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1. a) Given a digraph G = (V,E), prove that if we add a constant k to the length of every arc coming out from the root node r, the shortest path tree remains the same. Do this by using potentials:
i) Show there is a potential y* for the new costs for which the paths in the tree to each node v have cost y*v, and
ii) explain why this proves it. What is the relationship between the shortest path distances of the modified problem and those of the original problem?
b) Can adding a constant k to the length of every arc coming out from a non-root node produce a change in the shortest path tree? Justify your answer.
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What angle (to the nearest degree) corresponds to the cos 0.6 or what is cos-1(0.6)? (Note: Use Appendix I) What angle (to the nearest degree) corresponds to the sin 0.6 or what
* 2^(1/2)*4^(1/8)*8^(1/16)*16^(1/32) =
Variable stars are ones whose brightness varies periodically. One of the most visible is R Leonis; its brightness is modelled by the function where t is measured in days.
Assume that the amount of air in a balloon after t hours is specified by V (t ) = t 3 - 6t 2 + 35 Calculate the instantaneous
70 multiply 67
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If angle between asymtotes of hyperbola x^2/a^2-y^2/b^=1 is 120 degrees and product of perpendicular drawn from foci upon its any tangent is 9. Then find the locus of point of inte
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