Elementary Technical Mathematics
12th Edition
ISBN: 9781337630580
Author: Dale Ewen
Publisher: Cengage Learning
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Chapter 15, Problem 15T
To determine
To calculate: The probability of randomly selecting a spade from a deck of
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4. Suppose that A is made up of 5 column vectors in R³, and suppose that the
rank(A)=3.
a. How many solutions are there to Ax=0? Justify.
b. What is a geometric description for the nullspace(A)? Justify.
c. Do the column vectors of A span R³? Justify.
d. Is A invertible? Justify.
8.2.5 An article in Obesity Research [“Impaired Pressure
Natriuresis in Obese Youths” (2003, Vol. 11, pp. 745–751)]
described a study in which all meals were provided for 14 lean
boys for three days followed by one stress test (with a video-game
task). The average systolic blood pressure (SBP) during the
test was 118.3 mm HG with a standard deviation of 9.9 mm
HG. Construct a 99% one-sided upper confidence interval for
mean SBP.
8.2.6 An article in Medicine and Science in Sports and
Exercise [“Maximal Leg-Strength Training Improves Cycling
Economy in Previously Untrained Men” (2005, Vol. 37, pp.
131–136)] studied cycling performance before and after 8 weeks
of leg-strength training. Seven previously untrained males performed leg-strength training 3 days per week for 8 weeks (with
four sets of five replications at 85% of one repetition maximum).
Peak power during incremental cycling increased to a mean of
315 watts with a standard deviation of 16 watts. Construct a 95%
confidence…
3. Suppose that A is 5 x 5 and rank(A)=4. Use this information to answer the following.
a. Give a geometric description of nullspace(A). Justify.
b. Is A invertible? Justify.
c. Give a geometric description of the span of the column vectors of A. What
space are the column vectors of A in? Justify.
d. What is determinant of A? Justify.
Chapter 15 Solutions
Elementary Technical Mathematics
Ch. 15.1 - Find the approximate annual earnings of each of...Ch. 15.1 - Find the approximate annual earnings of each of...Ch. 15.1 - Find the approximate annual earnings of each of...Ch. 15.1 - Find the approximate annual earnings of each of...Ch. 15.1 - Find the approximate annual earnings of each of...Ch. 15.1 - Find the approximate annual earnings of each of...Ch. 15.1 - Find the approximate annual earnings of each of...Ch. 15.1 - Find the approximate annual earnings of each of...Ch. 15.1 - Find the approximate annual earnings of each of...Ch. 15.1 - Find the approximate annual earnings of each of...
Ch. 15.1 - Find the following information from Illustration...Ch. 15.1 - Find the following information from Illustration...Ch. 15.1 - Find the following information from Illustration...Ch. 15.1 - Find the following information from Illustration...Ch. 15.1 - Find the following information from Illustration...Ch. 15.1 - Find the following information from Illustration...Ch. 15.1 - Find the following information from Illustration...Ch. 15.1 - Find the following information from Illustration...Ch. 15.1 - Find the following information from Illustration...Ch. 15.1 - Find the following information from Illustration...Ch. 15.1 - A survey of 100 families was taken to find the...Ch. 15.1 - Illustration 3 shows the average text scores on...Ch. 15.1 - Prob. 23ECh. 15.1 - Prob. 24ECh. 15.1 - Prob. 25ECh. 15.2 - Find 26% of 360.Ch. 15.2 - Find 52% of 360Ch. 15.2 - Prob. 3ECh. 15.2 - Find 37.1% of 360Ch. 15.2 - Prob. 5ECh. 15.2 - Find 47.7% of 360Ch. 15.2 - Of 744 students, 452 are taking mathematics. What...Ch. 15.2 - Of 2017 students, 189 are taking technical...Ch. 15.2 - Prob. 9ECh. 15.2 - Candidate A was one of four candidates in an...Ch. 15.2 - A department spends $16,192 of its $182,100 budget...Ch. 15.2 - In June, the sales of an automobile dealership...Ch. 15.2 - Draw a circle graph for Exercises 1320: United...Ch. 15.2 - United States estimated population by age in 2016:...Ch. 15.2 - The suggested semester credit-hour requirements...Ch. 15.2 - A company interviewed its 473 employees to find...Ch. 15.2 - Total forest by continent in year 2015 in millions...Ch. 15.2 - The highest level of education for persons age 25...Ch. 15.2 - Prob. 19ECh. 15.2 - Some 2030 United Nations projected population data...Ch. 15.3 - The data in Illustration 1 are from the records of...Ch. 15.3 - An inspector recorded the number of faulty...Ch. 15.3 - Illustration 3 lists the 6months sales performance...Ch. 15.3 - A technician is often asked to read graphs drawn...Ch. 15.3 - A technician is often asked to read graphs drawn...Ch. 15.3 - A technician is often asked to read graphs drawn...Ch. 15.3 - A technician is often asked to read graphs drawn...Ch. 15.3 - A technician is often asked to read graphs drawn...Ch. 15.3 - A hygrothermograph is used by the weather services...Ch. 15.3 - A hygrothermograph is used by the weather services...Ch. 15.3 - Prob. 11ECh. 15.3 - A hygrothermograph is used by the weather services...Ch. 15.3 - A hygrothermograph is used by the weather services...Ch. 15.3 - A hygrothermograph is used by the weather services...Ch. 15.3 - According to National Oceanic and Atmospheric...Ch. 15.4 - Use Figure 15.6 to find the answers for Exercises...Ch. 15.4 - Use Figure 15.6 to find the answers for Exercises...Ch. 15.4 - Use Figure 15.6 to find the answers for Exercises...Ch. 15.4 - Use Figure 15.6 to find the answers for Exercises...Ch. 15.4 - Use Figure 15.6 to find the answers for Exercises...Ch. 15.4 - Use Figure 15.7 to find the answers for Exercises...Ch. 15.4 - Use Figure 15.7 to find the answers for Exercises...Ch. 15.4 - Use Figure 15.7 to find the answers for Exercises...Ch. 15.4 - Prob. 9ECh. 15.4 - Prob. 10ECh. 15.5 - Find the mean measurement for each set of...Ch. 15.5 - Find the mean measurement for each set of...Ch. 15.5 - Prob. 3ECh. 15.5 - Find the mean measurement for each set of...Ch. 15.5 - Prob. 5ECh. 15.5 - Find the mean measurement for each set of...Ch. 15.5 - Prob. 7ECh. 15.5 - Find the mean measurement for each set of...Ch. 15.5 - Prob. 9ECh. 15.5 - Find the mean measurement for each set of...Ch. 15.5 - Prob. 11ECh. 15.5 - Find the mean measurement for each set of...Ch. 15.5 - Find the mean measurement for each set of...Ch. 15.5 - Find the mean measurement for each set of...Ch. 15.5 - The mileage on six vehicles leased for 1 year was...Ch. 15.5 - A trucking company had hauls of 2018 km, 2101 km,...Ch. 15.5 - Over an 8day period of time the high temperature...Ch. 15.5 - A pharmacist weighed ten different capsules of the...Ch. 15.5 - A technician measured the power usage of six...Ch. 15.5 - A trucking company had seven items with the...Ch. 15.5 - According to the U.S. Energy Information...Ch. 15.5 - As trees grow in diameter, the wood produced in...Ch. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - Prob. 3ECh. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - Prob. 5ECh. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - Prob. 7ECh. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - Prob. 9ECh. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - Prob. 11ECh. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - Prob. 13ECh. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - Prob. 17ECh. