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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.
Uses of derivative in daily life with examples.
Scalar Equation of Plane A little more helpful form of the equations is as follows. Begin with the first form of the vector equation and write a vector for the difference. {
Balls are arranged in rows to form an equilateral triangle .The first row consists of one ball, the second two balls and so on. If 669 more balls are added, then all the balls ca
what is mean and mode
An IVP or Initial Value Problem is a differential equation with an appropriate number of initial conditions. Illustration 3 : The subsequent is an IVP. 4x 2 y'' + 12y' +
Hyperboloid of Two Sheets The equation which is given here is the equation of a hyperboloid of two sheets. - x 2 /a 2 - y 2 / b 2 + z 2 /c 2 = 1 Here is a diagram of
7(y + 3) - 2(x + 2) = 14, 4 (y - 2) + 3(x - 3) = 2 Ans: 7(y + 3) - 2 (x+ 2) = 14 --------- (1) 4(y- 2) + 3(x - 3) = 2 ----------(2) From (1) 7y +21 -
What is Chain Based Index Numbers? A chain based index is one whereas the index is calculated every year by using the previous year as the base year. This kind of index measur
Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Determine whether R is an equivalence relation or a p
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