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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.
Multiply the given below and write the answer in standard form. (2 - √-100 )(1 + √-36 ) Solution If we have to multiply this out in its present form we would get, (2 -
Type I and type II errors When testing hypothesis (H 0 ) and deciding to either reject or accept a null hypothesis, there are four possible happenings. a) Acceptance of a t
I don''t understand so what is 3 (8-x);24-15
round to the nearest ten to estimate , 422+296
Figure shows noise results for a prototype van measured on a rolling road. The vehicle had a four-cylinder-in-line engine. The engine speed was varied in 3rd gear from just above
I have an assignment of set theory, please Explain Methods of set representation.
assigenment of b.sc. 1st sem
Prove the subsequent Boolean expression: (x∨y) ∧ (x∨~y) ∧ (~x∨z) = x∧z Ans: In the following expression, LHS is equal to: (x∨y)∧(x∨ ~y)∧(~x ∨ z) = [x∧(x∨ ~y)] ∨ [y∧(x∨
Decimal representations of some basic angles: As a last quick topic let's note that it will, on occasion, be useful to remember the decimal representations of some basic angles. S
Proof of the Derivative of a Constant : d(c)/dx = 0 It is very easy to prove by using the definition of the derivative therefore define, f(x) = c and the utilize the definiti
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