 6.7.1: A ________ measures the acute angle a path or line of sight makes w...
 6.7.2: A point that moves on a coordinate line is said to be in simple ___...
 6.7.3: The time for one complete cycle of a point in simple harmonic motio...
 6.7.4: The number of cycles per second of a point in simple harmonic motio...
 6.7.5: A 30 , b 3
 6.7.6: B 54 , c 15
 6.7.7: B 71 , b 24
 6.7.8: A 8.4 , a 40.5
 6.7.9: a 3, b 4
 6.7.10: a 25, c 35
 6.7.11: b 16, c 52
 6.7.12: b 1.32, c 9.45
 6.7.13: A 12 15, c 430.5
 6.7.14: B 65 12, a 14.2
 6.7.15: 45 , b 6
 6.7.16: 18 , b 10
 6.7.17: 32 , b 8
 6.7.18: 27 , b 11
 6.7.19: LENGTH The sun is above the horizon. Find the length of a shadow ca...
 6.7.20: LENGTH The sun is above the horizon. Find the length of a shadow ca...
 6.7.21: HEIGHT A ladder 20 feet long leans against the side of a house. Fin...
 6.7.22: HEIGHT The length of a shadow of a tree is 125 feet when the angle ...
 6.7.23: HEIGHT From a point 50 feet in front of a church, the angles of ele...
 6.7.24: DISTANCE An observer in a lighthouse 350 feet above sea level obser...
 6.7.25: DISTANCE A passenger in an airplane at an altitude of 10 kilometers...
 6.7.26: ALTITUDE You observe a plane approaching overhead and assume that i...
 6.7.27: ANGLE OF ELEVATION An engineer erects a 75foot cellular telephone ...
 6.7.28: ANGLE OF ELEVATION The height of an outdoor basketball backboard is...
 6.7.29: ANGLE OF DEPRESSION A cellular telephone tower that is 150 feet tal...
 6.7.30: ANGLE OF DEPRESSION A Global Positioning System satellite orbits 12...
 6.7.31: HEIGHT You are holding one of the tethers attached to the top of a ...
 6.7.32: HEIGHT The designers of a water park are creating a new slide and h...
 6.7.33: SPEED ENFORCEMENT A police department has set up a speed enforcemen...
 6.7.34: AIRPLANE ASCENT During takeoff, an airplanes angle of ascent is and...
 6.7.35: NAVIGATION An airplane flying at 600 miles per hour has a bearing o...
 6.7.36: NAVIGATION A jet leaves Reno, Nevada and is headed toward Miami, Fl...
 6.7.37: NAVIGATION A ship leaves port at noon and has a bearing of S W. The...
 6.7.38: NAVIGATION A privately owned yacht leaves a dock in Myrtle Beach, S...
 6.7.39: NAVIGATION A ship is 45 miles east and 30 miles south of port. The ...
 6.7.40: NAVIGATION An airplane is 160 miles north and 85 miles east of an a...
 6.7.41: SURVEYING A surveyor wants to find the distance across a swamp (see...
 6.7.42: LOCATION OF A FIRE Two fire towers are 30 kilometers apart, where t...
 6.7.43: L1: L2: 3x 2y 5 x y 1
 6.7.44: L1: L2: 2x y x 5y 8 4 L
 6.7.45: GEOMETRY Determine the angle between the diagonal of a cube and the...
 6.7.46: GEOMETRY Determine the angle between the diagonal of a cube and its...
 6.7.47: GEOMETRY Find the length of the sides of a regular pentagon inscrib...
 6.7.48: GEOMETRY Find the length of the sides of a regular hexagon inscribe...
 6.7.49: HARDWARE Write the distance across the flat sides of a hexagonal nu...
 6.7.50: BOLT HOLES The figure shows a circular piece of sheet metal that ha...
 6.7.51: 35 35 10 10 10 10
 6.7.52: 36 ft 9 ft 6 ft 6 ft b c a
 6.7.53: 0 4 centimeters 2 seconds
 6.7.54: 0 3 meters 6 seconds
 6.7.55: 3 inches 3 inches 1.5 seconds
 6.7.56: 2 feet 2 feet 10 seconds
 6.7.57: d 9 cos cos 20t 6 5 t
 6.7.58: d
 6.7.59: d sin 792t 1 4 sin 6t
 6.7.60: d 1 64 d sin 792t
 6.7.61: TUNING FORK A point on the end of a tuning fork moves in simple har...
 6.7.62: WAVE MOTION A buoy oscillates in simple harmonic motion as waves go...
 6.7.63: OSCILLATION OF A SPRING A ball that is bobbing up and down on the e...
 6.7.64: NUMERICAL AND GRAPHICAL ANALYSIS The cross section of an irrigation...
 6.7.65: NUMERICAL AND GRAPHICAL ANALYSIS A 2meterhigh fence is 3 meters f...
 6.7.66: DATA ANALYSIS The table shows the average sales (in millions of dol...
 6.7.67: DATA ANALYSIS The number of hours of daylight in Denver, Colorado o...
 6.7.68: CAPSTONE While walking across flat land, you notice a wind turbine ...
 6.7.69: The Leaning Tower of Pisa is not vertical, but if you know the angl...
 6.7.70: N 24 E means 24 degrees north of east.
Solutions for Chapter 6.7: Applications and Models
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9781439048474
Solutions for Chapter 6.7: Applications and Models
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 70 problems in chapter 6.7: Applications and Models have been answered, more than 47407 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8. Chapter 6.7: Applications and Models includes 70 full stepbystep solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048474.

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

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.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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

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.

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.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

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).

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.

Outer product uv T
= column times row = rank one matrix.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

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

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.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).