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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
If the ratios of the polynomial ax 3 +3bx 2 +3cx+d are in AP, Prove that 2b 3 -3abc+a 2 d=0 Ans: Let p(x) = ax 3 + 3bx 2 + 3cx + d and α , β , r are their three Z
2 of 10 =
Quality Control Normally there is a quality control departments in every industry which is charged along with the responsibility of ensuring about the products made do meet th
Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc for all c. (b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
How will you find the vertex of a parabola given in 2nd degree form (the axis of parabola is not parallel to coordinate axes)? Ans) Write the equation in type of standard form.
Determine the differential for following. y = t 3 - 4t 2 + 7t Solution Before working any of these we have to first discuss just
-3x=-57
Product Moment Coefficient This gives an indication of the strength of the linear relationship among two variables. Note that this formula can be rearranged to have di
Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease . For instance, suppose we divide 417 by 3, we
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