True/False with explanation question (4 points): First write if the statement highlighted below is TRUE or FALSE. Then in one brief sentence explain why it is true or why it is false, or, alternatively, give an example of how it is true or how it is false. You need to both label the statement true or false and provide an explanation to get full credit. According to the creative problem solving (CPS) model we learned in class, the first step in the process is to start brainstorming ideas.

Choose the most commonly prescribed fertility medication used for ovulation induction

What is the definition of a genetically abnormal pregnancy that develops into a grape-like mass within the uterus?

Concepts into Practice Short answer (4 points): What was the most important thing you learned in the class thus far?  Briefly (a sentence or two) explain why was it important to you.

Which of the following sequences correctly represents the steps of the PDSA cycle and their purpose in quality improvement?

Which of the following is an example of an at-risk behavior?

Which level within the culture of safety ladder is described best by the statement “There are risk mitigation processes and error reporting systems in place to manage all hazards.”

A radiation event is described as (choose all that apply):

Instructions:  This is a closed-note, closed-book exam. On a separate sheet of paper, answer each of the exam problems shown below. Write your answers clearly. Unless otherwise stated, you will need to justify your answers to get the full credit. Problem 1. (10 pts)  Find the equilibrium pair (xe,ue){“version”:”1.1″,”math”:”\((x_e, u_e)\)”} corresponding to  u e = 2 {“version”:”1.1″,”math”:”\(u_e=2\)”} for the following nonlinear model, = y = x 1 2 + x 2 u . {“version”:”1.1″,”math”:”\begin{eqnarray*} \left&=&\left\\ y&=& x_1^2+x_2u. \end{eqnarray*}”} Problem 2. (10 pts)  Linearize the nonlinear model, = y = x 1 2 + x 2 u , {“version”:”1.1″,”math”:”\begin{eqnarray*} \left&=&\left\\ y&=& x_1^2+x_2u, \end{eqnarray*}”}about the equilibrium found in the previous problem. Problem 3. (10 pts)  For the system modeled by x ˙ = A x + b u = x + u , {“version”:”1.1″,”math”:”\begin{eqnarray*} \dot{x}&=&A x+ b u\\ &=&\left x+\leftu, \end{eqnarray*}”}construct a state-feedback control law, u=−kx+r{“version”:”1.1″,”math”:”\(u=- k x+r\)”}, such that the closed-loop system poles are located at −1{“version”:”1.1″,”math”:”\(-1\)”} and −2{“version”:”1.1″,”math”:”\(-2\)”}. Problem 4. (15 pts)  Design an asymptotic observer for the plant, x ˙ = A x + b u = x + u , y = c x + d u = x + 3 u . {“version”:”1.1″,”math”:”\begin{eqnarray*} \dot{x}&=&A x+ b u = \left x+\leftu,\\ y&=& c x+du = \left x + 3u. \end{eqnarray*}”}The observer poles are to be located at −3{“version”:”1.1″,”math”:”\(-3\)”} and −4{“version”:”1.1″,”math”:”\(-4\)”}. Write down the equations of your observer. Problem 5. (15 pts) Is the following quadratic form, f = x ⊤ Q x = x ⊤ x , {“version”:”1.1″,”math”:”\ x, \]”}positive definite, positive semi-definite, negative definite, negativesemi-definite, or indefinite? Carefully justify your answer. Problem 6. (20 pts)  EvaluateJ0=∫0∞y(t)2dt{“version”:”1.1″,”math”:”\”}subject to x ˙ = x , x ( 0 ) = y = x . {“version”:”1.1″,”math”:”\begin{eqnarray*} \dot{x}&=&\leftx, \quad x(0)=\left\\ y&=& \leftx. \end{eqnarray*}”} Problem 7. (10 pts)  Determine the weight  q {“version”:”1.1″,”math”:”\(q\)”} so that the pole of the system x ˙ ( t ) = x ( t ) + 2 u ( t ) , x ( 0 ) = 1 , {“version”:”1.1″,”math”:”\dot{x}(t)=x(t)+2u(t),\quad x(0)=1, “} driven by the optimal linear state-feedback controller,  u = − k x {“version”:”1.1″,”math”:”\(u=-kx\)”}, that minimizes J = ∫ 0 ∞ ( q x ( t ) 2 + 3 u ( t ) 2 ) d t {“version”:”1.1″,”math”:”J=\int_0^{\infty}\left(qx(t)^2+3u(t)^2\right) dt”}is located at  − 3 {“version”:”1.1″,”math”:”\(-3\)”}. Problem 8. (10 pts)  Determine the optimal state-feedback controller, u=−kx{“version”:”1.1″,”math”:”\(u=-kx\)”}, that minimizes J=∫0∞u(t)2dt{“version”:”1.1″,”math”:”\”} subject to x ˙ ( t ) = x ( t ) + 2 u ( t ) , x ( 0 ) = 2 , {“version”:”1.1″,”math”:”\”} and determine the optimal value of J{“version”:”1.1″,”math”:”\(J\)”}. *** Congratulations, you are almost done with Midterm Exam 1.  DO NOT end the Examity 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: Midterm Exam 1 Submit your exam to the assignment Midterm Exam 1.  Click the button below to agree to the honor statement. Click Submit Quiz to end the exam.  End the Examity session. 

Which anatomical structure does the inferior vena cava filter primarily affect?