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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.
Explain Comparing Fractions with example? If fractions are not equivalent, how do you figure out which one is larger? Comparing fractions involves finding the least common
Tom has five times as many marbles as Jim. together they have 42 marbles. how many marbles does each has?
examples of types of demand
a box contains 4 white and 6 green balls.Two balls are drawn randomly with replacement.Show the probability on tree dig.
A man invest ?13500 partly in shares paying 6% at ?140 and partly in 5% at 125.If he is tolal income is 560, how much has he invested in each?
Find the are of the rectilinear.if it is the difference between to isosceles trapezoid whose corrsponding sides are parallel.
Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a foot ball match? Ans: equally likely because they are mutual
3 1/2 x 1 4/7 x 1 1/3
We will begin this chapter by looking at integer exponents. Actually, initially we will suppose that the exponents are +ve as well. We will look at zero & negative exponents in a
f(x)=sin(x),All x belongs to [p/6, p]
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