Infinite intervals of
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- A circle in the XY-coordinate system is specified by the center coordinates (x, y) and radius (r). Read the values for 2 circles- x1, y1, r1 for C1 and x2, y2, r2 for C2. (i) Determine whether the 2 circles intersect. To solve the problem it suffices to check if the distance between the 2 centers is lesser than the sum of radii of the 2 circles. (ii) Find the smallest circle that encloses the two circles and return its center coordinates and radius. programming language - carrow_forward1. Prove the following formulas log X < X for all X > 0arrow_forward5. For each of the following functions over the positive integers, represented inunary, give the transition diagram of a TM that computes the function. (a). f(x) = ((x+1) mod 2) + 1 (b). g(x) — За +4arrow_forward
- Let f and g be functions from the positive integers to the positive integers defined by the equations f(x) = 3x + 1, g(x) = x2 + 2, h(x) = 7x - 3 Find the compositions a) g°h (x) b) g° f (x)arrow_forwardF(A,B,C)=A'B'+ABC'arrow_forwardQuestion Cumpletion Status QUESTION 1 Rank the following functions by increasing order of growth. That is find any arrangement g1 92. ..... g, of the functions satisfying 91 - 0(g,), 9: - 0(g,). 9, - O(g.), ........9e 0(g,) ni Note stands for n Choose k and KI(n-K)! (n) = n + lg(n) -Fin) = n + lg (n) -(n) =n lg (n)) (n) = Is(n) = n/2, -(n) = 2"arrow_forward
- it is often said 1 human-year is equivalent to 7 dog-years. however, this simple conversion fails to recognize that dogs reach adulthood in their end year of life. as a result the american kennel club suggests the following to calculate a dog's age in human-years. 15 human years are equivalent to the 1st year of a dog's life. a dog's 2nd year is equivalent to 9 human years. after a dog's 2nd year each human year is approximately 5 dogs years. please answer in python codingarrow_forward4. Look up the Pythagorean theorem if you are not already familiar with it. Use the following formula to solve for c in the formula: c = √a2 + b2. Use the proper functions from the cmath header file. Be sure to output the result..arrow_forwardQ3 Find the minimum sum-of-products expressions for each of the following functions (d denotes don't care terms). (a) f(A, B, C, D) = Σm(4,11,12,13,14) + Σm(5,6,7,8,9,10) (b) f(A, B, C, D) = Σm(3,11,12,13,14) + Σm(5,6,7,8,9,10) (c) f(A, B, C, D) = m(1,2,4,13,14) + Σm(5,6,7,8,9,10) (d) f(A, B, C, D) = Σm(4,15) + Σd (5,6,7,8,9,10)arrow_forward
- a. Choose the best answer and explain why? For the functions, n* and c", what is the asymptotic relationship between these functions? Assume that k >= 1 and c> 1 are constants. Choose all answers that apply: A nk is 0(c¹) Bn is (c) ©n is (c¹)arrow_forwardf(x) = sin (z*) %3D • Plot the function and a linear, quadratic and cubic Taylor series approximation about x=0 for x= 0 to 1.5 on the same plot. • Plot the function and a linear, quadratic and cubic Taylor series approximation about x=0.5 for x= 0 to 1.5 on the same plot.arrow_forward:) Consider the following theorem: if n° is an even integer, then n is an even integer. Give a proof by contradiction of this theorem. [Hints: Assume n is an odd integer. Then n= 2k +1 where k is an integer]arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole