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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.
Example: Find out which of the following equations functions are & which are not functions. y= 5x + 1 Solution The "working" definition of fu
What is Geometry?
If the hight of pipe is 18 inches, what is the volume of the shaded region in terms of π? a. 31.5π in 3 b. 126π in 3 c. 157.5 in 3 d. 58.5 in 3
assigenment of b.sc. 1st sem
E1) Why do we shift the place by one, of the result in the second row of the calculation, when we multiply, say, 35 by 237 E2) Write down the algorithm for the multiplication of
A bag of 28 tulip bulbs contains 12 red tulip bulbs,7 purple tulip bulbs and 9 yellow tulip bulbs,. Two bulbs are selected without replacement. Determine, a) The probability t
If a, b and c are in harmonic progression with b as their harmonic mean then, b = This is obtained as follows. Since a, b and c are in
Related Rates : In this section we will discussed for application of implicit differentiation. For these related rates problems usually it's best to just see some problems an
Example of Partial Fraction Decomposition Evaluate the following integral. ∫ (3x+11 / x 2 -x-6) (dx) Solution: The 1 st step is to factor the denominator so far as
How to raise Powers of Monomials ? To raise a monomial to a certain power: Step 1: Place the entire monomial inside parentheses, and place the desired power outside the paren
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