Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
13th Edition
ISBN: 9780321945525
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
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Chapter 1.2, Problem 26E
In Problems 29-34, sketch a graph of each equation or pair of equations in a rectangular
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1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set
Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k
components, where k is the greatest common divisor of {n, r,s}.
Question 3
over a field K.
In this question, MË(K) denotes the set of n × n matrices
(a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is
equivalent to A-¹? Justify your answer.
(b) Let B be given by
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0 -7 7
Working over the field F2 with 2 elements, compute the rank of B as an element
of M2(F2).
(c) Let
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and consider C as an element of M3(Q). Determine the minimal polynomial
mc(x) and hence, or otherwise, show that C can not be diagonalised.
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(d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write
down all the eigenvalues. Show your working.
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16. Solve the given differential equation:
y" + 4y sin (t)u(t 2π),
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Given,
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Chapter 1 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Ch. 1.1 - According to equality property 2, multiplying both...Ch. 1.1 - Replace ? with < or > in each of the following:...Ch. 1.1 - The solution to Example 5B shows the graph of the...Ch. 1.1 - Solve and check: 3x2(2x5)=2(x+3)8Ch. 1.1 - Solve and check: x+13x4=12Ch. 1.1 - Matched Problem 3 If a cardboard box has length L,...Ch. 1.1 - Replace each question mark with either < or >....Ch. 1.1 - (A) Write 7,4 as a double inequality and graph....Ch. 1.1 - Solve and graph: 3(x1)5(x+2)5Ch. 1.1 - Solve and graph: 83x57
Ch. 1.1 - Mary paid 8.5 sales tax and a 190 title and...Ch. 1.1 - How many DVDs would a multimedia company have to...Ch. 1.1 - What net annual salary in 1973 would have had the...Ch. 1.1 - Solve Problems 1-6. 2m+9=5m6Ch. 1.1 - Solve Problems 1-6. 3y4=6y19Ch. 1.1 - Solve Problems 1-6. 2x+34Ch. 1.1 - Solve Problems 1-6. 5x+21Ch. 1.1 - Solve Problems 1-6. 3x12Ch. 1.1 - Solve Problems 1-6. 4x8Ch. 1.1 - Solve Problems 7-10 and graph. 4x75Ch. 1.1 - Solve Problems 7-10 and graph. 2x+84Ch. 1.1 - Solve Problems 7-10 and graph. 2x+35Ch. 1.1 - Solve Problems 7-10 and graph. 42y39Ch. 1.1 - In Problems 19-32, find the solution set. x4+12=18Ch. 1.1 - In Problems 19-32, find the solution set. m34=23Ch. 1.1 - In Problems 19-32, find the solution set. y532Ch. 1.1 - In Problems 19-32, find the solution set. x456Ch. 1.1 - In Problems 19-32, find the solution set....Ch. 1.1 - In Problems 19-32, find the solution set....Ch. 1.1 - In Problems 19-32, find the solution set....Ch. 1.1 - In Problems 19-32, find the solution set. 34x=5x+1Ch. 1.1 - In Problems 19-32, find the solution set. 3y4y3Ch. 1.1 - In Problems 19-32, find the solution set. x22x5Ch. 1.1 - In Problems 19-32, find the solution set. x5x6=65Ch. 1.1 - In Problems 19-32, find the solution set. y4y3=12Ch. 1.1 - In Problems 19-32, find the solution set. m5335m2Ch. 1.1 - In Problems 19-32, find the solution set. u223u3+2Ch. 1.1 - In Problems 33-36, solve and graph. 