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - Prob. 19ECh. 15.6 - 120. Find the median measurement for each set of...Ch. 15.6 - Prob. 21ECh. 15.6 - Find the following percentiles for the data listed...Ch. 15.6 - Prob. 23ECh. 15.6 - Prob. 24ECh. 15.6 - Prob. 25ECh. 15.6 - Prob. 26ECh. 15.6 - Find the mode for each set of measurements in...Ch. 15.6 - Prob. 28ECh. 15.6 - Prob. 29ECh. 15.6 - Prob. 30ECh. 15.6 - Prob. 31ECh. 15.6 - Prob. 32ECh. 15.6 - Prob. 33ECh. 15.6 - Find the mode for each set of measurements in...Ch. 15.6 - Prob. 35ECh. 15.6 - Find the mode for each set of measurements in...Ch. 15.6 - The cross section of the oak tree mentioned in the...Ch. 15.6 - Prob. 38ECh. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - Prob. 3ECh. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - Prob. 5ECh. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - Prob. 9ECh. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - Prob. 11ECh. 15.7 - Prob. 12ECh. 15.7 - Prob. 13ECh. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - Prob. 16ECh. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - 1-20. Find the range for each set measurements in...Ch. 15.7 - Prob. 20ECh. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - Prob. 31ECh. 15.7 - Prob. 32ECh. 15.7 - Prob. 33ECh. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - Prob. 36ECh. 15.7 - 21-40. Find the sample standard deviation for each...Ch. 15.7 - Prob. 38ECh. 15.7 - Prob. 39ECh. 15.7 - Prob. 40ECh. 15.8 - From the following grouped data, find the mean....Ch. 15.8 - Make a frequency distribution of the following...Ch. 15.8 - A laboratory technician records the life span (in...Ch. 15.8 - The life expectancy of a fluorescent light bulb is...Ch. 15.8 - The shipment times in hours for a load of goods...Ch. 15.8 - The cost of goods stolen from a department store...Ch. 15.8 - The number of passengers and their luggage weight...Ch. 15.8 - The income of the residents in a neighborhood was...Ch. 15.8 - The number of defective parts per shipment has...Ch. 15.8 - The following dollar amounts are traffic fines...Ch. 15.8 - The length of hospital stays for patients at a...Ch. 15.8 - The frequency of repair for the trucks owned by a...Ch. 15.8 - The scores that golfers shot on 18 holes at a...Ch. 15.8 - The corn yield in bushels per acre for a certain...Ch. 15.8 - The following are the squad sizes of the football...Ch. 15.8 - Prob. 16ECh. 15.9 - 1-16. Find the sample standard deviation for each...Ch. 15.9 - Prob. 2ECh. 15.9 - Prob. 3ECh. 15.9 - 1-16. Find the sample standard deviation for each...Ch. 15.9 - Prob. 5ECh. 15.9 - 1-16. Find the sample standard deviation for each...Ch. 15.9 - Prob. 7ECh. 15.9 - Prob. 8ECh. 15.9 - Prob. 9ECh. 15.9 - Prob. 10ECh. 15.9 - Prob. 11ECh. 15.9 - Prob. 12ECh. 15.9 - Prob. 13ECh. 15.9 - Prob. 14ECh. 15.9 - Prob. 15ECh. 15.9 - 1-16. Find the sample standard deviation for each...Ch. 15.9 - Measuring the annual tree rings for the 100 +...Ch. 15.10 - A certain manufacturing process has a target value...Ch. 15.10 - A sporting goods manufacturer makes baseballs. The...Ch. 15.10 - The depth of a silicon wafer is targeted at 1.015...Ch. 15.10 - The illumination of a light bulb is targeted at...Ch. 15.11 - In Exercises 14, draw a histogram for the data...Ch. 15.11 - In Exercises 14, draw a histogram for the data...Ch. 15.11 - In Exercises 14, draw a histogram for the data...Ch. 15.11 - In Exercises 14, draw a histogram for the data...Ch. 15.11 - Use the data displayed in Table 15.1 on page 489...Ch. 15.11 - Prob. 6ECh. 15.11 - Prob. 7ECh. 15.11 - Precision Manufacturing produces 20,000 machine...Ch. 15.11 - Prob. 9ECh. 15.11 - Prob. 10ECh. 15.11 - Prob. 11ECh. 15.11 - In Exercises 912, a. Draw a scattergram for the...Ch. 15.12 - Given a normal distribution with a mean of 85 and...Ch. 15.12 - Given the 20 numbers 32, 34, 35, 41, 42, 43, 44,...Ch. 15.12 - In Exercises 36, use the frequency distribution to...Ch. 15.12 - In Exercises 36, use the frequency distribution to...Ch. 15.12 - In