Basic Technical Mathematics with Calculus (11th Edition)
11th Edition
ISBN: 9780134437736
Author: Allyn J. Washington, Richard Evans
Publisher: PEARSON
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Chapter 16.5, Problem 29E
To determine
Solve the system of equations using Gaussian elimination and show that the result is the same obtained using Cramer’s rule.
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6.
(i)
Sketch the trace of the following curve on R²,
(t) = (sin(t), 3 sin(t)),
tЄ [0, π].
[3 Marks]
Total marks 10
(ii)
Find the length of this curve.
[7 Marks]
helppp
7.
Let F(x1, x2) (F₁(x1, x2), F2(x1, x2)), where
=
X2
F1(x1, x2)
X1
F2(x1, x2)
x+x
(i) Using the definition, calculate the integral
LF.dy,
where (t) = (cos(t), sin(t)) and t = [0,2].
[5 Marks]
(ii) Explain why Green's Theorem cannot be used to find the
integral in part (i).
[5 Marks]
Chapter 16 Solutions
Basic Technical Mathematics with Calculus (11th Edition)
Ch. 16.1 - For matrices A and B, find A + B.
Ch. 16.1 - Prob. 2PECh. 16.1 - Prob. 3PECh. 16.1 - Prob. 1ECh. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Prob. 4ECh. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 6ECh. 16.1 - Prob. 7E
Ch. 16.1 - Prob. 8ECh. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 10ECh. 16.1 - Prob. 11ECh. 16.1 - Prob. 12ECh. 16.1 - Prob. 13ECh. 16.1 - Prob. 14ECh. 16.1 - Prob. 15ECh. 16.1 - Prob. 16ECh. 16.1 - Prob. 17ECh. 16.1 - Prob. 18ECh. 16.1 - Prob. 19ECh. 16.1 - Prob. 20ECh. 16.1 - Prob. 21ECh. 16.1 - Prob. 22ECh. 16.1 - Prob. 23ECh. 16.1 - Prob. 24ECh. 16.1 - Prob. 25ECh. 16.1 - Prob. 26ECh. 16.1 - Prob. 27ECh. 16.1 - Prob. 28ECh. 16.1 - Prob. 29ECh. 16.1 - Prob. 30ECh. 16.1 - Prob. 31ECh. 16.1 - Prob. 32ECh. 16.1 - Prob. 33ECh. 16.1 - Prob. 34ECh. 16.1 - Prob. 35ECh. 16.1 - Prob. 36ECh. 16.1 - Prob. 37ECh. 16.1 - Prob. 38ECh. 16.1 - Prob. 39ECh. 16.1 - Prob. 40ECh. 16.1 - Prob. 41ECh. 16.1 - Prob. 42ECh. 16.1 - Prob. 43ECh. 16.1 - Prob. 44ECh. 16.2 - Prob. 1PECh. 16.2 - Prob. 2PECh. 16.2 - Prob. 3PECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5ECh. