Explanation Look at diagram 27 ( B ) let T be the point above Q on A B ¯ let s = A T and D = A B so that T B = D - s Let ℓ be the total length of cable from A to B to Q By the Pythagorean Theorem applied to Δ A Q T we get ℓ = s 2 + x 2 + ( D − s ) 2 + x 2 From here it follows that d ℓ d s = s s 2 + To determine b) With x as in let f ( x ) be the total length of cable used show that f has unique critical point c that 0 ≤ c ≤ L if and only if D ≤ 2 3 L To determine c) Find the minimum of f on [ 0 , L ] in two case D = 2 , L = 4 and D = 8 , L = 2

Applied Calculus (with Infotrac) 3rd Edition By Waner, Stefan; Costenoble, Steven Published By Brooks Cole Hardcover

3rd Edition

ISBN: 9781319048518

Author: Colin Adams Jon Rogawski

Publisher: Macmillan Higher Education

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Question

Chapter 4.7, Problem 74E

To determine

a)

First that $P$ must lie directly above $C$ junction placed at Point $P$ lying above $C$

To determine

b)

With $x$ as in let $f (x)$ be the total length of cable used show that $f$ has unique critical point $c$ that $0 \leq c \leq L$ if and only if $D \leq 2 \sqrt{3} L$

To determine

c)

Find the minimum of $f$ on $[0, L]$ in two case $D = 2, L = 4$ and $D = 8, L = 2$

Expert Solution & Answer

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Chapter 4.7, Problem 73E

Chapter 4.7, Problem 75E

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Chapter 4 Solutions

Applied Calculus (with Infotrac) 3rd Edition By Waner, Stefan; Costenoble, Steven Published By Brooks Cole Hardcover

