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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.
(c) Prove that gcd(a, a + b) = gcd(a, b).
The adjoining figure shows the cross-section of a railway tunnel. The radius of the tunnel is 3.5m (i.e., OA=3.5m) and ∠AOB=90 o . Calculate : i. the height of the
Let ∑ = (0, 1). Define the following language: L = {x | x contains an equal number of occurrences of 01 and 10} Either prove L is regular (by constructing a DFA/NFA or a rege
a box contains 4 white and 6 green balls.Two balls are drawn randomly with replacement.Show the probability on tree dig.
Some Definitions of e 1. 2. e is the unique +ve number for which 3. The second one is the significant one for us since that limit is exactly the limit
Regression line drawn as y=c+1075x, when x was 2, and y was 239, given that y intercept was 11. Caculate the residual
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Logarithmic Differentiation : There is one final topic to discuss in this section. Taking derivatives of some complicated functions can be simplified by using logarithms. It i
4+8/56.75
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Parametric Equations and Curves Till to this point we have looked almost completely at functions in the form y = f (x) or x = h (y) and approximately all of the formulas that w
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