Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)
12th Edition
ISBN: 9780137442966
Author: Larry Goldstein, David Schneider
Publisher: PEARSON+
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Textbook Question
Chapter 1.2, Problem 35E
Cost Curve A manufacturer has fixed costs (such as rent and insurance) of $2000 per month. The cost of producing each unit of goods is $4. Give the linear equation for the cost of producing x units per month.
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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
8
B = 0 7 7
0 -7 7
Working over the field F2 with 2 elements, compute the rank of B as an element
of M2(F2).
(c) Let
1
C
-1 1
[4]
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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.
[7]
(d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write
down all the eigenvalues. Show your working.
[8]
16. Solve the given differential equation:
y" + 4y sin (t)u(t 2π),
-
y(0) = 1, y'(0) = 0
Given,
1
(x² + 1)(x²+4)
1/3
-1/3
=
+
x²+1 x² +4
Send your answer in
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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]
Chapter 1 Solutions
Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)
Ch. 1.1 - Plot the point (500,200).Ch. 1.1 - 2. Is the point on the graph of the linear...Ch. 1.1 - In Exercises 1–8, plot the given point.
1.
Ch. 1.1 - In Exercises 18, plot the given point. (1,4)Ch. 1.1 - In Exercises 1–8, plot the given point.
3.
Ch. 1.1 - In Exercises 18, plot the given point. (2,0)Ch. 1.1 - In Exercises 18, plot the given point. (2,1)Ch. 1.1 - In Exercises 18, plot the given point. (1,52)Ch. 1.1 - In Exercises 1–8, plot the given point.
7.
Ch. 1.1 - In Exercises 1–8, plot the given point.
8.
Ch. 1.1 - What are the coordinates of the point Q in Fig. 7?Ch. 1.1 - What are the coordinates of the point P in Fig. 7?Ch. 1.1 - In Exercises 11–14, determine whether the point is...Ch. 1.1 - In Exercises 1114, determine whether the point is...Ch. 1.1 - In Exercises 11–14, determine whether the point is...Ch. 1.1 - In Exercises 1114, determine whether the point is...Ch. 1.1 - In Exercises 15–18, each linear equation is in the...Ch. 1.1 - In Exercises 1518, each linear equation is in the...Ch. 1.1 - In Exercises 1518, each linear equation is in the...Ch. 1.1 - In Exercises 1518, each linear equation is in the...Ch. 1.1 - In Exercises 19–22, write each linear equation in...Ch. 1.1 - In Exercises 1922, write each linear equation in...Ch. 1.1 - In Exercises 1922, write each linear equation in...Ch. 1.1 - In Exercises 19–22, write each linear equation in...Ch. 1.1 - In Exercises 2326, find the x-intercept and the...Ch. 1.1 - In Exercises 2326, find the x-intercept and the...Ch. 1.1 - In Exercises 2326, find the x-intercept and the...Ch. 1.1 - In Exercises 2326, find the x-intercept and the...Ch. 1.1 - In Exercises 2734, graph the given linear...Ch. 1.1 - In Exercises 2734, graph the given linear...Ch. 1.1 - In Exercises 27–34, graph the given linear...Ch. 1.1 - In Exercises 2734, graph the given linear...Ch. 1.1 - In Exercises 27–34, graph the given linear...Ch. 1.1 - In Exercises 2734, graph the given linear...Ch. 1.1 - In Exercises 27–34, graph the given linear...Ch. 1.1 - In Exercises 2734, graph the given linear...Ch. 1.1 - Which of the following equations describe the same...Ch. 1.1 - Which of the following equations describe the same...Ch. 1.1 - 37. Each of the lines in Fig. 8 is the graph of...Ch. 1.1 - 38. Which of the following equations is graphed in...Ch. 1.1 - 39. Heating Water The temperature of water in a...Ch. 1.1 - Life Expectancy The average life expectancy y of a...Ch. 1.1 - 41. Cigarette Consumption The worldwide...Ch. 1.1 - 42. Ecotourism Income In a certain developing...Ch. 1.1 - Insurance Rates Yearly car insurance rates have...Ch. 1.1 - Simple Interest If $1000 is deposited at 3% simple...Ch. 1.1 - 45. College Freshmen The percentage, y, of college...Ch. 1.1 - College Freshmen The percentage, y, of college...Ch. 1.1 - College Tuition Average tuition (including room...Ch. 1.1 - 48. Bachelor’s Degrees The number of bachelor’s...Ch. 1.1 - 49. Find an equation of the line having...Ch. 1.1 - Find an equation of the line having x-intercept...Ch. 1.1 - Find an equation of the line having y-intercept...Ch. 1.1 - Find an equation of the line having x-intercept...Ch. 1.1 - 53. What is the equation of the x-axis?
