 1.3.1: Use the five step strategy for solving word problems to find the n...
 1.3.2: Use the five step strategy for solving word problems to find the n...
 1.3.3: Use the five step strategy for solving word problems to find the n...
 1.3.4: Use the five step strategy for solving word problems to find the n...
 1.3.5: Use the five step strategy for solving word problems to find the n...
 1.3.6: Use the five step strategy for solving word problems to find the n...
 1.3.7: Use the five step strategy for solving word problems to find the n...
 1.3.8: Use the five step strategy for solving word problems to find the n...
 1.3.9: Use the five step strategy for solving word problems to find the n...
 1.3.10: Use the five step strategy for solving word problems to find the n...
 1.3.11: In Exercises 1118, find all values of x satisfying the given condi...
 1.3.12: In Exercises 1118, find all values of x satisfying the given condi...
 1.3.13: In Exercises 1118, find all values of x satisfying the given condi...
 1.3.14: In Exercises 1118, find all values of x satisfying the given condi...
 1.3.15: In Exercises 1118, find all values of x satisfying the given condi...
 1.3.16: In Exercises 1118, find all values of x satisfying the given condi...
 1.3.17: In Exercises 1118, find all values of x satisfying the given condi...
 1.3.18: In Exercises 1118, find all values of x satisfying the given condi...
 1.3.19: How will you spend your averttf:tfi{ife expecJancy of 78 years? The...
 1.3.20: How will you spend your averttf:tfi{ife expecJancy of 78 years? The...
 1.3.21: The bar graph shoks average yearly earnings in tire United States f...
 1.3.22: The bar graph shoks average yearly earnings in tire United States f...
 1.3.23: Even as Americans inaeasingly view a college education as essential...
 1.3.24: Even as Americans inaeasingly view a college education as essential...
 1.3.25: A new car worth $24,000 is depreciating in value by $3000 per year....
 1.3.26: A new car worth $45,000 is depreciating in value by $5000 per year....
 1.3.27: You are choosing between two heaHh clubs. Club A offe rs membership...
 1.3.28: You need to rent a rug cleaner. Company A will rent the machine you...
 1.3.29: The bus fare in a city is S 1.25. People who use the bus have the o...
 1.3.30: A discount pass fo r a bridge costs $30 per month. The toll for the...
 1.3.31: In 2010. there were 13.300 students at college A. with a projected ...
 1.3.32: In 2000, the population of G reece was 10,600,000, with projections...
 1.3.33: After a 20% reduction, you purchase a television for $336. What was...
 1.3.34: After o 30% reduction, you purchase. o dictionary for $30.80. What ...
 1.3.35: Including 8% sales tax. an inn charges $162 per night. Find the inn...
 1.3.36: Including 5% sales tax. an inn charges $252 per night. Find the inn...
 1.3.37: Exercises 3738 involve markup, the amount added to the dealer's co...
 1.3.38: Exercises 3738 involve markup, the amount added to the dealer's co...
 1.3.39: You invested $7000 in two accounts paying 6% and 8% annual interest...
 1.3.40: You invested $11,000 in two accounts paying 5% and 8% annual intere...
 1.3.41: Things did not go quite as planned. You invested SllOOO, part or it...
 1.3.42: Things did not go quite as planned. You invested $12.000. part of i...
 1.3.43: A rectangular soccer field is twice as long as it ls wide. If the p...
 1.3.44: A rectangular swimming pool is three times as long as it is wide. I...
 1.3.45: The length of the rectangular tennis court at Wimbledon is 6 feet l...
 1.3.46: The length of a rectangular pool is 6 meters less than twice the wi...
 1.3.47: The rectangular painting in the figure shown measures 12 inches by ...
 1.3.48: The rectangular swimming pool in the figure shO\vn measures 40 fee....
 1.3.49: An automobile repair shop c.harged a customer $448. listing $63 for...
 1.3.50: A repair bill on a sailboat came to $ 1603, including S532 for part...
 1.3.51: An HMO pamphlet contains the following recommended weight for women...
 1.3.52: A job pays an annual salary of $33.150, which includes a holiday bo...
 1.3.53: Answer the question in the following Peanuts cartoon strip. (Note: ...
 1.3.54: 1l1e rate for a particular inte rnational person.toperson telephon...
 1.3.55: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.56: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.57: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.58: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.59: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.60: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.61: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.62: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.63: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.64: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.65: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.66: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.67: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.68: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.69: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.70: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.71: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.72: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.73: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.74: In Exercises 5574. solve each formula for the specified variable. ...
 1.3.75: In your own words, describe a stepbystep approach for solving alg...
 1.3.76: Write an original word problem that can be solved using a linear eq...
 1.3.77: Explain what it means to solve a formula for a variable.
 1.3.78: Did you have difficulties solvinng some of the problems that were a...
 1.3.79: Use a graphing utility to numerically or graphically verify your wo...
 1.3.80: A tennis d ub offers two payment options. Members can pay a monthl...
 1.3.81: In Exercises 8184, determine whether each statement makes sense or...
 1.3.82: In Exercises 8184, determine whether each statement makes sense or...
 1.3.83: In Exercises 8184, determine whether each statement makes sense or...
 1.3.84: In Exercises 8184, determine whether each statement makes sense or...
 1.3.85: At the north campus of a performing arts school, 10% of the student...
 1.3.86: The price of a dress is reduced by 40%. When the dress still does n...
Solutions for Chapter 1.3: Models and Applications
Full solutions for College Algebra  6th Edition
ISBN: 9780321782281
Solutions for Chapter 1.3: Models and Applications
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.3: Models and Applications includes 86 full stepbystep solutions. College Algebra was written by and is associated to the ISBN: 9780321782281. This textbook survival guide was created for the textbook: College Algebra , edition: 6. Since 86 problems in chapter 1.3: Models and Applications have been answered, more than 38869 students have viewed full stepbystep solutions from this chapter.

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

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

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].

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

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

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= 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).

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

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

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (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.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.