A new nurse is learning to use correct terminology when documenting skin lesions. Which of the following definitions are correct? Select all that apply

A mother brings her 8 week old child in for an examination and says, “My daughter rolled over against the wall, and now I have noticed that she has this spot that is soft on the top of her head. I think there is something wrong.” What is the nurse’s best response?

The nurse is obtaining an admission history and physical assessment for an adult who has been admitted to the acute-care hospital for sepsis. Which actions will the nurse implement to obtain objective data? Select all that apply.

Let r→(t)=\vec{r}(t)=. Write the parametric equations for the tangent line to r→\vec{r} at the point where t0=0t_0=0.

You are herding frugs up a trail on a hill (coincidentally, the hill is shaped like a perfectly round paraboloid). As you reach the most south-western part of the mountain trail the evil wolf Eerg appears and chases some of your frugs up the trail! Luckily, you know a shortcut. Write a vector (with numbers for full credit) that describes the direction you go to beat Eerg to the top and recollect your frugs. For the sake of this problem, let’s assume you run just as fast, regardless of the incline. The answer doesn’t depend on the equation for the mountain, but if you would like an example just use f(x,y)=25-x2-y2f(x,y)=25-x^2-y^2 and the points (-3,-3)(-3,-3).

Let F→(x,y,z)=\vec{F}(x,y,z)=. Find the divergence, ∇∙F→\nabla\bullet\vec{F} and the curl, ∇×F→\nabla\times\vec{F}.

Let SS be the plane 5x+3y-3z=155x+3y-3z=15 in octant V with a downward facing Normal, and F→=\vec{F}=.a) Evaluate ∫S∫(∇×F→)∙N→ dS\int_S\int{(\nabla\times\vec{F})\bullet\vec{N}\ dS}b) Find ∫CF→∙ dr→\int_C{\vec{F}\bullet\ d\vec{r}} where CC is the boundary curve of SS.Hint: it iS possible to answer This part (b) withOut showing any worK as long as you statE why/what theorem(s) you are uSing

Let QQ be the solid bounded by the paraboloid z=x2+y2z=x^2+y^2 and z=16z=16 with SS as its boundary surface oriented outward as usual. And let F→=\vec{F}=.a) Set up and simplify, with bounds, but do not evaluate, the integrals ∫S∫F→∙N→ dS\int_S\int{\vec{F}\bullet\vec{N}\ dS}Hint: the flat top of the solid is its own function and requires its own integralb) Use the divergence theorem to set up and evaluate the integral ∫∫Q∫∇∙F→ dV\int\int\limits_Q\int{\nabla\bullet\vec{F}\ dV}

Type your answers in as best you can. Avoid decimals: leave your answers with square roots and/or fractions if applicable. There is a math editor if you click the ⊕\oplus button. Don’t forget to upload your work through the provided link in blackboard or via email, even if you show it here to your recording, because that’s how I will be grading your exams.

Use Green’s Theorem to rewrite, but not evaluate, ∫Cxy2 dx+5x2y dy\int_C{xy^2\ dx + 5x^2y\ dy}, where CC is the boundary around the region given by y=0y=0, x=ex=e, and y=ln(x)y=\ln(x). Include bounds for your integral.