How can speed be attained from path function and time?

I was given a practice question for transforming equation. In the image I will have a slide the lecture note of an example of it being done but I do not understand what was done exactly. Please explain how to answer the question. Thank you

kindly create and explain an HOQ Analysis on this

Let there be five jobs of the same type and one machine to get those jobs done. The processing time of the job on the machine and the time allowed for the job to be completed for each job are given in the table below.  Job On the machinecompletion time(minute) Allowed To be finishedtime (minute) 1 3 4 2 6 8 3 8 12 4 4 15 5 2 11   Apply the branch-and-boundary method step by step to order the jobs in a way that minimizes the total delay time. State the optimal solution clearly.    Thank you so much.

Please give equations for A & B, no numerical values needed.

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 matrices that are not equal to each other. But, if I were to use the 'ZYX' sequence, I would get a matrix that is equal to the transpose of the matrix produced by my function.I mean that transpose(EA123toDCM) = E123toDCM if I changed the sequence to 'ZYX'. I never got two equal matrices. Can you fix my code so I would get two equal DCM matrices for the body 1-2-3 sequence? Also, for the E123toDCM line, I am using the sequence 'XYZ'. Is that correct or should it be 'ZYX'? 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), 'XYZ')   function [R] = EA123DCM(EA)     theta1 = EA(1,1);    theta2 = EA(2,1);    theta3 = EA(3,1);            R1 =…

Can you answer this?

2- Consider figure represented below: If the number of finished goods () is 10,000, then what is the input ()?

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

In this problem, you will have to first create a Python function called twobody_dynamics_first_order_EoMS. Given a time t and a state vector X, this function will return the derivatives of the state vector. Mathematically, this means you are computing X using some dynamics equation X = f(t, X). Once you have this function in Python, you can solve the differential equations it contains by using solve_ivp. The command will be similar to, but not necessarily exactly, what is shown below: solve_ivp(simple_pendulum_first_order_EoMS, t_span, initial_conditions, args=constants, rtol 1e-8, atol 1e-8) which integrates the differential equations of motion to give us solutions to the states (i.e., position and velocity of a satellite). In the above, t_span contains the initial time to and final time tƒ and it will compute the solution at every instant of time (you will define this later in Problem 1.3 below). The integration is done with initial state vector Xo which defines the initial position…