 4.8.4.8.1: An angle that measures from the horizontal upward to an object is c...
 4.8.4.8.2: A _______ measures the acute angle a path or line of sight makes wi...
 4.8.4.8.3: A point that moves on a coordinate line is said to be in simple ___...
 4.8.4.8.4: In Exercises 110, solve the right triangle shown in the figure
 4.8.4.8.5: In Exercises 110, solve the right triangle shown in the figure
 4.8.4.8.6: In Exercises 110, solve the right triangle shown in the figure
 4.8.4.8.7: In Exercises 110, solve the right triangle shown in the figure
 4.8.4.8.8: In Exercises 110, solve the right triangle shown in the figure
 4.8.4.8.9: In Exercises 110, solve the right triangle shown in the figure
 4.8.4.8.10: In Exercises 110, solve the right triangle shown in the figure
 4.8.4.8.11: In Exercises 1114, find the altitude of the isosceles triangle show...
 4.8.4.8.12: In Exercises 1114, find the altitude of the isosceles triangle show...
 4.8.4.8.13: In Exercises 1114, find the altitude of the isosceles triangle show...
 4.8.4.8.14: In Exercises 1114, find the altitude of the isosceles triangle show...
 4.8.4.8.15: Length A shadow of length is created by a 60foot silo when the sun...
 4.8.4.8.16: Length A shadow of length is created by an 850foot building when t...
 4.8.4.8.17: Height A ladder 20 feet long leans against the side of a house. The...
 4.8.4.8.18: Height The angle of elevation from the base to the top of a watersl...
 4.8.4.8.19: Height A 100foot line is attached to a kite. When the kite has pul...
 4.8.4.8.20: Depth The sonar of a navy cruiser detects a submarine that is 4000 ...
 4.8.4.8.21: Height From a point 50 feet in front of a church, the angles of ele...
 4.8.4.8.22: Height From a point 100 feet in front of a public library, the angl...
 4.8.4.8.23: Height You are holding one of the tethers attached to the top of a ...
 4.8.4.8.24: Height The designers of a water park are creating a new slide and h...
 4.8.4.8.25: Angle of Elevation An engineer erects a 75foot vertical cellularp...
 4.8.4.8.26: Angle of Elevation The height of an outdoor basketball backboard is...
 4.8.4.8.27: Angle of Depression A Global Positioning System satellite orbits 12...
 4.8.4.8.28: Angle of Depression Find the angle of depression from the top of a ...
 4.8.4.8.29: Airplane Ascent When an airplane leaves the runway, its angle of cl...
 4.8.4.8.30: Airplane Ascent How long will it take the plane in Exercise 29 to c...
 4.8.4.8.31: Mountain Descent A sign on the roadway at the top of a mountain ind...
 4.8.4.8.32: Ski Slope A ski slope on a mountain has an angle of elevation of Th...
 4.8.4.8.33: Navigation A ship leaves port at noon and has a bearing of The ship...
 4.8.4.8.34: Navigation An airplane flying at 600 miles per hour has a bearing o...
 4.8.4.8.35: Surveying A surveyor wants to find the distance across a pond (see ...
 4.8.4.8.36: Location of a Fire Two fire towers are 30 kilometers apart, where t...
 4.8.4.8.37: Navigation A ship is 45 miles east and 30 miles south of port. The ...
 4.8.4.8.38: Navigation A plane is 160 miles north and 85 miles east of an airpo...
 4.8.4.8.39: Distance An observer in a lighthouse 350 feet above sea level obser...
 4.8.4.8.40: Distance A passenger in an airplane flying at an altitude of 10 kil...
 4.8.4.8.41: Altitude A plane is observed approaching your home and you assume i...
 4.8.4.8.42: Height While traveling across flat land, you notice a mountain dire...
 4.8.4.8.43: Angle of Elevation The top of a drivein theater screen is 50 feet ...
 4.8.4.8.44: Moving A mattress of length L is being moved through two hallways t...
 4.8.4.8.45: Geometry In Exercises 45 and 46, find the angle between the two non...
 4.8.4.8.46: Geometry In Exercises 45 and 46, find the angle between the two non...
 4.8.4.8.47: Geometry Determine the angle between the diagonal of a cube and the...
 4.8.4.8.48: Geometry Determine the angle between the diagonal of a cube and its...
 4.8.4.8.49: Hardware Write the distance across the flat sides of a hexagonal nu...
 4.8.4.8.50: Hardware The figure shows a circular piece of sheet metal of diamet...
 4.8.4.8.51: Harmonic Motion In Exercises 5154, find a model for simple harmonic...
 4.8.4.8.52: Harmonic Motion In Exercises 5154, find a model for simple harmonic...
 4.8.4.8.53: Harmonic Motion In Exercises 5154, find a model for simple harmonic...
 4.8.4.8.54: Harmonic Motion In Exercises 5154, find a model for simple harmonic...
 4.8.4.8.55: Harmonic Motion In Exercises 5558, for the simple harmonic motion d...
 4.8.4.8.56: Harmonic Motion In Exercises 5558, for the simple harmonic motion d...
 4.8.4.8.57: Harmonic Motion In Exercises 5558, for the simple harmonic motion d...
 4.8.4.8.58: Harmonic Motion In Exercises 5558, for the simple harmonic motion d...
 4.8.4.8.59: Tuning Fork A point on the end of a tuning fork moves in the simple...
 4.8.4.8.60: Wave Motion A buoy oscillates in simple harmonic motion as waves go...
 4.8.4.8.61: Springs A ball that is bobbing up and down on the end of a spring h...
 4.8.4.8.62: Numerical and Graphical Analysis A twometerhigh fence is 3 meters...
 4.8.4.8.63: Numerical and Graphical Analysis The cross sections of an irrigatio...
 4.8.4.8.64: Data Analysis The table shows the average sales (in millions of dol...
 4.8.4.8.65: Data Analysis The times of sunset (Greenwich Mean Time) at north la...
 4.8.4.8.66: Writing Is it true that means 24 degrees north of east? Explain.
 4.8.4.8.67: True or False? In Exercises 67 and 68, determine whether the statem...
 4.8.4.8.68: True or False? In Exercises 67 and 68, determine whether the statem...
 4.8.4.8.69: In Exercises 6972, write the standard form of the equation of the l...
 4.8.4.8.70: In Exercises 6972, write the standard form of the equation of the l...
 4.8.4.8.71: In Exercises 6972, write the standard form of the equation of the l...
 4.8.4.8.72: In Exercises 6972, write the standard form of the equation of the l...
 4.8.4.8.73: In Exercises 7376, find the domain of the function.
 4.8.4.8.74: In Exercises 7376, find the domain of the function.
 4.8.4.8.75: In Exercises 7376, find the domain of the function.
 4.8.4.8.76: In Exercises 7376, find the domain of the function.
Solutions for Chapter 4.8: Applications and Models
Full solutions for Precalculus With Limits A Graphing Approach  5th Edition
ISBN: 9780618851522
Solutions for Chapter 4.8: Applications and Models
Get Full SolutionsSince 76 problems in chapter 4.8: Applications and Models have been answered, more than 32478 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Precalculus With Limits A Graphing Approach, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Precalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522. Chapter 4.8: Applications and Models includes 76 full stepbystep solutions.

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.

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

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

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

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

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 .

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.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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

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

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

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

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.