Using θ-notation, provide asymptotically tight bounds in terms of n for the solution to each of the following recurrences. assume each recurrence has a non-trivial base case of t(n) = θ(1) for all n ≤ n0 where n0 is a suitably large constant. for example, if asked to solve t(n) = 2t(n/2) + n, then your answer should be θ(n log n). you do not need to explain your answers. (a) t(n) = 9t(n/3) + n 2 (b) t(n) = t(n/2) + p n (c) t(n) = 5t(n/2) + n 2 (d) t(n) = t(n/4) + t(3n/4) + n (e) t(n) = t(n/6) + t(2n/3) + n

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d. what is the height of the tide after 93 hours?

Which is the focus of a parabola with equation y2=4x

Cd is the perpendicular bisector of both xy and st, and cy=20. find xy.