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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.
Ahmad borrowed $450000.00 at 3% compounded semi-annually for ten years to buy an apartment. Equal payments are made at the end of every six months. a) Determine the size of the se
Consider the function f(x) = 2x 2 + 1. Find the equation of the tangent to the graph of f(x) at x = 2. [NOTE: when calculating f'(2), use first principles.
an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 20 years hence is 2/3.Find the p
how do you regroup?
Proof of Sum/Difference of Two Functions : (f(x) + g(x))′ = f ′(x) + g ′(x) It is easy adequate to prove by using the definition of the derivative. We will start wi
Find the value of p and q for which the system of equations represent coincident lines 2x +3y = 7, (p+q+1)x +(p+2q+2)y = 4(p+q)+1 Ans: a 1 = 2, b 1 = 3, c 1 = 7 a 2 =
A 90% acid solution is mixed with a 97% acid solution to obtain 21 litres of a 95% solution. Findout the quantity of every solutions to get the resultant mixture.
Binomials, Trinomials and Polynomials which we have seen above are not the only type. We can have them in a single variable say 'x' and of the form x 2 + 4
Hi, this is EBADULLA its about math assignment. 1 application of complex analysis used in thermodynamics. . what all uses are there in that... plz let mee know this answer.
what marketing orientation is kelloggs influenced by?why do you think kelloggs use this approach?
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