When astronauts from the Apollo 15 spacecraft landed on the moon, one of the experiments they conducted was to test Galileo's theory that if two objects of different masses are in free fall in a vacuum, they will land at the same time, regardless of their weight. The moon was an ideal place to test this theory, since its gravitational pull is minimal and there is no air resistance. So, one of the astronauts let a hammer and a feather fall from his hands at about $1.22$ metres from the ground, and indeed they landed at the same time! The accele ration due to gravity on the moon is about $1.625 \mathrm{~ms}^{-2}$. This is far less than that on earth, which is about $9.8 \mathrm{~ms}^{-}$.

Write an equation relating an object's acceleration due to gravity on the moon with the rate of change of the object's velocity, $v$. Hence, find a formula for $v$ using the initial condition that at $t=0, v=0$.

A particle moves along a straight line. It's velocity at time $t$ seconds is modelled by the function $v(t)=t^2-\frac{4}{(t+1)^2} \mathrm{~cm} \mathrm{~s}^{-1}$, where $0 \leq t \leq 6$.

Sketch the graph of the particle's velocity for $0 \leq t \leq 6$.

Consider the differential equation $x \frac{\mathrm{d} y}{\mathrm{~d} x}=x+y$.

Is it possible to solve this differential equation using previous methods you have learned? Explain why, or why not.

Draw the graphs of the functions $y=\sqrt{x}$ and $y=x-2$. Label $R$ the region in the first quadrant which is bounded by the functions and the $x$-axis.

Find the area enclosed by the graphs of the functions $y=\frac{4}{x^2} ; y=x-\frac{1}{4} x^2 ; y=x^2+3 x$.

Use the substitution $v=\frac{y}{x}$ to solve the differential equations in this exercise.

a $x y^{\prime}=x^2 \cos x+y \quad$

b $x^2 \frac{\mathrm{d} y}{\mathrm{~d} x}=3 x^2-x y$

c $x^2 \frac{d y}{d x}=y^2+x y+4 x^2$

What do you obtain when you try to solve $\lim _{x \rightarrow 0} \frac{\sin x}{x}$ algebraically, that is, by substituting $x=0$ into the given function?

Samanca Cabinets makes custom wooden cabinets for high-end stereo systems from specialty woods. The company uses a job-order costing system. The capacity of the plant is determined by the capacity of its constraint, which is time on the automated handsaw that makes finely beveled cuts in wood according to the preprogrammed specifications of each cabinet. The handsaw can operate up to 150 hours per month. The estimated total manufacturing overhead at capacity is $11,000 per month. The company bases its predetermined overhead rate on capacity, so its predetermined overhead rate is$74 per hour of bandsaw use. The results of a recent month's operations appear below:

$$\begin{matrix} \text{Sales} & \text{\$ 39.860}\\ \text{Beginning inventories} & \text{\$ 0}\\ \text{Ending inventories} & \text{\$ 0}\\ \text{Direct materials} & \text{\$ 4.820}\\ \text{Direct labor (all variable)} & \text{\$ 9.640}\\ \text{Manufacturing overhead incurred} & \text{\$ 10.870}\\ \text{Selling and administrative expense} & \text{\$ 9.350}\\ \text{Actual hours of bandsaw use} & \text{124}\\ \end{matrix}$$

1. Prepare an income statement following the example in Appendix 4B in which any under-applied overhead is directly recorded on the income statement as an expense. 2. Why is overhead ordinarily underapplied when the predetermined overhead rate is based on capacity?

Tempe thinks she's pretty skilled at "mouth-catching" (no hands) bits of snack food that have been thrown to her from across a room. She wonders, though, if she's better at catching some foods than others, so she conducts an experiment. A friend tosses 150 pieces of each of three different kinds of snack food (in random sequence) and then records how often Tempe catches the food in her mouth. Here are the results.

$$\begin{array} {lc} & \text{Snack food} \\ \text {Caught?} & \begin{array}{l|c|c|c|c} & \text { Goldfish } & \text { Grapes } & \text { Gummies } & \text { Total } \\ \hline \text { Yes } & 90 & 100 & 115 & 305 \\ \hline \text { No } & 60 & 50 & 35 & 145 \\ \hline \text { Total } & 150 & 150 & 150 & 450 \end{array}\\ \end{array}$$

Is there an association between the two variables? Explain your reasoning. If an association does exist, briefly describe it.

