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1. Show that there do not exist integers x and y for which 110x + 315y = 12.
2. If a and b are odd integers, prove that a2 +b2 is divisible by 2 but is NOT divisible by 4. Hint:
Any odd number can be written 2k + 1 for some integer k.
3. Prove that for any prime number p, √ p is irrational. Hint: Follow the same method that was used to prove √ 2 is irrational, by first supposing √ p can be expressed as a=b.
Q. What are Complex numbers? Ans. Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is a special number called the imaginary unit, which
a) Write a summary on Tower of Hanoi Problem. How can it be solved using recursion ? b) Amit goes to a grocery shop and purchases grocery for Rs. 23.
which one of the following examples represents a repeating decimal? 0.123123,1.111114,0.777777,4.252525?
y'' + 2y = 2 - e-4t, y(0) = 1 use euler''s method with a step size of 0.2 to find and approximate values of y
2/3 divided 22 hours
Estimation of population mean If the sample size is small (n In this case Population mean µ = x¯ ± tS x¯ x¯ = Sample mean S x¯ = s/√n S = standard deviation
define regular pyramid
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The Definition of the Limit In this section we will look at the precise, mathematical definition of three types of limits we'll be looking at the precise definition of limits
what is the rate of 35:15?
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