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.2 - Prob. 8ECh. 16.2 - Prob. 9ECh. 16.2 - Prob. 10ECh. 16.2 - Prob. 11ECh. 16.2 - Prob. 12ECh. 16.2 - Prob. 13ECh. 16.2 - Prob. 14ECh. 16.2 - Prob. 15ECh. 16.2 - Prob. 16ECh. 16.2 - Prob. 17ECh. 16.2 - Prob. 18ECh. 16.2 - Prob. 19ECh. 16.2 - Prob. 20ECh. 16.2 - Prob. 21ECh. 16.2 - Prob. 22ECh. 16.2 - Prob. 23ECh. 16.2 - Prob. 24ECh. 16.2 - Prob. 25ECh. 16.2 - Prob. 26ECh. 16.2 - Prob. 27ECh. 16.2 - Prob. 28ECh. 16.2 - Prob. 29ECh. 16.2 - Prob. 30ECh. 16.2 - Prob. 31ECh. 16.2 - Prob. 32ECh. 16.2 - Prob. 33ECh. 16.2 - Prob. 34ECh. 16.2 - Prob. 35ECh. 16.2 - Prob. 36ECh. 16.2 - Prob. 37ECh. 16.2 - Prob. 38ECh. 16.2 - Prob. 39ECh. 16.2 - Prob. 40ECh. 16.2 - Prob. 41ECh. 16.2 - Prob. 42ECh. 16.2 - Prob. 43ECh. 16.2 - Prob. 44ECh. 16.2 - Prob. 45ECh. 16.2 - Prob. 46ECh. 16.2 - Prob. 47ECh. 16.2 - Prob. 48ECh. 16.3 - Prob. 1PECh. 16.3 - Prob. 2PECh. 16.3 - Prob. 1ECh. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.3 - Prob. 10ECh. 16.3 - Prob. 11ECh. 16.3 - Prob. 12ECh. 16.3 - Prob. 13ECh. 16.3 - Prob. 14ECh. 16.3 - Prob. 15ECh. 16.3 - Prob. 16ECh. 16.3 - Prob. 17ECh. 16.3 - Prob. 18ECh. 16.3 - Prob. 19ECh. 16.3 - In Exercises 11–20, find the inverse of each of...Ch. 16.3 - In Exercises 21–28, find the inverse of each of...Ch. 16.3 - In Exercises 21–28, find the inverse of each of...Ch. 16.3 - Prob. 23ECh. 16.3 - Prob. 24ECh. 16.3 - Prob. 25ECh. 16.3 - Prob. 26ECh. 16.3 - Prob. 27ECh. 16.3 - Prob. 28ECh. 16.3 - Prob. 29ECh. 16.3 - Prob. 30ECh. 16.3 - Prob. 31ECh. 16.3 - Prob. 32ECh. 16.3 - Prob. 33ECh. 16.3 - Prob. 34ECh. 16.3 - Prob. 35ECh. 16.3 - Prob. 36ECh. 16.3 - Prob. 37ECh. 16.3 - Prob. 38ECh. 16.3 - Prob. 39ECh. 16.3 - Prob. 40ECh. 16.3 - Prob. 41ECh. 16.3 - In Exercises 35–44, solve the given problems.
42....Ch. 16.3 - Prob. 43ECh. 16.3 - Prob. 44ECh. 16.4 - Prob. 1PECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.4 - Prob. 6ECh. 16.4 - Prob. 7ECh. 16.4 - Prob. 8ECh. 16.4 - Prob. 9ECh. 16.4 - Prob. 10ECh. 16.4 - Prob. 11ECh. 16.4 - Prob. 12ECh. 16.4 - Prob. 13ECh. 16.4 - Prob. 14ECh. 16.4 - Prob. 15ECh. 16.4 - Prob. 16ECh. 16.4 - Prob. 17ECh. 16.4 - Prob. 18ECh. 16.4 - Prob. 19ECh. 16.4 - Prob. 20ECh. 16.4 - Prob. 21ECh. 16.4 - Prob. 22ECh. 16.4 - Prob. 23ECh. 16.4 - Prob. 24ECh. 16.4 - Prob. 25ECh. 16.4 - Prob. 26ECh. 16.4 - Prob. 27ECh. 16.4 - Prob. 28ECh. 16.4 - Prob. 29ECh. 16.4 - Prob. 30ECh. 16.4 - In Exercises 29–40, solve the indicated systems of...Ch. 16.4 - Prob. 32ECh. 16.4 - Prob. 33ECh. 16.4 - Prob. 34ECh. 16.4 - Prob. 35ECh. 16.4 - Prob. 36ECh. 16.4 - Prob. 37ECh. 16.4 - Prob. 38ECh. 16.4 - Prob. 39ECh. 16.4 - Prob. 40ECh. 16.5 - Prob. 1PECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16.5 - Prob. 3ECh. 16.5 - Prob. 4ECh. 16.5 - Prob. 5ECh. 