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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.
if x+y+z=pi=180 prove that sin^2x+sin^2y+sin^z-2sinx*siny*sinz=2
tan[2x+pie/4]
The boundary of the shaded portion in the adjoining figure consists of our half-circles and two quarter-circles. Find the length of the boundary and the area of the shaded portion
I am student of M.com and also doing practice to crack bank or other competitive exam..please tell me shortcuts
(4 sqrt3+5 sqrt2)/(sqrt48+ srt18)
For a population with a mean of μ=70 and a standard deviation of o=20, how much error, on average, would you expect between the sample mean (M) and the population mean for each of
Properties of t distribution 1. The t distribution ranges from - ∞ to ∞ first as does the general distribution 2. The t distribution as the standard general distribution is
1000000 divided by 19
Finding the Slope of a Line, Given Two Points on it ? Find the slope of the line passing through the pairs of points (-5, -2) and (2, 4). One way to find the slope is
6 and 3/8 minus 1 and 3/4
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