To __________ a value means to increase it by one.

In following problem, solve given equation for q.

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

Solve the initial value problem.

$$y ^ { \prime \prime } - 2 y ^ { \prime } + 2 y = x + 1 ; y ( 0 ) = 3 , y ^ { \prime } ( 0 ) = 0$$

Another D-2-ketohexose, psicose, yields a mixture of allitol and altritol when reduced with ${NaBH}_4$ (see Problem 44). Determine the structure of psicose.

Problem 44:

One of the D-2-ketohexoses (see the previous problem) is called sorbose. On treatment with ${NaBH}_4$, sorbose yields a mixture of gulitol and iditol. What is the structure of D-sorbose? (Gulitol and iditol are the alditols acquired by reduction of gulose and idose.)

Previous problem:

How many D-2-ketohexoses are there? Sketch them.

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.

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

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!

A professor teaching a large lecture class of 350 students samples her class by rolling a die. Then, starting with the row number on the die (1 to 6), she passes out a survey to every fourth row of the large lecture hall. She says that this is a Simple Random Sample because everyone had an equal opportunity to sit in any seat and because she randomized the choice of rows. What do you think? Be specific.

In given problem, find the limits

$$\lim _{x \rightarrow 0^{+}} \frac{|x|}{x}$$

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?

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

Suppose points A and B were stretched away from the figure until the acute angles were decreased to 30$^{\circ}$, as shown in the figure. Would the total area increase or decrease? Prove your answer.

Three-year-old C.E. is admitted to the emergency department fast-track clinic. Her mother tells the nurse that C.E. has had a low-grade fever for 2 days and is complaining frequently of ear pain and a sore throat. C.E.'s mother also notes that C.E. has been coughing and is a little hoarse. C.E.'s mother states that C.E.'s appetite has been "off," but she has been drinking and using the bathroom as usual. As you get C.E. settled in the exam room, you suspect C.E. may have otitis media (OM).

You continue to obtain a history from C.E.'s mother and learn C.E. has had "ear problems" and throat infections since she was a baby. She is in daycare each weekday, the father smokes outside of the house, and there is a family history of seasonal allergies. C.E. is allergic to penicillin. Her weight is $14 \mathrm{~kg}$ (31 lbs).

The primary care provider (PCP) diagnoses C.E. with bilateral AOM and strep pharyngitis. C.E. is given a prescription for Augmentin $600 \mathrm{mg}$ twice daily $P O \times 7$ days and her mother is instructed to give acetaminophen $240 \mathrm{mg}$ every 4 hours as needed for pain. She is to be discharged to home with instructions to follow up with the ear, nose, and throat (ENT) specialist.

C.E.s mother is given a new prescription for azithromycin (Zithromax) PO $160 \mathrm{mg} /$ day $\times 5$ days. Azithromycin is dispensed as $200 \mathrm{mg} / 5 \mathrm{~mL}$.

You are providing C.E.'s mother with information on medication administration. You use the Teach-Back technique to assess C.E.'s mother's learning. Which statements by C.E.'s mother indicate the need for further teaching? Select all that apply, and explain your answers.

a. "This medicine can be given with or without food." b. "I don't have to finish the medication if she feels better after a few days." c. "I will place the correct amount of antibiotic in the ear canal once a day." d. "If C. refuses to take her medication, I will tell her it tastes like the candy we get at the movies." e. "I will monitor for vomiting, diarrhea, or stomachaches because this might be a side effect of the medication."

Solve previous problem using the mesh-current method.

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

The speed of a car traveling in a straight line is reduced from 45 to 30 miles per hour at a distance of 264 feet. Find the distance in which the car can be brought to rest from 30 miles per hour, assuming the same constant deceleration.