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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.
1. Construct an isosceles triangle whose base is 7cm and altitude 4cm and then construct another similar triangle whose sides are 1/2 times the corresponding sides of the isosceles
Example of Imaginary Numbers: Example 1: Multiply √-2 and √-32 Solution: (√-2)( √-32) = (√2i)( √32i) =√64 (-1) =8 (-1) =-8 Example 2: Divid
Vertical asymptote Definition : The function f(x) will contain a vertical asymptote at x = a if we contain any of the following limits at x = a . x→a- Note as well that it
Show the result of the following sequence of UNION operations using union-by-weight with the following assumptions Unions are performed on the representatives on the sets th
what is the difference between North America''s part of the total population and Africa''s part
i needed help with algebra
Consider the following linear programming problem: Min (12x 1 +18x 2 ) X 1 + 2x 2 ≤ 40 X 1 ≤ 50 X 1 + X 2 = 40 X
Proof of Sum/Difference of Two Functions : (f(x) + g(x))′ = f ′(x) + g ′(x) It is easy adequate to prove by using the definition of the derivative. We will start wi
Suppose that x = x (t ) and y = y (t ) and differentiate the following equation with respect to t. Solution x 3 y 6 + e 1- x - cos (5
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