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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 there are (2n+1)terms in an AP ,prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n Ans: Let a, d be the I term & Cd of the AP. ∴ ak =
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Indeterminate form : The 0/0 we initially got is called an indeterminate form. It means that we don't actually know what it will be till we do some more work. In the denominator
As noted, Euler's method is little used in practice, as there are much better ways of solving initial value problems. By better, we mean, "able to achieve a result of the same prec
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Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means
A national study found that treating people appropriately for high blood pressure decreased their overall mortality rate by 20%. Treating people adequately for hypertension has bee
If a school has lockers with 50 numbers on each combination lock, how many possible combinations using three numbers are there.
jobs a b c d e f 1 15 8 6 14 6 26 2 17 7 9 10 15 22 3 21 7 12 9 11 19 4 18 6 11 12 14 17
When I complete each of the three methods, should I get the same x and y values?
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