We have designed a divide-and-conquer algorithm that runs on an input of size n. This algorithm works by spending O(1) time splitting the problem in half, then does a recursive call on each half, then spends O(n2 ) time combining the solutions to the recursive calls. On small inputs, the algorithm takes a constant amount of time. We want to see how long this algorithm takes, in terms of n to perform the task. (a) First, write a recurrence relation that corresponds to the time-complexity of the above divide and conquer algorithm. (b) Then, solve the relation to come with the worst-case time taken for the algorithm. Please show all work in depth.

I am trying to find a Direction Cosine Matrix (DCM) for the Euler angle body 1-2-3 sequence. I tried making my own function and using the MATLAB function, but the result is a matrix that is transpose of each other. I mean that transpose(EA123toDCM) = E123toDCM. Why is that? Also, for the E123toDCM line, I am using the sequence 'ZYX'. Is that correct or should it be 'XYZ'? I know that that for a DCM of sequence 1-2-3 = R3(theta1)*R2(theta2)*R1(theta3). Is ZYX sequence the same as a 1-2-3 sequence?   EA = [pi/3; -pi/4; -pi/6];EA123toDCM = EA123DCM(EA) E123toDCM = angle2dcm(EA(1,1), EA(2,1), EA(3,1), 'ZYX')   function [R] = EA123DCM(EA)     theta1 = EA(1,1);    theta2 = EA(2,1);    theta3 = EA(3,1);            R1 = @(a)[1    0      0    ;              0  cos(a) -sin(a);              0  sin(a) cos(a)];              R2 = @(a)[cos(a)  0 sin(a) ;                0     1   0    ;              -sin(a) 0 cos(a)];              R3 = @(a)[ cos(a) -sin(a) 0;               sin(a) cos(a)  0;…

X(s) from the following block diagram. F(s) Obtain the transfer function F(s) + X(s) 9. 5 9 A) s - 6 9. B) s + 14 9. C) s+ 4 s + 4 D) s + 6

Please don't provide handwritten solution ......

HW 2_2 The volume of a partially-filled spherical tank can be computed as: V = πα 3 (3R – d); where d is the depth of the water in the tank (m) and R is the radius of the tank (m). Given that R=3m, to what depth must the tank be filled so that it holds 30 m³? Write a PYTHON code & implement the bisection algorithm to answer the question correct to 3 sig figs. Plot to select your own initial guesses. Display the answer in an informative sentence, using formatted printing.

Hello I'm having trouble with this assignment, I don't understand how the plot function works for ordered pairs. I undertand that the points of the line would be the origin(0,0) and (x = cos(theta) . y = sin(theta)).

How can speed be attained from path function and time?

The input and output relationship of a process plant is given by: 3s+1 Y(s) = U(s) s3+9s2+26s+ 24 Identify the correct diagonal canonical form for the process plant system from the list below: (Note: You should select the correct answer number and also provide us with the calculation notes. Remember, all your calculation notes must be attached and uploaded as a separate document. It should be clean and readable with question numbers and their corresponding solution notes. Failure to provide this calculation notes could result in the candidate being awarded zero marks. Also, you may use MATLAB or any other calculation tools to cross-check answers should you wish to). O a. -2 0 0 x = 0 -3 0 x+1|u; y = [2.5 6 8]x 0 0 -4] O b. 4 0 0 x = 0 -3 0 0 -2] -0.31 0 x+ 0.3 u; y = [18 26 9]x [-0.3] O c. 4 0 0 -2.51 x = -3 0x+ u; y = [0 3 1]x 0 0 -21 -5.5 O d. None of the above

Hi, I need help on this question:a) Choose boundary conditions (b.c.) for the boundaries A-G from the types of b.c. typically implemented with an incompressible CFD solver. State what quantities those b.c. impose, and which they leave undefined. Justify your choice of boundary condition. b) Discuss the most important errors your choice of b.c. may introduce and how those could be remedied. c) While walking past your desk, your team-leader reminds you that the quantity of interest is the massflow in the lower channel, and proposes to use a slip-wall condition for B. Unfortunately she doesn’t explain her reasoning. For the next team meeting, prepare a discussion of the pros and cons of that suggestion, and explain whether or not you think this suggestion should be followed.