Ch. 1.1 - 54. Can a line other than the x-axis have more...Ch. 1.1 - 55. What is the general form of the equation of a...Ch. 1.1 - What is the general form of the equation of a line...Ch. 1.1 - In Exercises 5760, find a general form of the...Ch. 1.1 - In Exercises 5760, find a general form of the...Ch. 1.1 - In Exercises 5760, find a general form of the...Ch. 1.1 - In Exercises 57–60, find a general form of the...Ch. 1.1 - Show that the straight line with x-intercept (a,0)...Ch. 1.1 - Use the result of Exercise 61 to find a general...Ch. 1.1 - In Exercises 6370, give the equation of a line...Ch. 1.1 - In Exercises 6370, give the equation of a line...Ch. 1.1 - In Exercises 63–70, give the equation of a line...Ch. 1.1 - In Exercises 63–70, give the equation of a line...Ch. 1.1 - In Exercises 63–70, give the equation of a line...Ch. 1.1 - In Exercises 6370, give the equation of a line...Ch. 1.1 - In Exercises 63–70, give the equation of a line...Ch. 1.1 - In Exercises 6370, give the equation of a line...Ch. 1.1 - 71. The lines with equations and have the same...Ch. 1.1 - The lines with equations 6x3y=9 and y=4x+b have...Ch. 1.1 - In Exercises 7376, (a) graph the line, (b) use the...Ch. 1.1 - In Exercises 73–76, (a) graph the line, (b) use...Ch. 1.1 - In Exercises 7376, (a) graph the line, (b) use the...Ch. 1.1 - In Exercises 73–76, (a) graph the line, (b) use...Ch. 1.1 - In Exercises 77 and 78, determine an appropriate...Ch. 1.1 - In Exercises 77 and 78, determine an appropriate...Ch. 1.2 - Suppose that the revenue y from selling x units of...Ch. 1.2 - Suppose that the revenue y from selling x units of...Ch. 1.2 - In Exercises 1–6, find the slope of the line...Ch. 1.2 - In Exercises 1–6, find the slope of the line...Ch. 1.2 - In Exercises 1–6, find the slope of the line...Ch. 1.2 - In Exercises 16, find the slope of the line having...Ch. 1.2 - In Exercises 16, find the slope of the line having...Ch. 1.2 - In Exercises 1–6, find the slope of the line...Ch. 1.2 - In Exercises 710, plot each pair of points, draw...Ch. 1.2 - In Exercises 710, plot each pair of points, draw...Ch. 1.2 - In Exercises 7–10, plot each pair of points, draw...Ch. 1.2 - In Exercises 710, plot each pair of points, draw...Ch. 1.2 - What is the slope of any line parallel to the...Ch. 1.2 - Why doesnt it make sense to talk about the slope...Ch. 1.2 - In Exercises 1316, graph the given linear equation...Ch. 1.2 - In Exercises 13–16, graph the given linear...Ch. 1.2 - In Exercises 1316, graph the given linear equation...Ch. 1.2 - In Exercises 1316, graph the given linear equation...Ch. 1.2 - In Exercises 17–24, find the equation of line...Ch. 1.2 - In Exercises 17–24, find the equation of line...Ch. 1.2 - In Exercises 17–24, find the equation of line...Ch. 1.2 - In Exercises 1724, find the equation of line LCh. 1.2 - In Exercises 17–24, find the equation of line...Ch. 1.2 - In Exercises 17–24, find the equation of line...Ch. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - In Exercises 25–28, give the slope–intercept form...Ch. 1.2 - Prob. 26ECh. 1.2 - In Exercises 2528, give the slopeintercept form of...Ch. 1.2 - In Exercises 2528, give the slopeintercept form of...Ch. 1.2 - 29. Find the equation of the line passing through...Ch. 1.2 - 30. Find the equation of the line passing through...Ch. 1.2 - 31. Find the y-intercept of the line passing...Ch. 1.2 - 32. Find the y-intercept of the line passing...Ch. 1.2 - 33. Find the equation of the line passing through ...Ch. 1.2 - Find the equation of the line passing through the...Ch. 1.2 -
35. Cost Curve A manufacturer has fixed costs...Ch. 1.2 - Demand Curve The price p that must be set in order...Ch. 1.2 - 37. Boiling Point of Water At sea level, water...Ch. 1.2 - Cricket Chirps Biologists have found that the...Ch. 1.2 - Prob. 39ECh. 1.2 - Exercises 4042 are related. Cost Equation Suppose...Ch. 1.2 - Exercises 40–42 are related.
