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This question tests your understanding of decision trees. You can draw the portion of the decision tree for insertion sort on 5 elements (a1, a2, a3, a4, a5)  to the leaf node annotated by the permutation . Each of the following sub-questions asks you about the element-wise comparisons made at the k-th node from the root node to the given leaf node, where the 1-st node denotes the root node. The comparison at the root node (first node) is “a1 > a2?” (a) What is the comparison made at the 2nd node from the root to the leaf node annotated by the permutation ? [a]   (b) What is the comparison made at the 3rd node from the root to the leaf node annotated by the permutation ? [b]   (c) What is the comparison made at the 5th node from the root to the leaf node annotated by the permutation ? [c]   (d) What is the comparison made at the 7th node from the root to the leaf node annotated by the permutation ? [d]  

(8pts) Use transformations to sketch the following functions.  No calculators.  Please label all transformations, and include 3 points on the graph.  You do not need to graph each transformation, just the final graph.

(4 pts) Find the domain of  

What type of project does BIM particularly help with, as demonstrated by the Shanghai Tower?

What is one of the main benefits of BIM?

Which of the following is a major benefit of better visualization in BIM?

At which level of BIM maturity does 3D modeling first get integrated with 2D drawings?

Consider the simply supported beam shown below.     a) The pin support at A has a 10 kN vertical reaction force. What is the magnitude of the shear force at A?   b) what is the magnitude of the shear force at the application point of the 20 kN load?   c) what is the magnitude of the shear force 2 meters to the right of A?

Consider a simply supported beam subjected to a concentrated load, as shown below.  The beam has two vertical reactions. There is a reaction force at A and there is one at B. Is it true that these reaction forces are equal in magnitude?  

The beam shown below consists of 4 segments labeled AB, BC, CD, and DE.     a) What is the magnitude of the shear force in segment AB?   c) What is the magnitude of the shear force in segment BC?   b) What is the magnitude of the shear force in segment CD?   d) What is the magnitude of the shear force in segment DE?