How does the author's observation of women farmers in Senegal help you understand the title of the article? "Some of my most vivid images of the Sahel food crisis are of hands and feet. When I traveled to Senegal recently to document Oxfam's work on the crisis, I met with women farmers who lost their last harvest to erratic rains. Several times I noticed an injury to a woman's foot or finger-usually something simple that without medical care had become so serious that it was disabling or worse: from the look of it, some would require amputation. But none of the women had any food stocks left and, with prices on the rise, none could afford to purchase enough for her family to eat, so a visit to the doctor was out of the question."

The next few visits are uneventful. C.E. has continued to not smoke and is doing better with managing episodes of dyspnea. At your next visit, you greet C.E., immediately note that he sounds congested, and comment that he sounds like he has a cold. He replies, "Oh, our great-grandchildren were over to visit several days ago and they all had snotty noses."
What basic hygiene measures would you include in a teaching plan for C.E. and his wife to prevent his developing an infection? Select all that apply.
a. Practice good hand washing technique, and wash hands often.
b. Avoid people with cold and flu infections, and screen visitors.
c. Avoid enclosed, public a reas at all times.
d. Get pneumonia and flu vaccines every year.
e. Use the dishwasher to wash eating utensils, glasses, and plates.
f. Use antibacterial wipes daily to clean frequently touched surfaces.

You are: a Certified Medical Assistant working with Susan Lee, MD, a primary care physician at Fulwood Medical Center.

Your patient is: Mrs. Helen Schreiber, a 45-year-old high school principal. Your task is to document her care.

Documentation.

Mrs. Helen Schreiber, a 45-year-old high school principal, presents with a 6-month history of dry mouth, bleeding gums, and difficulty in chewing and swallowing food.

Questioning by Dr. Susan Lee, her primary care physician, reveals that she also has dry eyes, is having pain in some joints of both hands, and has felt fatigued. Her previous medical history is uneventful. Physical examination shows a dry mouth, mild gingivitis, and an ulcer on the back of the lower lip. Her salivary glands are not swollen. Her eyes show no ulceration or conjunctivitis. The metacarpophalangeal joints of both index fingers are swollen, stiff, and tender. All other systems show no abnormality.

Initial laboratory reports show anemia, decreased WBC count, and an elevated ESR. Dr. Lee made a provisional diagnosis of Sjogren syndrome. The results of blood studies for SSA and SSB antibodies (Sjögren syndrome antibodies A and B) and for rheumatoid factor titers are pending, as are $x$-rays of her hands. Mrs. Schreiber was given advice about symptomatic treatment for her dry mouth and will be seen again in 1 week. Luisa Guitterez, CMA 06/12/12, 1530 hrs.

Based on the above case report, answer the following question.

What does Dr. Lee find on physical examination of the patient? $\rule{7cm}{0.15mm}$

$\rule{10cm}{0.15mm}$.

In Game 3 of the 1970 NBA championship series, the L.A. Lakers were down by two points with three seconds left in the game. The ball was inbounded to Jerry West, whose image is silhouetted in today's NBA logo. He launched and made a miraculous shot from beyond midcourt, a distance of 60 feet, to send the game over time (there was no 3-point line at that time).

Through careful analysis of the game tape, one could determine the height at which Jerry West released the ball, as well as the amount of time that elapsed between the time the ball left his hands and the time the ball reached the basket. This information could then be used to write a rule for the ball's height $h$ in the fort as a function of time in flight $t$ in seconds.

Write a rule giving $h$ as a function of $t$.

From the list below, supply the words needed to complete the paragraph. Some words will not be used. gauche, banter, motley, docile, emaciated, heresy, libation. The actors gathered in the banquet room after the closing night of the hit play. Sounds of lighthearted _____ filled the room; some of the more _____ performers thought nothing of picking two or more cold _____ at a time from the trays of the servers. The players were still in costumes depicting various cultures and historic eras, and arriving guests paused at the door to take in the _____ sight. The company had just completed its twentieth and final show of a successful run, and the performers were happy to relax. The spirited staff, laughing and carousing, became _____ only when the director raised her hands to quiet the room. Anticipating her words of encouragement, none of the actors suspected that she was about to announce her retirement.