Exercises 36, use the frequency distribution to...Ch. 15.12 - Prob. 6ECh. 15.12 - Prob. 7ECh. 15.12 - A trouser manufacturer has an order for 80,000...Ch. 15.13 - Prob. 1ECh. 15.13 - Prob. 2ECh. 15.13 - Prob. 3ECh. 15.13 - Prob. 4ECh. 15.13 - Prob. 5ECh. 15.13 - Prob. 6ECh. 15.13 - Prob. 7ECh. 15.13 - Prob. 8ECh. 15.13 - Prob. 9ECh. 15.13 - From the sample space in Exercise 1, what is the...Ch. 15.13 - Prob. 11ECh. 15.13 - Prob. 12ECh. 15.13 - Prob. 13ECh. 15.13 - Prob. 14ECh. 15.13 - Prob. 15ECh. 15.13 - A bag contains 6 red and 4 white marbles. One...Ch. 15.13 - Prob. 17ECh. 15.13 - In a classroom, there are 18 female students and 7...Ch. 15.14 - A bag contains 1 red marble, 1 blue marble, 1...Ch. 15.14 - A card is chosen from a deck of 52 cards. It is...Ch. 15.14 - Prob. 3ECh. 15.14 - A large box of vegetables contains 4 tomatoes, 3...Ch. 15.14 - Prob. 5ECh. 15.14 - A card is chosen from a deck of cards and placed...Ch. 15.14 - Prob. 7ECh. 15.14 - A card is drawn and replaced four times from a...Ch. 15.14 - A card is drawn and replaced four times from a...Ch. 15.14 - A pair of dice is rolled. What is the probability...Ch. 15.14 - Prob. 11ECh. 15.14 - Prob. 12ECh. 15.14 - Prob. 13ECh. 15.14 - Prob. 14ECh. 15.14 - Prob. 15ECh. 15.14 - Prob. 16ECh. 15 - Prob. 1RCh. 15 - Find 56.1% of 360.Ch. 15 - Prob. 3RCh. 15 - Prob. 4RCh. 15 - Prob. 5RCh. 15 - For Exercises 68, use the following data. A...Ch. 15 - For Exercises 68, use the following data. A...Ch. 15 - For Exercises 68, use the following data. A...Ch. 15 - Given the frequency distribution in Illustration...Ch. 15 - For Exercises 1012, use the data below. A students...Ch. 15 - Prob. 11RCh. 15 - For Exercises 1012, use the data below. A students...Ch. 15 - Prob. 13RCh. 15 - Prob. 14RCh. 15 - Prob. 15RCh. 15 - A bag contains 4 white marbles, 3 red marbles, 1...Ch. 15 - See Illustration 1. What country has the longest...Ch. 15 - See Illustration 1. What country has a life...Ch. 15 - Prob. 3TCh. 15 - Prob. 4TCh. 15 - Prob. 5TCh. 15 - Prob. 6TCh. 15 - Prob. 7TCh. 15 - See Illustration 2. What is the power gain when...Ch. 15 - Prob. 9TCh. 15 - Prob. 10TCh. 15 - Prob. 11TCh. 15 - For Exercises 1214, use the data in Illustration...Ch. 15 - For Exercises 1214, use the data in Illustration...Ch. 15 - For Exercises 1214, use the data in Illustration...Ch. 15 - Prob. 15TCh. 15 - Find the sample standard deviation for each set of...
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- 2. Consider the matrix: A || 1 1 -3 14 2 1 01 4 1 2 2 -26 1 -3 1 5] a) What is rank(A)? b) Is A invertible? Justify. c) Find the nullspace(A). Justify. d) Is the trivial solution the only solution to Ax=0? Justify. e) What is the span of the column vectors of A? Justify.arrow_forwardE 5. Suppose that S={v € R²: v = [2x² - 3]}. Is S a subspace of R²? Prove or disprovearrow_forward6. Suppose that V1, V2 ER", show that span{v1, v2} is a subspace of Rn.arrow_forward
- Ra X 2) slots per pole per phase 3/31 180 Ko Sin (1) Kdl 1 sin (4) sin(3) Sin (30) اذا مرید شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 Fo lasa! G s.1000-950 20:05 1000 Capper losses: 5kw Rotor input lookw 0.05 ined sove in peaper I need a detailed solution on paper please 6) 1 ۳/۱ وه اذا ميريد شرح الكتب فقط look DC 7) rotov Find the general solution of the following equations: +4y=tan2x 3 7357 Find the general solution of the following equations: - Qll y + y (³) = 0. 