41. Revenue Equation...Ch. 1.2 - Exercises 4042 are related. Profit Equation...Ch. 1.2 - Prob. 43ECh. 1.2 - Cash Reserves A corporation receives payment for a...Ch. 1.2 - 45. Weekly Pay A furniture salesperson earns $220...Ch. 1.2 - 46. Weekly Pay A salesperson’s weekly pay depends...Ch. 1.2 - In Exercises 47–58, find an equation for each of...Ch. 1.2 - In Exercises 47–58, find an equation for each of...Ch. 1.2 - In Exercises 4758, find an equation for each of...Ch. 1.2 - In Exercises 4758, find an equation for each of...Ch. 1.2 - In Exercises 47–58, find an equation for each of...Ch. 1.2 - In Exercises 4758, find an equation for each of...Ch. 1.2 - In Exercises 47–58, find an equation for each of...Ch. 1.2 - In Exercises 4758, find an equation for each of...Ch. 1.2 - In Exercises 4758, find an equation for each of...Ch. 1.2 - In Exercises 47–58, find an equation for each of...Ch. 1.2 - Prob. 57ECh. 1.2 - Prob. 58ECh. 1.2 - Prob. 59ECh. 1.2 - In each of Exercises 5962, we specify a line by...Ch. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Prob. 64ECh. 1.2 - Prob. 65ECh. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - Prob. 68ECh. 1.2 - Prob. 69ECh. 1.2 - Prob. 70ECh. 1.2 - Prob. 71ECh. 1.2 - 72. Dating of Artifacts An archaeologist dates a...Ch. 1.2 - Prob. 73ECh. 1.2 - 74. College Enrollments Two-year college...Ch. 1.2 - Gas Mileage A certain car gets 25 miles per gallon...Ch. 1.2 - 76. Home Health Aid Jobs According to the U.S....Ch. 1.2 - Prob. 77ECh. 1.2 - Pizza Stores According to Pizza Marketing...Ch. 1.2 - 79. Super Bowl Commercials The average cost of a...Ch. 1.2 - 80. Straight-Line Depreciation A multi-function...Ch. 1.2 - Supply Curve Suppose that 5 million tons of apples...Ch. 1.2 - Demand Curve Suppose that 5 million tons of apples...Ch. 1.2 - Show that the points (1,3),(2,4),and(3,1) are not...Ch. 1.2 - For what value of k will the three points...Ch. 1.2 - Find the value of a for which the line through the...Ch. 1.2 - 86. Rework Exercise 85, where the word parallel is...Ch. 1.2 - Prove the parallel property. [Hint: If...Ch. 1.2 - Prob. 88ECh. 1.2 - Prob. 89ECh. 1.2 - Prob. 90ECh. 1.2 - 91. Costs and Revenue A T-shirt company has fixed...Ch. 1.2 - 92. Costs and Revenue A company produces a single...Ch. 1.2 - Demand and Revenue Suppose that the quantity q of...Ch. 1.2 - 94. Demand and Revenue Suppose that the number n...Ch. 1.2 - Setting a Price During 2015, a manufacturer...Ch. 1.2 - 96. Setting a Price Rework Exercise 95 with a 2015...Ch. 1.2 - 97. Graph the three lines together, and then...Ch. 1.2 - Prob. 98ECh. 1.2 - Prob. 99ECh. 1.2 - Prob. 100ECh. 1.2 - Prob. 101ECh. 1.3 - Figure 9 shows a type of polygon that plays a...Ch. 1.3 - Figure 