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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.
A firm buys a product using the price schedule given in the table: The company estimate holding costs at 10% of the purchase price per year and ordering costs at $40 per order .
The 5% sales tax on a basket was $0.70. What was the price of the basket? Use a proportion to solve the problem; part/whole = %/100. The whole is the price of the basket (wh
The Distributive Law : If you were asked to mentally multiply 37 with 9, how would you proceed? 1 would do it as follows - 37 is 30 + 7, 30 x 9 = 270, 7 x 9 = 63, so 270 + 63, th
Conditional probability - Rules of Probability This is the probability associated with combinations of events but given that some prior result has already been achieved with o
A boy standing on a horizontal plane finds a bird flying at a distance of 100m from him at an elevation of 300. A girl standing on the roof of 20 meter high building finds the angl
The sum of the digit number is 7. If the digits are reversed , the number formed is less than the original number. find the number
hi i would like to ask you what is the answer for [-9]=[=5] grade 7
hi i am doing the oaks test do you have somthing that could help me
Illustration of Rank Correlation Coefficient Sometimes numerical data such refers to the quantifiable variables may be described after which a rank correlation coefficient may
#question when equation of tangent T=0 and why
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