--discreteMath let’s examine FSAs whose transition functions are FULL BINARY TREES. We can call these objects FBTSAs to help you remember that they are full binary trees. The alphabet of an FBTSA is Σ = {0, 1}, the start state is at the root, transition arrows must go away from the root and toward the leaves, and all transitions out of the leaves are to a fail state (not drawn). Like a normal FSA, any state can be either accepting or rejecting, except the fail state, which always rejects.   Using big-O notation, give an upper bound for the word length in the language of any FBTSA in terms of the number of states |S|. Please explain your answer.

Find parametric equations for the line through Po = (10,-1, 1) perpendicular to the plane 2x + 3y - 14z = 1. (Express numbers in exact form. Use symbolic notation and fractions where needed.) X = y = Z =

Discuss the relevance of Hobb's method and other centering algorithms to the described occurrences.

Exercise 1. A student is asked to prove If m is even and n is odd, then m² +n² is odd. The student provides the following proof: Proof. If m is even and n is odd, then m² + n² is odd. Since m is even, m = = 2k for any integer k. Since n is odd, n = 2k + 1. Note that m² + n² = (2k)² + (2k + 1)² = 8k² + 4k +1 So m² + n² is odd because it is an even number plus 1. (a) Identify the errors in the proof above. There are multiple errors. Explain each error. Your explanation should be written to the student who made the error and should try to help the student understand why what they wrote is incorrect. (b) In addition to errors, provide suggestions to improve the student's proof writing. That is, explain what parts of the proof are unclear or unjustified. Explain how such parts of the proof prevent some students from fully following the ment made. (c) Finally, provide a correct proof of the theorem above.