23x714Ch. 1.1 - In Problems 33-36, solve and graph. 45x+621Ch. 1.1 - In Problems 33-36, solve and graph. 495C+3268Ch. 1.1 - In Problems 33-36, solve and graph. 123t+511Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 37-42, solve for the indicated...Ch. 1.1 - In Problems 43 and 44, solve and graph. 347x18Ch. 1.1 - In Problems 43 and 44, solve and graph. 1083u6Ch. 1.1 - What can be said about the signs of the numbers...Ch. 1.1 - What can be said about the signs of the numbers...Ch. 1.1 - If both a and b are positive numbers and b/a. is...Ch. 1.1 - If both a and b are negative numbers and b/a is...Ch. 1.1 - In Problems 41-46, discuss the validity of each...Ch. 1.1 - In Problems 41-46, discuss the validity of each...Ch. 1.1 - In Problems 41-46, discuss the validity of each...Ch. 1.1 - In Problems 41-46, discuss the validity of each...Ch. 1.1 - In Problems 41-46, discuss the validity of each...Ch. 1.1 - In Problems 41-46, discuss the validity of each...Ch. 1.1 - Ticket sales. A rock concert brought in $432,500...Ch. 1.1 - Parking meter coins. An all-day parking meter...Ch. 1.1 - IRA. You have $500,000 in an IRA (Individual...Ch. 1.1 - IRA. Refer to Problem 49. How should you divide...Ch. 1.1 - Car prices. If the price change of cars parallels...Ch. 1.1 - Home values. If the price change in houses...Ch. 1.1 - Retail and wholesale prices. Retail prices in a...Ch. 1.1 - Retail and sale prices. Sale prices in a...Ch. 1.1 - Equipment rental. A golf course charges $52 for a...Ch. 1.1 - Equipment rental. The local supermarket rents...Ch. 1.1 - Sales commissions. One employee of a computer...Ch. 1.1 - Sales commissions. A second employee of the...Ch. 1.1 - Break-even analysis. A publisher for a promising...Ch. 1.1 - Break-even analysis. The publisher of a new book...Ch. 1.1 - Break-even analysis. The publisher in Problem 59...Ch. 1.1 - Break-even analysis. The publisher in Problem 60...Ch. 1.1 - Wildlife management. A naturalist estimated the...Ch. 1.1 - Temperature conversion. If the temperature for a...Ch. 1.1 - Psychology. The IQ (intelligence quotient) is...Ch. 1.1 - Psychology. Refer to Problem 65. If the IQ of a...Ch. 1.2 - (A) As noted earlier, (4,3) is a solution of the...Ch. 1.2 - (A) Graph y=x+b for b=5,3,0,3 and 5 simultaneously...Ch. 1.2 - Graph:4x3y=12Ch. 1.2 - Graph 4x-3y=12 on a graphing calculator and find...Ch. 1.2 - (A) Graph x=5andy=3 simultaneously in the same...Ch. 1.2 - Find the slope of the line through each pair of...Ch. 1.2 - Write the equation of the line with slope 12 and y...Ch. 1.2 - (A) Find an equation for the line that has slope...Ch. 1.2 - Answer parts (A) and (B) in Example 7 for fixed...Ch. 1.2 - At a price of $12.59 per box of grapefruit, the...Ch. 1.2 - \ Problems 1-4 refer to graphs (A)-(D). Identify...Ch. 1.2 - Problems 1-4 refer to graphs (A)-(D). Identify the...Ch. 1.2 - Problems 1-4 refer to graphs (A)-(D). Identify the...Ch. 1.2 - Problems 1-4 refer to graphs (A)-(D). Identify the...Ch. 1.2 - In Problems 5-8, sketch a graph of each equation...Ch. 1.2 - In Problems 5-8, sketch a graph of each equation...Ch. 1.2 - In Problems 5-8, sketch a graph of each equation...Ch. 1.2 - In Problems 5-8, sketch a graph of each equation...