2.Find the ronte with mininum cast in the fallowing figees. 10/ 12 8
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- Determine the validity of the ff. proof: Theorem: "the sum of any two rational numbers is a rational number" Proof: "Proof: Suppose r and s are rational numbers. By definition of rational, r = a/b for some integers a and b with b + 0, and s = a/b for some integers a and b with b + 0. Then 2a a r+s ==+ b b a - = b Let p = 2a. Then p is an integer since it is a prod- uct of integers. Hence r+s = p/b, where p and b are integers and b + 0. Thus r+ s is a rational number by definition of rational. This is what was to be shown." Maybe O Yes, it is valid Insufficient information to find the answer Not validDefinition. A Pythagorean triple (x, y, z) is a triple of positive integers where x² + y² = z². This can be thought of as describing an x × y rectangle with the property that the diagonal z is also of integer length. A Pythagorean triple (x, y, z) is primitive if x, y, z are coprime (i.e. there is no integer k > 1 which divides all of them). (a) Write a Python function PrimPyth (n) which returns a list of primitive Pythagorean triples (x, y, z) where 0 < x < y < z#2Write code that generates 100 million random points (X,Y) that are uniformly dis- tributed on the triangular region with vertices (0,0), (1,0), and (0.5,0.5) in the x-yplane using the accept/reject technique. C++Correct answer will be upvoted else downvoted. Computer science. section grouping is a string containing just characters "(" and ")". A standard section succession is a section grouping that can be changed into a right number juggling articulation by embedding characters "1" and "+" between the first characters of the arrangement. For instance, section successions "()()" and "(())" are normal (the subsequent articulations are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not. You need to find a string b that comprises of n characters to such an extent that: b is a standard section grouping; in the event that for some I and j (1≤i,j≤n) ai=aj, bi=bj. As such, you need to supplant all events of 'A' with a similar kind of section, then, at that point, all events of 'B' with a similar sort of section and all events of 'C' with a similar sort of section. Your undertaking is to decide whether such a string b exists. Input The primary line contains a solitary…3. Prof. Poirot needs help. He has a regular expression r and wants to write a regular expression s that generates the the complement of L(r). Can you give him an algorithm for this task? Write it in precise and clear English.20) Prove or disprove: The sum of two odd numbers is even.3. Two 7-digit integers (leading zeros allowed) are considered to be equivalent if one can be obtained from the other by rearranging its digits. For example, 0012234, 0312042, 3220014 and 2100243 are all considered equivalent, whereas 0012234 and 0001234 are not equivalent. How many nonequivalent 7-digit integers are there in which the digits 0, 2, 4 and 6 can each appear at most once?Electrical Engineering - data truct EENG242 (project)Computer science. Correct answer will be upvoted else downvoted. Think about a n by n chessboard. Its columns are numbered from 1 to n from the top to the base. Its sections are numbered from 1 to n from the passed on to one side. A cell on a convergence of x-th line and y-th section is indicated (x,y). The fundamental corner to corner of the chessboard is cells (x,x) for all 1≤x≤n. A stage of {1,2,3,… ,n} is composed on the fundamental slanting of the chessboard. There is actually one number composed on every one of the cells. The issue is to segment the cells under and on the principle askew (there are by and large 1+2+… +n such cells) into n associated areas fulfilling the accompanying imperatives: Each district ought to be associated. That implies that we can move from any cell of a locale to some other cell of a similar area visiting just cells of a similar district and moving from a cell to a neighboring cell. The x-th area ought to contain cell on the fundamental…I am what you call a perfectionist. I always strive for perfection, and I appreciate everyone and everything that is perfect. That is why I have recently acquired an appreciation for perfect numbers! I absolutely need to know which numbers from 1 to 1000 are considered perfect. From what I recall, a perfect number is a positive integer that is equal to the sum of all its divisors other than itself. Example: 6 is a perfect number because the divisors of 6 other than itself are 1, 2, and 3, and 1 + 2 + 3 = 6. c++ codeMatlab onesSEE MORE QUESTIONS