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1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
a²+b²=1 a+b
Multiplication of complex numbers: Example 1: Combine the subsequent complex numbers: (4 + 3i) + (8 - 2i) - (7 + 3i) = Solution: (4 + 3i) + (8 - 2i) - (7 + 3i
Calculate the Probability A bag contains 80 balls of such 20 are red, 25 are blue and 35 are white. A ball is picked at random what is the probability that the ball picked is
In a group of 1000 people, there are 750 people will speak English and 400 people will speak Russian. How many may speak English only? How many will speak Russian? How many can spe
without a calculator give the exact value of each of the following logarithms. (a) (b) log1000 (c) log 16 16 (d) log 23 1 (e) Solution (b) log10
Integrate following. ∫ -2 2 4x 4 - x 2 + 1dx Solution In this case the integrand is even & the interval is accurate so, ∫ -2 2 4x 4 - x 2 + 1dx = 2∫ o
what is 15,909 in roman numeral
Suppose we are required to find the difference between 3abc and 7abc. We look at two scenarios. The value we would obtain by subtracting a larger quantity from th
A person spent 12.5% of his money and then rs.1600 and then 40% of the remaining,now left rs.960 with him.What is his original money?
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