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 9-14, find the slope and y intercept...Ch. 1.2 - In Problems 21-24, write an equation of the line...Ch. 1.2 - In Problems 21-24, write an equation of the line...Ch. 1.2 - In Problems 21-24, write an equation of the line...Ch. 1.2 - In Problems 21-24, write an equation of the line...Ch. 1.2 - In Problems 25-28, use the graph of each line to...Ch. 1.2 - In Problems 25-28, use the graph of each line to...Ch. 1.2 - In Problems 25-28, use the graph of each line to...Ch. 1.2 - In Problems 25-28, use the graph of each line to...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 29-34, sketch a graph of each equation...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - In Problems 35-40, find the slope of the graph of...Ch. 1.2 - Given Ax+By=12, graph each of the following three...Ch. 1.2 - Given Ax+By=24, graph each of the following three...Ch. 1.2 - Graph y=25x+200,x0.Ch. 1.2 - Graph y=40x+160,x0.Ch. 1.2 - (A) Graph y=1.2x4.2 in a rectangular coordinate...Ch. 1.2 - (A) Graph y=1.2x4.2 in a graphing calculator. (B)...Ch. 1.2 - In Problems 47-50, write the equations of the...Ch. 1.2 - In Problems 47-50, write the equations of the...Ch. 1.2 - In Problems 47-50, write the equations of the...Ch. 1.2 - In Problems 47-50, write the equations of the...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 51-58, write the slope-intercept form...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - In Problems 59-66, (A) Find the slope of the line...Ch. 1.2 - Discuss the relationship among the graphs of the...Ch. 1.2 - Discuss the relationship among the graphs of the...Ch. 1.2 - Cost analysis. A donut shop has a fixed cost of...Ch. 1.2 - Cost analysis. A small company manufactures picnic...Ch. 1.2 - Cost analysis. A plant can manufacture 80 golf...Ch. 1.2 - Cost analysis. A plant can manufacture 50 tennis...Ch. 1.2 - Business-Markup policy. A drugstore sells a drug...Ch. 1.2 - Business-Markup policy. A clothing store sells a...Ch. 1.2 - Business-Depreciation. A farmer buys a new tractor...Ch. 1.2 - Business-Depreciation. A charter fishing company...Ch. 1.2 - Boiling point. The temperature at which water...Ch. 1.2 - Boiling point. The temperature at which water...Ch. 1.2 - Flight conditions. In stable air, the air...Ch. 1.2 - Flight navigation. The airspeed indicator on some...Ch. 1.2 - Demographics. The average number of persons per...Ch. 1.2 - Demographics. The median household income divides...Ch. 1.2 - Cigarette smoking. The percentage of female...Ch. 1.2 - Cigarette smoking. The percentage of male...Ch. 1.2 - Supply and demand. At a price of $2.28 per bushel,...Ch. 1.2 - Supply and demand. At a price of $1.94 per bushel,...Ch. 1.2 - Physics. Hooke’s law states that the relationship...Ch. 1.2 - Physics. The distance d between a fixed spring and...Ch. 1.3 - As illustrated in Example 1A, the slope m of a...Ch. 1.3 - As stated previously, we used linear regression to...Ch. 1.3 - The equation a=28.55w+118.7 expresses BSA for...Ch. 1.3 - A 400-pound load of grain is dropped from an...Ch. 1.3 - Prices for emerald-shaped diamonds from an online...Ch. 1.3 - Using the model of Example 4, estimate the...Ch. 1.3 - Figure 5 shows the scatter plot for white spruce...Ch. 1.3 - Ideal weight. Dr. J. D. Robinson published the...Ch. 1.3 - Ideal weight. Dr. J. D. Robinson also published...Ch. 1.3 - Underwater pressure. At sea level, the weight of...Ch. 1.3 - Underwater pressure. Refer to Problem 3. In fresh...Ch. 1.3 - Rate of descent Parachutes. At low altitudes, the...Ch. 1.3 - Rate of descent Parachutes. The U.S Army is...Ch. 1.3 - Speed of sound. The speed of sound through air is...Ch. 1.3 - Speed