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Prove that quadrilateral L(3,-3), M(-2,2), N(3,6) and O(8,2) is a trapezoid.
Problem 2 If MN is parallel to PQ in circumcircle O, prove that quadrilateral MNPQ is an isosceles trapezoid opposite anges a
What is the value of x in the isosceles trapezoid below? L M 7x 2x + 5 o N 7 5 O 2 0 1 1 What is the value of y in the kite below? (4x + 13) (- 9) (5x - 15) 9 32 94.5 49.5 What is the value of x in the kite below? (4x + 13) (y - 90° (5x - 15) 28 9 125 20 stack C D with bar on topis the midsegment...
You are given the four points in the plane a=(-2,2), b=(1,-3), c=(3,6), and d=(7,-3). The graph of the function consists of the three line segments AB, BC and CD. Find the integral by interpreting the integral in terms of sums and/or differences of areas of elementary figures
real analysis. questions Prove that if lima In = 0 and > M for some M >0 and in 10 > 0, then lima (ny) - Asume 30 = 2,2-20+ In+1 = In + Prove that this sequence has a limit and find the limit. Prove that lim = L with L < if and only if every subsequence limo n L. Suppose that the sequence {an) is increasing and the sequence {yn) is decreasing. Moreover, lim a n -...
(a) Prove that n log^3 n is O(n^2). Prove that n^3 is not O(n^2 log n). (b) The multi Pop (i) method pops i items from the top of a stack. Analyse the amortized complexity of the multiPop (i) method.
3. [5 marks] Is the language L = {o € {a, b}* | |0la- l0b is divisible by 2",n 2 1} regular? Be sure to prove your answer 3. [5 marks] Is the language L = {o € {a, b}* | |0la- l0b is divisible by 2",n 2 1} regular? Be sure to prove your answer
Prove L = { 0m1n2n | m,n are natural numbers } is not regular
3) Let N- 11,2,3,... and Nx N -(m,n) | m,n E N. Consider f NxN-N given by f(1,2)-3 | f(2,2)-6 | fa, 21-12 f (1,3)-5 f (2,3)10f (3,3)- 20 f (1,4) 7 f (2,4) 14 f (3,4) 28 2m-i (2n-1). Show, that f is one-to-one and In general "f(m, n) onto. 3) Let N- 11,2,3,... and Nx N -(m,n) | m,n E N. Consider f NxN-N given by f(1,2)-3 | f(2,2)-6 | fa, 21-12 f (1,3)-5 f (2,3)10f (3,3)- 20...
1. Prove that there are no Let m, n E Z with m, n > 3 and gcd(m, n) of mn. primitive roots 1. Prove that there are no Let m, n E Z with m, n > 3 and gcd(m, n) of mn. primitive roots
Prove that the language L = {0^n1^m0^n | m, n greaterthanorequalto 0} is not regular.