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1. a) Find the shortest paths from r to all other nodes in the digraph G=(V,E) shown below using the Bellman-Ford algorithm (as taught in class). Please show your work, and draw the final shortest dipath tree on a copy of a diagram of the digraph.
b) Using the potential y found in a), find a new set of costs c* for G which are non-negative, and preserve shortest dipaths.
Find out if the following sets of functions are linearly dependent or independent. (a) f ( x ) = 9 cos ( 2 x ) g ( x ) = 2 cos2 ( x ) - 2 sin 2 ( x ) (b) f
Theorem Consider the subsequent IVP. y′ = p (t ) y = g (t ) y (t 0 )= y 0 If p(t) and g(t) are continuous functions upon an open interval a o , after that there i
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Example Sketch the graph of following f( x ) = 2x and g( x ) = ( 1 /2) x Solution Let's firstly make a table of values for these two functions. Following is
what is the changen intemperature bewtween the highest and the lowest temperture high-40c low-0c
A pilot is flying over a straight length of road. He determines the angles of depression of two mileposts, 5 miles apart, to be 32° and 48°. a) Find the distance of the plane f
We know that 2 4 = 16 and also that 2 is referred to as the base, 4 as the index or power or the exponent. The same if expressed in terms of logarithms would be log 2
the area of a triangle is 20 and its base is 16. Find the base of a similar triangle whose area is 45. Given is a regular pentagon. Find the measure of angle LHIK.
Differentiate y = x x Solution : We've illustrated two functions similar to this at this point. d ( x n ) /dx = nx n -1 d (a x ) /dx= a
Kyra's weekly wages are $895. A Social Security tax of 7.51% and a State Disability Insurance of 1.2% are taken out of her wages. What is her weekly paycheck, assuming there are no
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