16.5 - Prob. 6ECh. 16.5 - Prob. 7ECh. 16.5 - Prob. 8ECh. 16.5 - Prob. 9ECh. 16.5 - Prob. 10ECh. 16.5 - Prob. 11ECh. 16.5 - Prob. 12ECh. 16.5 - Prob. 13ECh. 16.5 - Prob. 14ECh. 16.5 - Prob. 15ECh. 16.5 - Prob. 16ECh. 16.5 - Prob. 17ECh. 16.5 - Prob. 18ECh. 16.5 - Prob. 19ECh. 16.5 - Prob. 20ECh. 16.5 - Prob. 21ECh. 16.5 - Prob. 22ECh. 16.5 - Prob. 23ECh. 16.5 - Prob. 24ECh. 16.5 - Prob. 25ECh. 16.5 - Prob. 26ECh. 16.5 - Prob. 27ECh. 16.5 - Prob. 28ECh. 16.5 - Prob. 29ECh. 16.5 - Prob. 30ECh. 16.5 - Prob. 31ECh. 16.5 - Prob. 32ECh. 16.5 - Prob. 33ECh. 16.5 - Prob. 34ECh. 16.6 - Prob. 1PECh. 16.6 - Prob. 1ECh. 16.6 - Prob. 2ECh. 16.6 - Prob. 3ECh. 16.6 - In Exercises 3–6, evaluate each determinant by...Ch. 16.6 - Prob. 5ECh. 16.6 - In Exercises 3–6, evaluate each determinant by...Ch. 16.6 - Prob. 7ECh. 16.6 - Prob. 8ECh. 16.6 - Prob. 9ECh. 16.6 - Prob. 10ECh. 16.6 - Prob. 11ECh. 16.6 - Prob. 12ECh. 16.6 - Prob. 13ECh. 16.6 - Prob. 14ECh. 16.6 - Prob. 15ECh. 16.6 - Prob. 16ECh. 16.6 - Prob. 17ECh. 16.6 - Prob. 18ECh. 16.6 - Prob. 19ECh. 16.6 - Prob. 20ECh. 16.6 - Prob. 21ECh. 16.6 - Prob. 22ECh. 16.6 - Prob. 23ECh. 16.6 - Prob. 24ECh. 16.6 - Prob. 25ECh. 16.6 - Prob. 26ECh. 16.6 - Prob. 27ECh. 16.6 - Prob. 28ECh. 16.6 - Prob. 29ECh. 16.6 - Prob. 30ECh. 16.6 - Prob. 31ECh. 16.6 - Prob. 32ECh. 16.6 - Prob. 33ECh. 16.6 - Prob. 34ECh. 16.6 - Prob. 35ECh. 16.6 - Prob. 36ECh. 16.6 - Prob. 37ECh. 16.6 - Prob. 38ECh. 16 - Prob. 1RECh. 16 - Prob. 2RECh. 16 - Prob. 3RECh. 16 - Prob. 4RECh. 16 - Prob. 5RECh. 16 - Prob. 6RECh. 16 - Prob. 7RECh. 16 - Prob. 8RECh. 16 - Prob. 9RECh. 16 - Prob. 10RECh. 16 - Prob. 11RECh. 16 - Prob. 12RECh. 16 - Prob. 13RECh. 16 - Prob. 14RECh. 16 - Prob. 15RECh. 16 - Prob. 16RECh. 16 - Prob. 17RECh. 16 - Prob. 18RECh. 16 - Prob. 19RECh. 16 - Prob. 20RECh. 16 - Prob. 21RECh. 16 - Prob. 22RECh. 16 - Prob. 23RECh. 16 - Prob. 24RECh. 16 - Prob. 25RECh. 16 - Prob. 26RECh. 16 - Prob. 27RECh. 16 - Prob. 28RECh. 16 - Prob. 29RECh. 16 - Prob. 30RECh. 16 - Prob. 31RECh. 16 - Prob. 32RECh. 16 - Prob. 33RECh. 16 - Prob. 34RECh. 16 - Prob. 35RECh. 16 - Prob. 36RECh. 16 - Prob. 37RECh. 16 - Prob. 38RECh. 16 - Prob. 39RECh. 16 - Prob. 40RECh. 16 - Prob. 41RECh. 16 - Prob. 42RECh. 16 - Prob. 43RECh. 16 - Prob. 44RECh. 16 - Prob. 45RECh. 16 - Prob. 46RECh. 16 - Prob. 47RECh. 16 - Prob. 48RECh. 16 - Prob. 49RECh. 16 - Prob. 50RECh. 16 - Prob. 51RECh. 16 - Prob. 52RECh. 16 - Prob. 53RECh. 16 - Prob. 54RECh. 16 - Prob. 55RECh. 16 - Prob. 56RECh. 16 - Prob. 57RECh. 16 - Prob. 58RECh. 16 - Prob. 59RECh. 16 - Prob. 60RECh. 16 - Prob. 61RECh. 16 - Prob. 62RECh. 16 - Prob. 63RECh. 16 - Prob. 64RECh. 16 - Prob. 65RECh. 16 - Prob. 66RECh. 16 - Prob. 67RECh. 16 - In Exercises 67–70, use the determinants for...Ch. 16 - Prob. 69RECh. 16 - Prob. 70RECh. 16 - Prob. 71RECh. 16 - Prob. 72RECh. 16 - Prob. 73RECh. 16 - Prob. 74RECh. 16 - Prob. 75RECh. 16 - In Exercises 73–76, solve the given...Ch. 16 - Prob. 77RECh. 16 - Prob. 78RECh. 16 - Prob. 79RECh. 16 - Prob. 80RECh. 16 - Prob. 81RECh. 16 - Prob. 82RECh. 16 - Prob. 83RECh. 16 - Prob. 84RECh. 16 - Prob. 85RECh. 16 - Prob. 86RECh. 16 - Prob. 87RECh. 16 - Prob. 88RECh. 16 - Prob. 89RECh. 16 - Prob. 90RECh. 16 - Prob. 91RECh. 16 - Prob. 92RECh. 16 - Prob. 93RECh. 16 - Prob. 94RECh. 16 - Prob. 95RECh. 16 - Prob. 96RECh. 16 - Prob. 97RECh. 16 - Prob. 1PTCh. 16 - Prob. 2PTCh. 16 - Prob. 3PTCh. 16 - Prob. 4PTCh. 16 - Prob. 5PTCh. 16 - Prob. 6PTCh. 16 - Prob. 7PTCh. 16 - Prob. 8PTCh. 16 - Prob. 9PTCh. 16 - Prob. 10PT
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- 6. Sketch the trace of the following curve on R², п 3п (t) = (t2 sin(t), t2 cos(t)), tЄ 22 [3 Marks] Find the length of this curve. [7 Marks]arrow_forwardTotal marks 10 Total marks on naner: 80 7. Let DCR2 be a bounded domain with the boundary OD which can be represented as a smooth closed curve : [a, b] R2, oriented in the anticlock- wise direction. Use Green's Theorem to justify that the area of the domain D can be computed by the formula 1 Area(D) = ½ (−y, x) · dy. [5 Marks] (ii) Use the area formula in (i) to find the area of the domain D enclosed by the ellipse y(t) = (10 cos(t), 5 sin(t)), t = [0,2π]. [5 Marks]arrow_forwardTotal marks 15 Total marks on paper: 80 6. Let DCR2 be a bounded domain with the boundary ǝD which can be represented as a smooth closed curve : [a, b] → R², oriented in the anticlockwise direction. (i) Use Green's Theorem to justify that the area of the domain D can be computed by the formula 1 Area(D) = . [5 Marks] (ii) Use the area formula in (i) to find the area of the domain D enclosed by the ellipse (t) = (5 cos(t), 10 sin(t)), t = [0,2π]. [5 Marks] (iii) Explain in your own words why Green's Theorem can not be applied to the vector field У x F(x,y) = ( - x² + y²²x² + y² ). [5 Marks]arrow_forward
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