9 shows a type of polygon that plays a...Ch. 1.3 - Figure 9 shows a type of polygon that plays a...Ch. 1.3 - In Exercises 16, find the point of intersection of...Ch. 1.3 - In Exercises 16, find the point of intersection of...Ch. 1.3 - In Exercises 16, find the point of intersection of...Ch. 1.3 - In Exercises 1–6, find the point of intersection...Ch. 1.3 - In Exercises 16, find the point of intersection of...Ch. 1.3 - Prob. 6ECh. 1.3 - 7. Does satisfy the following system of linear...Ch. 1.3 - Does (12,4) satisfy the following system of linear...Ch. 1.3 - In Exercises 9-12, solve the systems of linear...Ch. 1.3 - In Exercises 9-12, solve the systems of linear...Ch. 1.3 - In Exercises 9-12, solve the systems of linear...Ch. 1.3 - In Exercises 9-12, solve the systems of linear...Ch. 1.3 - In Exercises 13–16, find the coordinates of the...Ch. 1.3 - In Exercises 13–16, find the coordinates of the...Ch. 1.3 - In Exercises 13–16, find the coordinates of the...Ch. 1.3 - In Exercises 1316, find the coordinates of the...Ch. 1.3 - Supply Curve The supply curve for a certain...Ch. 1.3 - 18. Demand Curve The demand curve for a certain...Ch. 1.3 - 19. Supply and Demand Suppose that supply and...Ch. 1.3 - Supply and Demand A discount book seller has...Ch. 1.3 - 21. Supply and Demand Suppose that the demand...Ch. 1.3 - Prob. 22ECh. 1.3 - Temperature Conversion The formula for converting...Ch. 1.3 - Prob. 24ECh. 1.3 - 25. Manufacturing A clothing store can purchase a...Ch. 1.3 - 26. Time Apportionment A plant supervisor must...Ch. 1.3 - Calling Card Options A calling card offers two...Ch. 1.3 - 28. Towing Fees Sun Towing Company charges $50...Ch. 1.3 - In Exercises 29 and 30, find the area of the...Ch. 1.3 - Prob. 30ECh. 1.3 - Prob. 31ECh. 1.3 - 32. Sales Determination An appliance store sells a...Ch. 1.3 - Prob. 33ECh. 1.3 - In Exercises 33-36, graph the lines and estimate...Ch. 1.3 - Prob. 35ECh. 1.3 - In Exercises 33-36, graph the lines and estimate...Ch. 1.4 - 1. Can a vertical distance be negative?
Ch. 1.4 - Under what condition will a vertical distance be...Ch. 1.4 - Suppose that the line y=3x+1 is used to fit the...Ch. 1.4 - 2. Suppose that the line is used to fit the four...Ch. 1.4 - 3. Find the sum-of-squares error E for the...Ch. 1.4 - Find the sum-of-squares error E for the...Ch. 1.4 - Complete Table 6, and find the values of m and b...Ch. 1.4 - 6. Complete Table 7, and find the values of m and...Ch. 1.4 - Consider the data points (1,2),(2,5),and(3,11)....Ch. 1.4 - 8. Consider the data points . Find the straight...Ch. 1.4 - 9. Consider the data points, and . Find the...Ch. 1.4 - Consider the data points (1,5),(2,7),(3,6), and...Ch. 1.4 - 11. Consider the data points and .
