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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.
1/8 +2 3/4
A class has 175 learners. The given table describes the number of learners studying one or more of the subsequent subjects in this case Subjects
principal=2000 rate=5% time=2 years find compound interest
Area between Two Curves We'll start with the formula for finding the area among y = f(x) and y = g(x) on the interval [a,b]. We will also suppose that f(x) ≥ g(x) on [a,b].
factorize the following algebraic expressions
A bag of 28 tulip bulbs contains 12 red tulip bulbs, 9 yellow tulip bulbs, and 7 purple tulip bulbs. Two bulbs are selected without replacement. Determine, a) The probability th
We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a
(1) Prove that Zorn's lemma is equivalent to axiom of choice. (2) Use Zorn's Lemma to prove the existence of E.
A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 3.5 cm and the height of the cone is 4 cm. The solid is placed in a cylindr
f Y is a discrete random variable with expected value E[Y ] = µ and if X = a + bY , prove that Var (X) = b2Var (Y ) .
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