of sound. The speed of sound through sea...Ch. 1.3 - Energy production. Table 5 lists U.S. fossil fuel...Ch. 1.3 - Energy consumption. Table 6 lists U.S. fossil fuel...Ch. 1.3 - Cigarette smoking. The data in Table 7 shows that...Ch. 1.3 - Cigarette smoking. The data in Table 7 shows that...Ch. 1.3 - Undergraduate enrollment. Table 8 lists enrollment...Ch. 1.3 - Graduate student enrollment. A linear regression...Ch. 1.3 - Licensed drivers. Table 9 contains the state...Ch. 1.3 - Licensed drivers. Table 10 contains the state...Ch. 1.3 - Net sales. A linear regression model for the net...Ch. 1.3 - Operating income. A linear regression model for...Ch. 1.3 - Freezing temperature. Ethylene glycol and...Ch. 1.3 - Freezing temperature. A linear regression model...Ch. 1.3 - Forestry. The figure contains a scatter plot of...Ch. 1.3 - Forestry. The figure contains a scatter plot of...Ch. 1.3 - Cable television. Table 13 shows the increase in...Ch. 1.3 - Cable television. The figure shows a scatter plot...Ch. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Problems 27-30 require a graphing calculator or a...Ch. 1.3 - Prob. 28ECh. 1.3 - Supply and demand. Table 16 contains price supply...Ch. 1.3 - Supply and demand. Table 17 contains price supply...Ch. 1 - Solve2x+3=7x11.Ch. 1 - Solvex12x33=12.Ch. 1 - Solve2x+5y=9fory.Ch. 1 - Solve3x4y=7forx.Ch. 1 - Solve Problems 5-7 and graph on a real number...Ch. 1 - Solve Problems 5-7 and graph on a real number...Ch. 1 - Solve Problems 5-7 and graph on a real number...Ch. 1 - Sketch a graph of 3x+2y=9.Ch. 1 - Write an equation of a line with x intercept 6 and...Ch. 1 - Sketch a graph of 2x3y=18. What are the intercepts...Ch. 1 - Write an equation in the form y=mx+b for a line...Ch. 1 - Write the equations of the vertical line and the...Ch. 1 - Write the equation of a line through each...Ch. 1 - Write the equation of the line through the two...Ch. 1 - Solve Problems 15-19. 3x+25=5xCh. 1 - Solve Problems 15-19. u5=u6+65Ch. 1 - Solve Problems 15-19. 5x34+x2=x24+1Ch. 1 - Solve Problems 15-19. 0.05x+0.2530x=3.3Ch. 1 - Solve Problems 15-19. 0.2x3+0.05x=0.4Ch. 1 - Solve Problems 20-24 and graph on a real number...Ch. 1 - Solve Problems 20-24 and graph on a real number...Ch. 1 - Solve Problems 20-24 and graph on a real number...Ch. 1 - Solve Problems 20-24 and graph on a real number...Ch. 1 - Solve Problems 20-24 and graph on a real number...Ch. 1 - Given Ax+By=30, graph each of the following cases...Ch. 1 - Describe the graphs of x=3 and y=2 Graph both...Ch. 1 - Describe the lines defined by the following...Ch. 1 - Solve Problems 28 and 29 for the indicated...Ch. 1 - Solve Problems 28 and 29 for the indicated...Ch. 1 - For what values of a and b is the inequality a+bba...Ch. 1 - If a and b are negative numbers and ab, then is...Ch. 1 - Graph y=mx+bandy=1mx+b simultaneously in the same...Ch. 1 - Investing. An investor has $300,000 to invest. If...Ch. 1 - Break-even analysis. A producer of educational...Ch. 1 - Sports medicine. A simple rule of thumb for...Ch. 1 - Linear depreciation. A bulldozer was purchased by...Ch. 1 - Business Pricing. A sporting goods store sells...Ch. 1 - Income. A salesperson receives a base salary of...Ch. 1 - Price demand. The weekly demand for mouthwash in a...Ch. 1 - Freezing temperature. Methanol, also known as wood...Ch. 1 - Prob. 41RECh. 1 - Consumer Price Index. The U.S. Consumer Price...Ch. 1 - Forestry. The figure contains a scatter plot of 20...