(a) Find the...Ch. 1.4 - Prob. 12ECh. 1.4 - According to Example 2, the sum-of-squares error...Ch. 1.4 - Prob. 14ECh. 1.4 - Fuel Economy The following table gives the city...Ch. 1.4 - 16. Pizzerias The following table gives the number...Ch. 1.4 - Lung cancer and Smoking The following table gives...Ch. 1.4 - Cigarette Use The percentage of college freshmen...Ch. 1.4 - 19. College Graduates Figure 15 gives the percent...Ch. 1.4 - Average College Costs Figure 16 gives the average...Ch. 1.4 - Life Expectancy The following table is an...Ch. 1.4 - Banking Two Harvard economists studied countries...Ch. 1.4 - 23. Consumer Price Index The following table gives...Ch. 1.4 - Greenhouse Gases Although greenhouse gases are...Ch. 1 - How do you determine the coordinates of a point in...Ch. 1 - 2. What is meant by the graph of an equation in x...Ch. 1 - 3. What is the y-intercept of a line? How do you...Ch. 1 - 4. What is the x-intercept of a line? How do you...Ch. 1 - Prob. 5FCCECh. 1 - Prob. 6FCCECh. 1 - Prob. 7FCCECh. 1 - Prob. 8FCCECh. 1 - Prob. 9FCCECh. 1 - Prob. 10FCCECh. 1 - Prob. 11FCCECh. 1 - What can you say about the slopes of perpendicular...Ch. 1 - Prob. 13FCCECh. 1 - Prob. 14FCCECh. 1 - What is the least-squares line approximation to a...Ch. 1 - 1. What is the equation of the y-axis?
Ch. 1 - Prob. 2RECh. 1 - Find the point of intersection of the pair of...Ch. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Find the y-coordinate of the point having...Ch. 1 - Prob. 9RECh. 1 - Solve the system of linear equations....Ch. 1 - Prob. 11RECh. 1 - Cost of Moving The fee charged by a local moving...Ch. 1 - Are the points (1,2),(2,0), and (3,1) on the same...Ch. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - 22. Supply and Demand Consider the following four...Ch. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Car Rentals One-day car rentals cost $50 plus 10...Ch. 1 - 26. Inflation In 2003, bacon cost an average of...Ch. 1 - Medical assistant Jobs According to the U.S....Ch. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - 32. Life Expectancy The following table gives the...Ch. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - 37. When is the x-intercept of a line the same as...Ch. 1 - 38. Suppose that you have found the least-squares...Ch. 1 - Does every line have an x-intercept? A...Ch. 1 - 40. Consider the line having the slope–intercept...Ch. 1 - Break-Even Analysis
We discussed linear demand...Ch. 1 - Break-Even Analysis We discussed linear demand...Ch. 1 - Break-Even Analysis
We discussed linear demand...Ch. 1 - Break-Even Analysis We discussed linear demand...Ch. 1 - Break-Even Analysis
We discussed linear demand...Ch. 1 - Break-Even Analysis
We discussed linear demand...Ch. 1 - Break-Even Analysis We discussed linear demand...Ch. 1 - Break-Even Analysis
We discussed linear demand...
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- Task 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_forwardActiv Determine compass error using amplitude (Sun). Minimum number of times that activity should be performed: 3 (1 each phase) Sample calculation (Amplitude- Sun): On 07th May 2006 at Sunset, a vessel in position 10°00'N 010°00'W observed the Sun bearing 288° by compass. Find the compass error. LMT Sunset: LIT: (+) 00d 07d 18h 00h 13m 40m UTC Sunset: 07d 18h 53m (added- since longitude is westerly) Declination (07d 18h): N 016° 55.5' d (0.7): (+) 00.6' Declination Sun: N 016° 56.1' Sin Amplitude = Sin Declination/Cos Latitude = Sin 016°56.1'/ Cos 10°00' = 0.295780189 Amplitude=W17.2N (The prefix of amplitude is named easterly if body is rising, and westerly if body is setting. The suffix is named same as declination) True Bearing=287.2° Compass Bearing= 288.0° Compass Error = 0.8° Westarrow_forward
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Publisher:OpenStax - Rice University
What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY