A nurse is preparing to administer 400 mL or 0.9% sodium chloride IV over 8 hours. The drop factor of the manual IV tubing is 60 gtt/mL. The nurse should set the manual IV infusion to deliver how many gtt/min?Do not provide the unit of measurement. Only provide the number. Round to the nearest whole number.

The nurse is assessing a peripheral venous catheter after removal, and it appears that the catheter tip is missing. What does the nurse do next?

Which instruction does the nurse give to an unlicensed assistive personnel (UAP) who has been delegated to check blood pressure on six clients being infused with peripheral IV fluids?

What is the minimum size peripheral IV catheter through which a blood transfusion can be infused?

The physician orders an IV of 40 mEq of potassium chloride in 500 mL 0.9% NS to infuse over 4 hours. Calculate the flow rate in milliliters per hour. _______________Do not provide the unit of measurement. Only provide the number. Round to the nearest whole number.

A nurse notes that a client’s IV tubing has disconnected from the IV catheter, resulting in the client’s blood spilling onto the sides of the bed and the floor. Which of the following solutions should the nurse use to disinfect the spill?

The physician orders a continuous IV hydromorphone drip at 0.5 mg/h. The medication is supplied in 10 mg/100 mL. Calculate the flow rate in milliliters per hour. ___________Do not provide the unit of measurement. Only provide the number. Round to the nearest whole number.

A student nurse is preparing an IV bag with IV administration tubing. Which action by the student nurse necessitates intervention by the supervising nurse?

Honorlock Essay Prompt:Write a response essay about your personal experiences with growth mindset and fixed mindset. In your essay, you must: Describe a time in your life when you did not use a growth mindset (a fixed-mindset moment). Explain what you believed in that moment, how you responded to the situation, and what the outcome was. Describe a time in your life when you did use a growth mindset. Explain what you did differently, how you handled challenge/feedback/effort, and what the outcome was. Explain how you can maintain a growth mindset in the future. Include at least two specific strategies you will use (for example: how you will respond to mistakes, how you will handle feedback, or how you will keep motivation when something feels difficult). Suggested Structure (Recommended) Introduction (1 paragraph): Briefly explain growth mindset vs. fixed mindset and state your main point (thesis). Preview your two experiences and your plan for maintaining a growth mindset. Body Paragraph 1: Fixed-mindset moment (what happened, what you believed, how it affected your choices/outcome). Body Paragraph 2: Growth-mindset moment (what happened, what you believed, what you did, what changed). Body Paragraph 3: Maintaining growth mindset (two or more strategies + why they will work for you). Conclusion (1 paragraph): Summarize key insights and explain how your mindset will shape your future learning and goals.

