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Let a and b be fixed real numbers such that a The open interval (a, b): We define an open interval (a, b) with end points a and b as a set of all r
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.
Determine y′ for xy = 1 . Solution : There are in fact two solution methods for this problem. Solution 1: It is the simple way of doing the problem. Just solve for y to
Create a detailed diagram to describe the equation of an ellipse in terms of it’s eccentricity and indicate how the foci and major and minor semi-axes are involved. Y
In 5 pages, please try to prove Theorem 3 based on Montel''s Theorem. please use "Latex" Knuth Donald to write this paper. It is known that Theorem 3 on page 137 of the attached
What kinds of classroom activities can you think of for helping children to make groups of 5 and 10? Once they have enough practice with such activities, children can be helped
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Question 1: (a) Show that, for all sets A, B and C, (i) (A ∩ B) c = A c ∩B c . (ii) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). (iii) A - (B ∪ C) = (A - B) ∩ (A - C).
If 0.3 is added to 0.2 times the quantity x - 3, the result is 2.5. What is the value of x? The statement, "If 0.3 is added to 0.2 times the quantity x - 3, the result is 2.5,
Define regression. The main reason of curve fitting is to estimate one of the variables (the dependent variable) from the other (the independent variable). The procedure of est
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