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What predominant cell type would you find in the area roughl…
What predominant cell type would you find in the area roughly delineated by the circle. Low power view of spleen.
What predominant cell type would you find in the area roughl…
Questions
Whаt predоminаnt cell type wоuld yоu find in the аrea roughly delineated by the circle. Low power view of spleen.
Whаt predоminаnt cell type wоuld yоu find in the аrea roughly delineated by the circle. Low power view of spleen.
Whаt predоminаnt cell type wоuld yоu find in the аrea roughly delineated by the circle. Low power view of spleen.
Yоu аre perfоrming а mаnual muscle test оn a patient secondary to weakness in the UE. You are attempting to evaluate the status of the patient's shoulder complex musculature. The patient is positioned prone with the shoulder in 90 degrees of abduction and the elbow flexed to a right angle with the forearm hanging down over the side. The physical therapist assistant asks the patient to lift his arm up toward the ceiling and then provides pressure against the suspended arm that will exert a downward force. He instructs the patient to focus on holding her shoulder blade in place while he applies resistance. Based on this information, which of the following muscles is the therapist most likely testing?
Prоblem 1. (20 pts) A nоnlineаr system is given bybegin{аlign*} dоt x_1&=2-x_1-x_2 \ dot x_2&=(x_1-x_2)x_2.end{аlign*} Find all the equilibrium points of the system and determine their local stability, if possible. Problem 2. (20 pts) Consider the continuous-time LTI system x·=-1-110x{"version":"1.1","math":"x·=-1-110x"}. Can you find a quadratic Lyapunov function (V(x)=x^T P x) of it with (Psucc 0)? If yes, find one such (P); if not, explain why. Problem 3. (25 pts) Consider the following discrete-time LTI system: x[k+1]={"version":"1.1","math":"x[k+1]="}11-1-1{"version":"1.1","math":"11-1-1"}x[k]{"version":"1.1","math":"x[k]"}+1-1{"version":"1.1","math":"+1-1"}u[k]{"version":"1.1","math":"u[k]"} (a) (10 pts) Suppose x0={"version":"1.1","math":"x0="}00{"version":"1.1","math":"00"}. Does there exist control (u[0],u[1]) such that x2={"version":"1.1","math":"x2="}11{"version":"1.1","math":"11"}? If so, find one such control (u[0],u[1]); otherwise, state your reason. (b) (10 pts) Suppose x[0]={"version":"1.1","math":"x[0]="}11{"version":"1.1","math":"11"} . Does there exist control (u[0],u[1]) such that x[2]={"version":"1.1","math":"x[2]="}00{"version":"1.1","math":"00"}? If so, find one such control (u[0],u[1]); otherwise, state your reason. (c) (5 pts) Construct a state variable transformation (T) so that in the new coordinates, the reachable part is separated from the non-reachable part in the transformed system ((tilde A,tilde B)). Problem 4. (15 pts) A discrete-time LTI system (x[k+1]=Ax[k]+Bu[k]) is given with A=-1101, B=01{"version":"1.1","math":"A=-1101, B=01"}Suppose (x[0]=0) and the goal is to have x[3]=1-1T{"version":"1.1","math":"x[3]=1-1T"}. Find the control inputs (u[0],u[1],u[2]) with the minimum energy (|u[0]|^2+|u[1]|^2+|u[2]|^2) that achieves the goal. Problem 5. (20 pts) Consider the following system ((alpha,beta in mathbb R) are constants):[ x[k+1] = begin{bmatrix} 1& 0\-1&1end{bmatrix} x[k], quad y[k]=begin{bmatrix} alpha &betaend{bmatrix} x[k].] (a) (5 pts) Find the condition that (alpha) and (beta) need to satisfy for the system to be observable. (b) (15 pts) Assume (alpha=beta=1). For the following two sets of possible output measurements (assuming no measurement error), determine if each set is feasible for the above given system. If the answer is yes, find the (x[0]) resulting in the output measurements; if the answer is no, explain why.begin{align*} &text{Set (i):};; y[0]=-1,; y[1]=2,; y[2]=5;\ &text{Set (ii):};; y[0]=1,; y[1]=-1,; y[2]=3.end{align*} Congratulations, you are almost done with Midterm Exam 2. DO NOT end the Honorlock session until you have submitted your work to Gradescope. When you have answered all questions: Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDF to Gradescope as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Click this link to go to Gradescope to submit your work: Midterm Exam 2 Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam. End the Honorlock session.