve defined by the g...
 11.7.47: In 4548, use a graphing utility to graph the curve defined by the g...
 11.7.48: In 4548, use a graphing utility to graph the curve defined by the g...
 11.7.49: Projectile Motion Bob throws a ball straight up with an initial spe...
 11.7.50: Projectile Motion Alice throws a ball straight up with an initial s...
 11.7.51: Catching a Train Bills train leaves at 8:06 AM and accelerates at t...
 11.7.52: Catching a Bus Jodis bus leaves at 5:30 PM and accelerates at the r...
 11.7.53: Projectile Motion Ichiro throws a baseball with an initial speed of...
 11.7.54: Projectile Motion Mark Texeira hit a baseball with an initial speed...
 11.7.55: Projectile Motion Suppose that Adam hits a golf ball off a cliff 30...
 11.7.56: Projectile Motion Suppose that Karla hits a golf ball off a cliff 3...
 11.7.57: Uniform Motion AToyota Camry (traveling east at 40 mph) and a Chevy...
 11.7.58: Uniform Motion A Cessna (heading south at 120 mph) and a Boeing 747...
 11.7.59: The Green Monster The left field wall at Fenway Park is 310 feet fr...
 11.7.60: Projectile Motion The position of a projectile fired with an initia...
 11.7.61: Show that the parametric equations for a line passing through the p...
 11.7.62: Hypocycloid The hypocycloid is a curve defined by the parametric eq...
 11.7.63: In 62, we graphed the hypocycloid. Now graph the rectangular equati...
 11.7.64: Look up the curves called hypocycloid and epicycloid.Write a report...
Solutions for Chapter 11.7: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 11.7
Get Full SolutionsAlgebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.7 includes 64 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. Since 64 problems in chapter 11.7 have been answered, more than 55819 students have viewed full stepbystep solutions from this chapter.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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 IIĀ· Condition numbers measure the sensitivity of the output to change in the input.

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

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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

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

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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

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).

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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.