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1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
Q. Basic Set Union Operation? Ans. Suppose instead that your school needs to know which students are taking either art or business or both. Then the students who are ta
You plan to retire when you are 65th years old. You are now 25 years old. You plan to buy a pension annuity that will pay you $100,000 per year starting one year after you turn 6
Solve 2 ln (√x) - ln (1 - x ) = 2 . Solution: Firstly get the two logarithms combined in a single logarithm. 2 ln (√x) - ln (x - l) = 2 ln ((√x) 2 ) ln (1 - x ) = 2
Limit Comparison Test Assume that we have two series ∑a n and ∑b n with a n , b n ≥ 0 for all n. Determine, If c is positive (i.e. c > 0 ) and is finite (i.e. c
What are the key features of Greek Mathematics? How does the emphasis on proof affect the development of Greek Mathematics?
Measures Of Skewness - These are numerical values such assist in evaluating the degree of deviation of a frequency distribution from the general distribution. - Given are t
Example Reduce 24/36 to its lowest terms. 24/36=12/18=6/9=2/3. In the first step we divide the numerator and the denominator by 2. The fraction gets reduced
Q. How to Convert Percentages to Decimals? Ans. Since percent stands for "hundredths", to write a percentage as a decimal you just need to find how many hundredths it repr
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 ? ⇒
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