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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.
what is the lowest term of 11/121
Interpretations of Definite Integral There are some quick interpretations of the definite integral which we can give here. Firstly, one possible interpretation of the defini
If cos?+sin? = √2 cos?, prove that cos? - sin? = √2 sin ?. Ans: Cos? + Sin? = √2 Cos? ⇒ ( Cos? + Sin?) 2 = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒
trigonometric ratios of sum and difference of two angles
The Addition Rule: Mutually Exclusive Events P(A or B or C) = P(A) + P(B) + P(C) This can be represented by the Venn diagram as follows:
write the value of the 3 in each number
to use newspaperto study and report on shares and dividend
Illustration 2 In a described farm located in the UK the average salary of the employees is £ 3500 along with a standard deviation of £150 The similar firm has a local
Two circles touching internally at O. OXY, OAB straight lines, the latter passing through the centres. Prove that OX : OY = OA : OB. Given : Two circles touching internally a
Derivative and Differentiation The process of acquiring the derivative of a function or slope or gradient is referred to as differentiation or derivation. The derivative is de
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