Answer the exercise given below.

Let $f(x)=x^2-2 x$. Find:

(a) $f^{\prime}(x)$

(b) $f^{\prime}(-1), f^{\prime}(1), f^{\prime}(2)$

Complete the following sentence using the imperfect form of the verb in parentheses. Follow the model.

Modelo Nosotros (ir) íbamos_______ a la escuela todos los días.

¡Mi mamá (ser)_______ muy traviesa de niña!

What is Le Ch$\^{a}$telier's principle? Consider the reaction $2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+$ $\mathrm{Cl}_2(\mathrm{~g})$. If this reaction is at equilibrium, what happens when the following changes occur?

For this change, what happens to the value of $K$ for the reaction as equilibrium is reached again? Give an example of a reaction for which the addition or removal of one of the reactants or products has no effect on the equilibrium position.

$\mathrm{Cl}_2(g)$ is removed.

In general, how will the equilibrium position of a gas-phase reaction be affected if the volume of the reaction vessel changes? Are there reactions that will not have their equilibria shifted by a change in volume? Explain. Why does changing the pressure in a rigid container by adding an inert gas not shift the equilibrium position for a gas-phase reaction?

Solve the initial value problem. $y^{\prime \prime}+2 y^{\prime}+10 y=0, y(0)=1, y^{\prime}(0)=0$

The element molybdenum (Mo) is another micronutrient that can limit primary production in the oceans. If the researchers found the following results for additions of Mo, what would you conclude about its relative importance for growth?

$$\begin{array}{lr} N+P+M o & 6.0 \\ N+P+F e+M o & 72.0 \end{array}$$

Ten days later, A.P.'s mother calls you and states, "I think she has lice again! We worked so hard to get rid of them and clean everything. Is there something else we can use to treat her? What do we do now?" 9. What would you tell A.P.'s mother at this time? 10. List 3 Internet resources A.P.'s mother may find helpful. 11. A.P.'s pediatrician prescribes spinosad (Natroba) at this time. You will provide teaching to A.P.'s mother. Which statements are correct? Select all that apply, and correct the ones that are incorrect. a. Apply Natroba to wet hair. b. Shake the bottle before using. c. Leave it on the scalp without rinsing for 24 hours. d. An adult needs to apply the medication to A.P.'s scalp. e. A second treatment, if needed, may be applied in 1 week. f. After the medication is washed off, use a fine-tooth comb to remove treated lice and nits from the hair and scalp.

Find the first four terms as well as the tenth term of the sequence with the given $n$th term.

$$a_n=(-1)^n \frac{2^n}{n}$$

In following problem, solve given equation for q.

$$q^2 + 7731q = 0$$

Solve previous problem using the mesh-current method.

J.D., age 45, noticed a red spot on his calf after a day of yard work. It did not bother him at first, and he thought it may have been a spider bite. The next morning, he noticed that the spot had grown to the size of a nickel, and it was hardened and very painful. His wife asked him to get it checked, but he said he could take care of it, and tried to pierce it with a pocketknife he had sterilized with a match in an attempt to drain it. Nothing came out when he tried this, so he put some antibacterial ointment over it and covered it with a bandage. Two days later, he realized that the wound was draining yellowish fluid, and the skin around the wound was red and tender. He decides to see his healthcare provider (HCP), who told J.D. that he had developed cellulitis around the wound, which was infected.

J.D. is sent home with a prescription for doxycycline capsules. Two days later, the results from the cultures are reported to the HCP. J.D. is asked to go to the hospital for treatment for an MRSA infection.

Wound Culture and Sensitivity Report:

$$\begin{array}{ll}\text { Staphylococcus aureus (MRSA) } & \geq \mathbf{1 0 0 , 0 0 0} \text { colonies } \\ \text { Amoxicillin } & \mathrm{R} \\ \text { Ceftriaxone } & \mathrm{R} \\ \text { Ciprofloxacin } & \mathrm{R} \\ \text { Clindamycin } & \mathrm{R} \\ \text { Doxycycline } & \mathrm{R} \\ \text { Levofloxacin } & \mathrm{R} \\ \text { Linezolid } & \mathrm{S} \\ \text { Trimethoprim-sulfa } & \mathrm{R} \\ \text { Vancomycin } & \mathrm{R}\end{array}$$

Anaerobic Culture:

No growth after 2 days

Contact Precautions are implemented. In addition to intravenous linezolid antibiotic treatment, the HCP performs an incision and drainage procedure. Wound care is ordered every 12 hours with sterile normal saline wet-to-dry dressings. Which nursing actions are appropriate to delegate to the UAP? Select all that apply.

a. Taking vital signs b. Assessment of the wound c. Obtaining a wound culture d. Teaching about wound care e. Changing the sterile dressing f. Maintaining contact precautions

A.P. is an 8-year-old who is sent to the nurse's office because she has had a 2-day history of scratching her head so badly that she complains that her "head hurts." You complete a general examination of A.P.'s head and notice that she has red, irritated areas with several scratch marks; a few open sores; and sesame seed-sized, silvery-white, and yellow nodules (bugs) that are adhered to many of her hair shafts. You determine that A.P. has pediculosis capitis.

Ten days later, A.P.'s mother calls you and states, "I think she has lice again! We worked so hard to get rid of them and clean everything. Is there something else we can use to treat her? What do we do now?" A.P.'s pediatrician prescribes spinosad (Natroba) at this time. You will provide teaching to A.P.'s mother. Which statements are correct? Select all that apply, and correct the ones that are incorrect.

a. Apply Natroba to wet hair. b. Shake the bottle before using. c. Leave it on the scalp without rinsing for 24 hours. d. An adult needs to apply the medication to A.P.'s scalp. e. A second treatment, if needed, may be applied in 1 week. f. After the medication is washed off, use a fine-tooth comb to remove treated lice and nits from the hair and scalp.

What is Le Ch$\^{a}$telier's principle? Consider the reaction $2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+$ $\mathrm{Cl}_2(\mathrm{~g})$. If this reaction is at equilibrium, what happens when the following changes occur?

For this change, what happens to the value of $K$ for the reaction as equilibrium is reached again? Give an example of a reaction for which the addition or removal of one of the reactants or products has no effect on the equilibrium position.

$\mathrm{NOCl}(g)$ is removed.

In general, how will the equilibrium position of a gas-phase reaction be affected if the volume of the reaction vessel changes? Are there reactions that will not have their equilibria shifted by a change in volume? Explain. Why does changing the pressure in a rigid container by adding an inert gas not shift the equilibrium position for a gas-phase reaction?

For the following exercise,

Use the definition of derivative $\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$ to calculate the derivative of each function.

$$f(x)=-2 x+1$$

Evaluate $f^{\prime \prime \prime}(-2)$ where $f(x)=2 \ln |x|+3$