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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).
We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f
Rates of Change and Tangent Lines : In this section we will study two fairly important problems in the study of calculus. There are two cause for looking at these problems now.
In this section we will be looking exclusively at linear second order differential equations. The most common linear second order differential equation is in the type. p (t ) y
5.02
In the given figure, ∠AEF=∠AFE and E is the mid-point of CA. Prove that BD/CD = BF/CE Ans: Draw CG ¦DF In ΔBDF CG ¦ DF ∴ BD/CD = BF/GF .............(1)
If 65% of the populations have black eyes, 25% have brown eyes and the remaining have blue eyes. What is the probability that a person selected at random has (i) Blue eyes (ii) Bro
There actually isn't a whole lot to do throughout this case. We'll find two solutions which will form a basic set of solutions and therefore our general solution will be as,
in and ap 1,2,3,4,5,6,7,8,9 11,12,13,14,15,16,17,18,19 and like that nonzzero digit find tn Solution) First break the ''n'' number in terms of 10''s power. For e.g if n=3259 wri
The mode - It is one of the measures of central tendency. The mode is defined as a value in a frequency distribution that has the highest frequency. Occasionally a single valu
How many integers satisfy the inequality |10(x+1)/x^2+2x+3|=1? Solution) first thing thats not an inequality, and second thing its very easy if thats the question. the LHS = |10/
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