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The point P(x, y) that minimize the sum of distances between the fixed points lying in a plane.
(a)
To Show:
That the condition is equivalent to .
(b)
To Show:
That the function is differentiable except at points A, B and C and the minimum of occurs either at P satisfying the equation , where e, f and g are the unit
(c)
To Prove:
That the equation , where e, f and g are the unit vectors in the direction of vectors holds if and only if P is the Fermat point, defined as the point P for which the angles between the segments and are all 120°.
(d)
To Show:
That the Fermat point does not exist if one of the angles in is greater than 120° and the point which exist in this case is different from Fermat point.
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Chapter 14 Solutions
CALCULUS:EARLY TRANS.-SAPLINGPLUS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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