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- R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]arrow_forwardQuestion 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]arrow_forwardpart b pleasearrow_forward
- Question 5 (a) Let a, b, c, d, e, ƒ Є K where K is a field. Suppose that the determinant of the matrix a cl |df equals 3 and the determinant of determinant of the matrix a+3b cl d+3e f ГЪ e [ c ] equals 2. Compute the [5] (b) Calculate the adjugate Adj (A) of the 2 × 2 matrix [1 2 A = over R. (c) Working over the field F3 with 3 elements, use row and column operations to put the matrix [6] 0123] A = 3210 into canonical form for equivalence and write down the canonical form. What is the rank of A as a matrix over F3? 4arrow_forwardQuestion 2 In this question, V = Q4 and - U = {(x, y, z, w) EV | x+y2w+ z = 0}, W = {(x, y, z, w) € V | x − 2y + w − z = 0}, Z = {(x, y, z, w) € V | xyzw = 0}. (a) Determine which of U, W, Z are subspaces of V. Justify your answers. (b) Show that UW is a subspace of V and determine its dimension. (c) Is VU+W? Is V = UW? Justify your answers. [10] [7] '00'arrow_forwardGood explanation it sure experts solve itarrow_forward
- Best explains it not need guidelines okkarrow_forwardTask number: A1.1, A1.7 Topic: Celestial Navigation, Compass - Magnetic and Gyro Activ Determine compass error (magnetic and gyro) using azimuth choosing a suitable celestial body (Sun/ Stars/ Planets/ Moon). Apply variation to find the deviation of the magnetic compass. Minimum number of times that activity should be recorded: 6 (2 each phase) Sample calculation (Azimuth- Planets): On 06th May 2006 at 22h20m 10s UTC, a vessel in position 48°00'N 050°00'E observed Mars bearing 327° by compass. Find the compass error. If variation was 4.0° East, calculate the deviation. GHA Mars (06d 22h): Increment (20m 10s): 089° 55.7' 005° 02.5' v (0.9): (+) 00.3' GHA Mars: 094° 58.5' Longitude (E): (+) 050° 00.0' (plus- since longitude is easterly) LHA Mars: 144° 58.5' Declination (06d 22h): d (0.2): N 024° 18.6' (-) 00.1' Declination Mars: N 024° 18.5' P=144° 58.5' (If LHA<180°, P=LHA) A Tan Latitude/ Tan P A Tan 48° 00' Tan 144° 58.5' A = 1.584646985 N (A is named opposite to latitude, except when…arrow_forwardTask number: A1.1, A1.7 Topic: Celestial Navigation, Compass - Magnetic and Gyro Activ Determine compass error (magnetic and gyro) using azimuth choosing a suitable celestial body (Sun/ Stars/ Planets/ Moon). Apply variation to find the deviation of the magnetic compass. Minimum number of times that activity should be recorded: 6 (2 each phase) Sample calculation (Azimuth- Planets): On 06th May 2006 at 22h20m 10s UTC, a vessel in position 48°00'N 050°00'E observed Mars bearing 327° by compass. Find the compass error. If variation was 4.0° East, calculate the deviation. GHA Mars (06d 22h): Increment (20m 10s): 089° 55.7' 005° 02.5' v (0.9): (+) 00.3' GHA Mars: 094° 58.5' Longitude (E): (+) 050° 00.0' (plus- since longitude is easterly) LHA Mars: 144° 58.5' Declination (06d 22h): d (0.2): N 024° 18.6' (-) 00.1' Declination Mars: N 024° 18.5' P=144° 58.5' (If LHA<180°, P=LHA) A Tan Latitude/ Tan P A Tan 48° 00' Tan 144° 58.5' A = 1.584646985 N (A is named opposite to latitude, except when…arrow_forward
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