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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.
Variance Consider the example of investment opportunities. The expected gains were Rs.114 and Rs.81 respectively. The fact is that an investor also looks at the dispersion befo
how do u add and subtract integers
Example of Integrals Involving Trig Functions Example: Estimate the following integral. ∫ sin 5 x dx Solution This integral no longer contains the cosine in it that
The cost of shipping a package by Shipping Express is $4.85 plus $2 per ounce of the weight of the package. Sally only has $10 to spend on shipping costs. Which of the subsequent c
If a, b and c are in harmonic progression with b as their harmonic mean then, b = This is obtained as follows. Since a, b and c are in
A plastic manufacturer has 1200 boxes of transparent wrap in stock at one factory and 1000 boxes at his second factory.The manufacturer has order for this product from 3 different
Two stations due south of a leaning tower which leans towards the north are at distances a and b from its foot. If α , β be the elevations of the top of the tower from these
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Rationalize the denominator for following. Suppose that x is positive. Solution We'll have to start this one off along with first using the third property of radica
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