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Calculus(20/09/2024)

  In search of his fortune, a prospector named Jack had heard tales of a legendary gold mine hidden deep in the mountains. Inspired by stories of riches, he set out to explore three promising locations: Point A, Point B, and Point C.  Using his metal detector, he discovered at point A, a signal modeled by the function f ( t ) = 2 sin ⁡ ( 3 t ) + 4 t f(t) = 2\sin(3t) + 4t ; at Point B, the signal was represented by g ( t ) = 3 sin ⁡ ( 2 t ) + 5 t g(t) = 3\sin(2t) + 5t ; and at Point C, the function was h ( t ) = 4 sin ⁡ ( t ) + 2 t h(t) = 4\sin(t) + 2t Jack knew that the greater the difference between the maximum value of the derivative of the signal and a threshold of 8 , the more likely he was to stumble upon gold. Select the correct alternative. a) He is more likely to find gold at Point A. b) He is more likely to find gold at Point B. c) He is more likely to find gold at Point C. d) He is equally likely to find gold at all points. e) None of the above. Original idea by: João Vitor
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BFS (06/09/2024)

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John is a tourist from Minas Gerais who is on vacation and want to explore the cities in UaiSo. There are 3 main cities that he would like to visit: CheeseBreadLand, DulceDeLecheTown and TorresmoCity, that are painted in blue in the map. But John only moves following a BFS order , and he only has the time to visit 5 cities . Help John optimize his management so he can visit the most possible interesting cities. Consider that the BFS always choose the neighbours in ascending order and the following map is an undirected graph .   To visit the most number of cities he would like, what John should do? a) John should start his trip on city 1, so he can visit 2 cities of interest. b) John should start his trip on city 4, so he can visit 2 cities of interest. c) John should start his trip either on city 2 or 4, to visit 2 cities of interest. d) John should start his trip on city 2, so he can visit 2 cities of interest. e) None of the above Original idea by: João Vitor Baptista Moreira
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Graph Teory (23/08/2024)

Consider an adjacency matrix A A , such that A i j = 1  if there is an edge from vertex  j  to vertex  i ,   A_{ij} = 1 \text{ if there is an edge from vertex } j \text{ to vertex } A i j = 0  otherwise . Select the correct alternative: a) If the graph is undirected, A = A T A = A^T . b) If the graph is directed, the main diagonal is always equal to 1. c) If the graph is undirected, the main diagonal is always equal to 0. d) If the graph is directed, A A is invertible. e) None of the above Original idea by: João Vitor Baptista Moreira
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Edge classification (16/08/2024)

After running a DFS algorithm in a directed graph, the following table represents the start and end time of each node. Node Start time End time A 1 10 B 8 9 C 2 7 D 3 4 E 5 6   Select the correct alternative about the edges:   a) The edge A -> C is a backward edge b) The edge D -> E is a forward edge c) The edge B -> C is a cross edge d) The edge E-> D is a forward edge e) None of the above Original idea by: João Vitor  
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