Instructions:  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)  Compute the linear, l(x1,x2){“version”:”1.1″,”math”:”\(l(x_1,x_2)\)”}, and quadratic, q(x1,x2){“version”:”1.1″,”math”:”\( q(x_1,x_2)\)”}, approximations of the function  f ( x 1 , x 2 ) = 5 x 1 2 x 2 − x 1 4 x 2 − 3 x 1 + 1 , {“version”:”1.1″,”math”:”f(x_1,x_2)=5x_1^2x_2 – x_1^4x_2 – 3x_1+1, “} at the point  x ( 0 ) = [ 0 1 ] ⊤ {“version”:”1.1″,”math”:”x^{(0)}=\begin{bmatrix} 0 & 1\end{bmatrix}^\top”} Problem 2. (10 pts) Given a point  x ( 0 ) = 0 {“version”:”1.1″,”math”:”x^{(0)}=0″} and the equation  f = f ( x ) = − x 3 + 5 x 2 − 2 x − 3. {“version”:”1.1″,”math”:”f=f(x)=-x^3+5x^2-2x-3.”}Find x(1){“version”:”1.1″,”math”:”\( x^{(1)}\)”}using Newton’s method of tangents for finding a root of  f = 0. {“version”:”1.1″,”math”:”\(f=0.\)”} Problem 3. (10 pts)  Consider a rectangle with the shorter side  a = 1 {“version”:”1.1″,”math”:”\( a=1\)”} and the longer side  b . {“version”:”1.1″,”math”:”\(b.\)”} Find  b {“version”:”1.1″,”math”:”\(b\)”} for which the sides of the rectangle satisfy the golden section. In your manipulations you may find useful that  5 = 2.236 {“version”:”1.1″,”math”:”\( \sqrt{5}=2.236 \)”}  Problem 4. (10 pts)  What is the largest a {“version”:”1.1″,”math”:”\(a \)”} for which the quadratic form,  f = f ( x 1 , x 2 , x 3 ) = x 1 2 − 2 x 1 x 2 − 2 x 1 x 3 + a x 2 2 + 2 x 3 2 , {“version”:”1.1″,”math”:”f=f(x_1,x_2,x_3)=x_1^2-2x_1x_2-2x_1x_3+ax_2^2+2x_3^2,”}is positive semi-definite and not positive definite? Problem 5. (20 pts) (10 pts) Does the function  f ( x 1 , x 2 ) = 1 2 x 1 2 − x 1 x 2 + 3 2 x 2 2 + x 2 + 3 {“version”:”1.1″,”math”:”f(x_1,x_2)=\frac{1}{2}x_1^2-x_1x_2+\frac{3}{2}x_2^2 + x_2 +3 “} have a minimizer or a maximizer? If it does, then find it; otherwise explain why it does not. (10 pts) Does the function  f ( x 1 , x 2 ) = − x 1 2 + x 1 x 2 − x 2 2 − x 2 + 1 {“version”:”1.1″,”math”:”f(x_1,x_2)=-x_1^2+x_1x_2-x_2^2 – x_2 +1 “}{“version”:”1.1″,”math”:”f(x_1,x_2)=2x_1^2+4x_1x_2+2x_2^2 – x_1 +3 “}have a minimizer or a maximizer? If it does, then find it; otherwise explain why it does not. Problem 6. (15 pts)  Bracket the minimizer of  f = 2 x 1 2 + x 2 2 {“version”:”1.1″,”math”:”f=2x_1^2+x_2^2 “} on the line passing through the point  x ( 0 ) = [ − 5 0 ] ⊤ {“version”:”1.1″,”math”:”x^{(0)}=\left[\begin{array}{cc} -5 & 0 \end{array}\right]^{\top}”} in the direction  d = [ 10 10 ] ⊤ {“version”:”1.1″,”math”:”\( d =\left[\begin{array}{cc} 10 & 10 \end{array}\right]^{\top}\)”}. Use  ε = 0.1 {“version”:”1.1″,”math”:”\(\varepsilon=0.1\)”}. Problem 7. (15 pts)  It is well known that Newton’s method (also known as the Newton-Raphson method) seeks a point that satisfies the FONC for an extremizer. Apply the Newton’s algorithm to the function,  f ( x 1 , x 2 ) = − 1 2 x 1 2 + 1 2 x 2 2 − 12 x 1 + x 2 + 5. {“version”:”1.1″,”math”:” f(x_1,x_2)= -\frac{1}{2}x_1^2 + \frac{1}{2}x_2^2 -12x_1+ x_2 + 5. “} The starting point is  x ( 0 ) = [ 0 − 1 ] ⊤ {“version”:”1.1″,”math”:”\(x^{(0)}=\begin{bmatrix} 0 & -1\end{bmatrix}^\top \)”}. Is the point that you obtain a maximizer, a minimizer, or neither? Justify your answer. Problem 8. (10 pts)  Given  Q = [ 1 1 1 a ] , {“version”:”1.1″,”math”:”Q=\begin{bmatrix} 1 & 1\\1 & a \end{bmatrix},”}where  a ∈ R {“version”:”1.1″,”math”:”\( a\in \mathbb{R} \)”}, and vectors  d ( 0 ) = [ − 3 1 ] and d ( 1 ) = [ − 1 2 ] . {“version”:”1.1″,”math”:”d^{(0)}=\begin{bmatrix} -3\\1\end{bmatrix}\quad \mbox{and}\quad d^{(1)}=\begin{bmatrix} -1\\2\end{bmatrix}.”}Find  a {“version”:”1.1″,”math”:”\(a\)”} for which vectors   d ( 0 ) {“version”:”1.1″,”math”:”\( d^{(0)}\)”} and  d ( 1 ) {“version”:”1.1″,”math”:”\( d^{(1)}\)”} are  Q − {“version”:”1.1″,”math”:”\( Q-\)”}orthogonal. *** Congratulations, you are almost done with Midterm Exam 1.  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: Midterm Exam 1 Click the button below to agree to the honor statement. Click Submit Quiz to end the exam.  End the Honorlock session.