101arrow_forwardNC Current Students - North Ce X | NC Canvas Login Links - North ( X Final Exam Comprehensive x Cengage Learning x WASTAT - Final Exam - STAT → C webassign.net/web/Student/Assignment-Responses/submit?dep=36055360&tags=autosave#question3659890_9 Part (b) Draw a scatter plot of the ordered pairs. N Life Expectancy Life Expectancy 80 70 600 50 40 30 20 10 Year of 1950 1970 1990 2010 Birth O Life Expectancy Part (c) 800 70 60 50 40 30 20 10 1950 1970 1990 W ALT 林 $ # 4 R J7 Year of 2010 Birth F6 4+ 80 70 60 50 40 30 20 10 Year of 1950 1970 1990 2010 Birth Life Expectancy Ox 800 70 60 50 40 30 20 10 Year of 1950 1970 1990 2010 Birth hp P.B. KA & 7 80 % 5 H A B F10 711 N M K 744 PRT SC ALT CTRLarrow_forwardB: 18060 msl Kd Ka, Sin (n) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW /0001 Rotor input 5 : loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط ١٥٠ 7) rotov DC ined sove in Deaper I need a detailed solution on paper please dy x+2y-4 = dx 2x-y-3 Find the general solution of the following equations: 02//yl-4y+13y=esinarrow_forward
- 1) R₂ = X2 2) slots per pole per phase = 3/31 B msl kd 180 60 Kal Sin (1) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW Rotor input: 5 0.05 loo kw 6) 1 /0001 اذا ميريد شرح الكتب فقط look 7) rotov DC ined sove in peaper I need a detailed solution on paper please Q1// Find the solution of: 'y' = x² +376 x4+316 xyo Q2 Find the solution of the initial-valued problems: ex-y y' +exarrow_forwardR₂ = X2 2) slots per pole per phase = 3/31 B-18060 msl kd Kasi Sin (1) I sin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed s = 1000-950 1000 Copper losses: 5kw Rotor input 5 0.05 6) 1 120 x 50 G loo kw ined sove in peaper I need a detailed solution on paper please Q3// x²y// +xy/ + (x² - ½) y = x³/². اذا ميريد شرح الكتب فقط look 7) rotor DC Q4// x²y// - (2x+x²)y/ + (2 + x)y = x³. dy 2x+2y+4 = dx 2x-y-3arrow_forward۳/۱ R2X2 2) slots per pole per phase = 3/31 B, 18060 msl Kas Sin() 1sin() sin(30) Sin (30) kd اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speeds S = 1000-950 1000 Copper bosses 5kw 120*50 loca G Rotor input 5 loo kw 6) 1 0.05 اذا ميريد شرح الكتب فقط lookw 7) rotor DC ined sove in peaper I need a detailed solution on paper please 064 Q1// Find the solution of QI/Find the solution of Inxy= 7357 x+2y³ y' = xy3arrow_forward
- R₂ = X2 2) slots per pole per phase 3/31 msl 180 60 Kd Ka Sin (1) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120*50 1000 6 S = 1000-950 1000 Copper bosses: 5kw Rotor input 5 0.05 : loo kw 6) 1 اذا ميريد شرح الكتب فقط 100 7) rotor DC ined sove in peaper I need a detailed solution on paper please Find the general solution of the following equations: Q2lyl-4y+13y=esinx. Find the general solution of the following equations: " Qly (49) - 16y= 0. 151arrow_forward۳/۱ R₂ = X2 2) slots per pole per phase = 3/31 B-18060 msl kd Kasi Sin (1) I sin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed s = 1000-950 1000 Copper losses: 5kw Rotor input 5 0.05 6) 1 120 x 50 G loo kw اذا میرید شرح الكتب فقط look 7) rotor DC ined sove in peaper I need a detailed solution on paper dy please 04 12=-cosx.y + 2cosx with y(x) = 1 か 'Oy + xlny + xe")dx + (xsiny + xlnx +*dy=0. 01arrow_forward٣/١ R2X2 2) slots per pole per phase = 3/31 B, 18060 msl kd Kas Sin (1) 1sin() sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speeds S = 1000-950 1000 Copper bosses 5kw 120*50 loca G Rotor input 5 loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط lookw 7) rotor ined sove in peaper I need a detailed solution on paper please DC 口 04 on its wheels as shown in figure. The the door is 8 m below the free surface o is located at the center of the d no water leaks an accident and lands at the bottom of the lake 12m high and I m wide, and the top edge of water Determine the hydrostatic force on the discuss if the driver can open the door, if ong person can lift 100 kg, the passenger The door can be approximated as a vertical rec | 279|-|(23+2+12+20=2) AA Find the general solution of the following equations: 11 - 1/4+xy/-(1-x²³)= 0. 2arrow_forward
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