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - Prob. 48E Ch. 4.1 - Prob. 49E Ch. 4.1 - Prob. 50E Ch. 4.1 - Prob. 51E Ch. 4.1 - Prob. 52E Ch. 4.1 - Prob. 53E Ch. 4.1 - Prob. 54E Ch. 4.1 - Prob. 55E Ch. 4.1 - Prob. 56E Ch. 4.1 - Prob. 57E Ch. 4.1 - Prob. 58E Ch. 4.1 - Prob. 59E Ch. 4.1 - Prob. 60E Ch. 4.1 - Prob. 61E Ch. 4.1 - Prob. 62E Ch. 4.1 - Prob. 63E Ch. 4.1 - Prob. 64E Ch. 4.1 - Prob. 65E Ch. 4.1 - Prob. 66E Ch. 4.1 - Prob. 67E Ch. 4.1 - Prob. 68E Ch. 4.1 - Prob. 69E Ch. 4.1 - Prob. 70E Ch. 4.1 - Prob. 71E Ch. 4.1 - Prob. 72E Ch. 4.1 - Prob. 73E Ch. 4.1 - Prob. 74E Ch. 4.1 - Prob. 75E Ch. 4.1 - Prob. 76E Ch. 4.2 - Prob. 1PQ Ch. 4.2 - Prob. 2PQ Ch. 4.2 - Prob. 3PQ Ch. 4.2 - Prob. 4PQ Ch. 4.2 - Prob. 1E Ch. 4.2 - Prob. 2E Ch. 4.2 - Prob. 3E Ch. 4.2 - Prob. 4E Ch. 4.2 - Prob. 5E Ch. 4.2 - Prob. 6E Ch. 4.2 - Prob. 7E Ch. 4.2 - Prob. 8E Ch. 4.2 - Prob. 9E Ch. 4.2 - Prob. 10E Ch. 4.2 - Prob. 11E Ch. 4.2 - Prob. 12E Ch. 4.2 - Prob. 13E Ch. 4.2 - Prob. 14E Ch. 4.2 - Prob. 15E Ch. 4.2 - Prob. 16E Ch. 4.2 - Prob. 17E Ch. 4.2 - Prob. 18E Ch. 4.2 - Prob. 19E Ch. 4.2 - Prob. 20E Ch. 4.2 - Prob. 21E Ch. 4.2 - Prob. 22E Ch. 4.2 - Prob. 23E Ch. 4.2 - Prob. 24E Ch. 4.2 - Prob. 25E Ch. 4.2 - Prob. 26E Ch. 4.2 - Prob. 27E Ch. 4.2 - Prob. 28E Ch. 4.2 - Prob. 29E Ch. 4.2 - Prob. 30E Ch. 4.2 - Prob. 31E Ch. 4.2 - Prob. 32E Ch. 4.2 - Prob. 33E Ch. 4.2 - Prob. 34E Ch. 4.2 - Prob. 35E Ch. 4.2 - Prob. 36E Ch. 4.2 - Prob. 37E Ch. 4.2 - Prob. 38E Ch. 4.2 - Prob. 39E Ch. 4.2 - Prob. 40E Ch. 4.2 - Prob. 41E Ch. 4.2 - Prob. 42E Ch. 4.2 - Prob. 43E Ch. 4.2 - Prob. 44E Ch. 4.2 - Prob. 45E Ch. 4.2 - Prob. 46E Ch. 4.2 - Prob. 47E Ch. 4.2 - Prob. 48E Ch. 4.2 - Prob. 49E Ch. 4.2 - Prob. 50E Ch. 4.2 - Prob. 51E Ch. 4.2 - Prob. 52E Ch. 4.2 - Prob. 53E Ch. 4.2 - Prob. 54E Ch. 4.2 - Prob. 55E Ch. 4.2 - Prob. 56E Ch. 4.2 - Prob. 57E Ch. 4.2 - Prob. 58E Ch. 4.2 - Prob. 59E Ch. 4.2 - Prob. 60E Ch. 4.2 - Prob. 61E Ch. 4.2 - Prob. 62E Ch. 4.2 - Prob. 63E Ch. 4.2 - Prob. 64E Ch. 4.2 - Prob. 65E Ch. 4.2 - Prob. 66E Ch. 4.2 - Prob. 67E Ch. 4.2 - Prob. 68E Ch. 4.2 - Prob. 69E Ch. 4.2 - Prob. 70E Ch. 4.2 - Prob. 71E Ch. 4.2 - Prob. 72E Ch. 4.2 - Prob. 73E Ch. 4.2 - Prob. 74E Ch. 4.2 - Prob. 75E Ch. 4.2 - Prob. 76E Ch. 4.2 - Prob. 77E Ch. 4.2 - 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Prob. 78E Ch. 4.3 - Prob. 79E Ch. 4.3 - Prob. 80E Ch. 4.3 - Prob. 81E Ch. 4.4 - Prob. 1PQ Ch. 4.4 - Prob. 2PQ Ch. 4.4 - Prob. 3PQ Ch. 4.4 - Prob. 4PQ Ch. 4.4 - Prob. 1E Ch. 4.4 - Prob. 2E Ch. 4.4 - Prob. 3E Ch. 4.4 - Prob. 4E Ch. 4.4 - Prob. 5E Ch. 4.4 - Prob. 6E Ch. 4.4 - Prob. 7E Ch. 4.4 - Prob. 8E Ch. 4.4 - Prob. 9E Ch. 4.4 - Prob. 10E Ch. 4.4 - Prob. 11E Ch. 4.4 - Prob. 12E Ch. 4.4 - Prob. 13E Ch. 4.4 - Prob. 14E Ch. 4.4 - Prob. 15E Ch. 4.4 - Prob. 