Use the Master theorem to find Θ bounds for each of the recurrence relations below. If the Master theorem does not apply, say so and explain why. You need to justify your answers to get full credit for this question. If you are applying Case 1 or Case 3 of the Master theorem, you need to show that one of the functions grows polynomially faster than the other and specify the ϵ for which it is true. If you are applying Case 3 of the Master theorem, make sure to check the regularity condition.
(a) T(0) = T(1) = C1
T(n) = 8T(n/2) + n³ + n*log n + 2ˡᵒᵍⁿ
(b) T(0) = T(1) = C1
T(n) = 2T(n/4) + n³/²
(c) T(0) = T(1) = C1
T(n) = 9T(n/3) + n³ + n² log n

The pyraminx is a rubik's cube-type toy in the shape of a tetrahedron (not a pyramid). the pyraminx shown below has edges 15\,\text{cm}15cm15, space, c, m long and vertical height h=12.2\,\text{cm}h=12.2cmh, equals, 12, point, 2, space, c, m. the triangle drawn with dashed lines is a right triangle. what is the distance rrr? round your answer to the nearest tenth.

Amanda needs to create an informative print brochure for her local library’s fundraiser dinner. what critical detail must she have before she starts designing the brochure?

The volume v and paper surface area a of a conical paper cup are given by where r is the radius of the base of the cone and h is the height of the cone. a. by eliminating h, obtain the expression for a as a function of r and v. b. create a user-de ned function that accepts r as the only argument and computes a for a given value of v. declare v to be global within the function. c. for v ! 10 in.3 , use the function with the fminbnd function to compute the value of r that minimizes the area a. what is the corresponding value of the height h? investigate the sensitivity of the solution by plotting v versus r. how much can r vary about its optimal value before the area increases 10 percent above its minimum value?