16E Ch. 4.4 - Prob. 17E Ch. 4.4 - Prob. 18E Ch. 4.4 - Prob. 19E Ch. 4.4 - Prob. 20E Ch. 4.4 - Prob. 21E Ch. 4.4 - Prob. 22E Ch. 4.4 - Prob. 23E Ch. 4.4 - Prob. 24E Ch. 4.4 - Prob. 25E Ch. 4.4 - Prob. 26E Ch. 4.4 - Prob. 27E Ch. 4.4 - Prob. 28E Ch. 4.4 - Prob. 29E Ch. 4.4 - Prob. 30E Ch. 4.4 - Prob. 31E Ch. 4.4 - Prob. 32E Ch. 4.4 - Prob. 33E Ch. 4.4 - Prob. 34E Ch. 4.4 - Prob. 35E Ch. 4.4 - Prob. 36E Ch. 4.4 - Prob. 37E Ch. 4.4 - Prob. 38E Ch. 4.4 - Prob. 39E Ch. 4.4 - Prob. 40E Ch. 4.4 - Prob. 41E Ch. 4.4 - Prob. 42E Ch. 4.4 - Prob. 43E Ch. 4.4 - Prob. 44E Ch. 4.4 - Prob. 45E Ch. 4.4 - Prob. 46E Ch. 4.4 - Prob. 47E Ch. 4.4 - Prob. 48E Ch. 4.4 - Prob. 49E Ch. 4.4 - Prob. 50E Ch. 4.4 - Prob. 51E Ch. 4.4 - Prob. 52E Ch. 4.4 - Prob. 53E Ch. 4.4 - Prob. 54E Ch. 4.4 - Prob. 55E Ch. 4.4 - Prob. 56E Ch. 4.4 - Prob. 57E Ch. 4.4 - Prob. 58E Ch. 4.4 - Prob. 59E Ch. 4.4 - Prob. 60E Ch. 4.4 - Prob. 61E Ch. 4.4 - Prob. 62E Ch. 4.4 - Prob. 63E Ch. 4.4 - Prob. 64E Ch. 4.4 - Prob. 65E Ch. 4.4 - Prob. 66E Ch. 4.4 - Prob. 67E Ch. 4.4 - Prob. 68E Ch. 4.4 - Prob. 69E Ch. 4.4 - Prob. 70E Ch. 4.4 - Prob. 71E Ch. 4.4 - Prob. 72E Ch. 4.5 - Prob. 1PQ Ch. 4.5 - Prob. 2PQ Ch. 4.5 - Prob. 1E Ch. 4.5 - Prob. 2E Ch. 4.5 - Prob. 3E Ch. 4.5 - Prob. 4E Ch. 4.5 - Prob. 5E Ch. 4.5 - Prob. 6E Ch. 4.5 - Prob. 7E Ch. 4.5 - Prob. 8E Ch. 4.5 - Prob. 9E Ch. 4.5 - Prob. 10E Ch. 4.5 - Prob. 11E Ch. 4.5 - Prob. 12E Ch. 4.5 - Prob. 13E Ch. 4.5 - Prob. 14E Ch. 4.5 - Prob. 15E Ch. 4.5 - Prob. 16E Ch. 4.5 - Prob. 17E Ch. 4.5 - Prob. 18E Ch. 4.5 - Prob. 19E Ch. 4.5 - Prob. 20E Ch. 4.5 - Prob. 21E Ch. 4.5 - Prob. 22E Ch. 4.5 - Prob. 23E Ch. 4.5 - Prob. 24E Ch. 4.5 - Prob. 25E Ch. 4.5 - Prob. 26E Ch. 4.5 - Prob. 27E Ch. 4.5 - Prob. 28E Ch. 4.5 - Prob. 29E Ch. 4.5 - Prob. 30E Ch. 4.5 - Prob. 31E Ch. 4.5 - Prob. 32E Ch. 4.5 - Prob. 33E Ch. 4.5 - Prob. 34E Ch. 4.5 - Prob. 35E Ch. 4.5 - Prob. 36E Ch. 4.5 - Prob. 37E Ch. 4.5 - Prob. 38E Ch. 4.5 - Prob. 39E Ch. 4.5 - Prob. 40E Ch. 4.5 - Prob. 41E Ch. 4.5 - Prob. 42E Ch. 4.5 - Prob. 43E Ch. 4.5 - Prob. 44E Ch. 4.5 - Prob. 45E Ch. 4.5 - Prob. 46E Ch. 4.5 - Prob. 47E Ch. 4.5 - Prob. 48E Ch. 4.5 - Prob. 49E Ch. 4.5 - Prob. 50E Ch. 4.5 - Prob. 51E Ch. 4.5 - Prob. 52E Ch. 4.5 - Prob. 53E Ch. 4.5 - Prob. 54E Ch. 4.5 - Prob. 55E Ch. 4.5 - Prob. 56E Ch. 4.5 - Prob. 57E Ch. 4.5 - Prob. 58E Ch. 4.5 - Prob. 59E Ch. 4.5 - Prob. 60E Ch. 4.5 - Prob. 61E Ch. 4.5 - Prob. 62E Ch. 4.5 - Prob. 63E Ch. 4.5 - Prob. 64E Ch. 4.5 - Prob. 65E Ch. 4.5 - Prob. 66E Ch. 4.5 - Prob. 67E Ch. 4.5 - Prob. 68E Ch. 4.5 - Prob. 69E Ch. 4.5 - Prob. 70E Ch. 4.5 - Prob. 71E Ch. 4.5 - Prob. 72E Ch. 4.5 - Prob. 73E Ch. 4.5 - Prob. 74E Ch. 4.5 - Prob. 75E Ch. 4.5 - Prob. 76E Ch. 4.5 - Prob. 77E Ch. 4.5 - Prob. 78E Ch. 4.5 - Prob. 79E Ch. 4.5 - Prob. 80E Ch. 4.5 - Prob. 81E Ch. 4.5 - Prob. 82E Ch. 4.6 - Prob. 1PQ Ch. 4.6 - Prob. 2PQ Ch. 4.6 - Prob. 3PQ Ch. 4.6 - Prob. 1E Ch. 4.6 - Prob. 2E Ch. 4.6 - Prob. 3E Ch. 4.6 - Prob. 4E Ch. 4.6 - Prob. 5E Ch. 4.6 - Prob. 6E Ch. 4.6 - Prob. 7E Ch. 4.6 - Prob. 8E Ch. 4.6 - Prob. 9E Ch. 4.6 - Prob. 10E Ch. 4.6 - Prob. 11E Ch. 4.6 - Prob. 12E Ch. 4.6 - Prob. 13E Ch. 4.6 - Prob. 14E Ch. 4.6 - Prob. 15E Ch. 4.6 - Prob. 16E Ch. 4.6 - Prob. 17E Ch. 4.6 - Prob. 18E Ch. 4.6 - Prob. 19E Ch. 4.6 - Prob. 20E Ch. 4.6 - Prob. 21E Ch. 4.6 - Prob. 22E Ch. 4.6 - Prob. 23E Ch. 4.6 - Prob. 24E Ch. 4.6 - Prob. 25E Ch. 4.6 - Prob. 26E Ch. 4.6 - Prob. 27E Ch. 4.6 - Prob. 28E Ch. 4.6 - Prob. 29E Ch. 4.6 - Prob. 30E Ch. 4.6 - Prob. 31E Ch. 4.6 - Prob. 32E Ch. 4.6 - Prob. 33E Ch. 4.6 - Prob. 34E Ch. 4.6 - Prob. 35E Ch. 4.6 - Prob. 36E Ch. 4.6 - Prob. 37E Ch. 4.6 - Prob. 38E Ch. 4.6 - Prob. 39E Ch. 4.6 - Prob. 40E Ch. 4.6 - Prob. 41E Ch. 4.6 - Prob. 42E Ch. 4.6 - Prob. 43E Ch. 4.6 - Prob. 44E Ch. 4.6 - Prob. 45E Ch. 4.6 - Prob. 46E Ch. 4.6 - Prob. 47E Ch. 4.6 - Prob. 48E Ch. 4.6 - Prob. 49E Ch. 4.6 - Prob. 50E Ch. 4.6 - Prob. 51E Ch. 4.6 - Prob. 52E Ch. 4.6 - Prob. 53E Ch. 4.6 - Prob. 54E Ch. 4.6 - Prob. 55E Ch. 4.6 - Prob. 56E Ch. 4.6 - Prob. 57E Ch. 4.6 - Prob. 58E Ch. 4.6 - Prob. 59E Ch. 4.6 - Prob. 60E Ch. 4.6 - Prob. 61E Ch. 4.6 - Prob. 62E Ch. 4.6 - Prob. 63E Ch. 4.6 - Prob. 64E Ch. 4.6 - Prob. 65E Ch. 4.6 - Prob. 66E Ch. 4.6 - Prob. 67E Ch. 4.6 - Prob. 68E Ch. 4.6 - Prob. 69E Ch. 4.6 - Prob. 70E Ch. 4.6 - Prob. 71E Ch. 4.6 - Prob. 72E Ch. 4.6 - Prob. 73E Ch. 4.6 - Prob. 74E Ch. 4.6 - Prob. 75E Ch. 4.6 - Prob. 76E Ch. 4.6 - Prob. 77E Ch. 4.6 - Prob. 78E Ch. 4.6 - Prob. 79E Ch. 4.7 - Prob. 1PQ Ch. 4.7 - Prob. 2PQ Ch. 4.7 - Prob. 3PQ Ch. 4.7 - Prob. 1E Ch. 4.7 - Prob. 2E Ch. 4.7 - Prob. 3E Ch. 4.7 - Prob. 4E Ch. 4.7 - Prob. 5E Ch. 4.7 - 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Prob. 88CRE Ch. 4 - Prob. 89CRE Ch. 4 - Prob. 90CRE Ch. 4 - Prob. 91CRE

Knowledge Booster

a) First that P must lie directly above C junction placed at Point P lying above C

a) First that P must lie directly above C junction placed at Point P lying above C

b) With x as in let f(x) be the total length of cable used show that f has unique critical point c that 0≤c≤L if and only if D≤23L

c) Find the minimum of f on [0,L] in two case D=2,L=4 and D=8,L=2

Want to see the full answer?

Chapter 4 Solutions

a)

First that $P$ must lie directly above $C$ junction placed at Point $P$ lying above $C$

b)

With $x$ as in let $f (x)$ be the total length of cable used show that $f$ has unique critical point $c$ that $0 \leq c \leq L$ if and only if $D \leq 2 \sqrt{3} L$

c)

Find the minimum of $f$ on $[0, L]$ in two case $D = 2, L = 4$ and $D = 8, L = 2$