(a) Verify that the one-parameter family $y^2 - 2y = x^2 - x + c$ is an implicit solution of the differential equation $(2y - 2)y' = 2x - 1$. (b) Find a member of the one-parameter family in part (a) that satisfies the initial condition $y(0) = 1$. (c) Use your result in part (b) to find an explicit function $y = \phi(x)$ that satisfies $y(0) = 1$. Give the domain of $\phi$. Is $y = \phi(x)$ a solution of the initial-value problem? If so, give its interval $I$ of definition; if not, explain.

According to Bureau of the Census data, in 2005 in the United States there were about $113,000,000$ total households $58,000,000$ married-couple households $5,000,000$ family households with a male head of household $14,000,000$ family households with a female head of household $30,000,000$ households consisting of one person (NotE: Figures have been rounded to simplify calculations.) b. What fraction of U.S. households in 2005 consisted of individuals living alone? To what fraction with a denominator of 100 is this closest?

In the human body, the value of $\theta$ that makes the following expression zero is the angle at which an artery of radius $r$ will branch off from a larger artery of radius $R$ In the given figure to minimize the energy loss due to friction. Show that the following expression is zero when $\cos \theta=r^4 / R^4$.

$$r^4 \csc ^2 \theta-R^4 \csc \theta \cot \theta$$

It's your birthday! Your family wants to serve you breakfast in bed. Draw your breakfast on the tray. Then write sentences telling what you would like to have.

Which answer below is closest to the wall tension in a typical arteriole of radius $0.15 \mathrm{mm}$ and $60 \mathrm{mm} \mathrm{Hg}$ blood pressure? (a)$0.001 \mathrm{N} / \mathrm{m}$ (b)$0.01 \mathrm{N} / \mathrm{m}$ (c)$0.1 \mathrm{N} / \mathrm{m}$ (d)$1 \mathrm{N} / \mathrm{m}$ (e)$10 \mathrm{N} / \mathrm{m}$

On a separate sheet of paper, write the term that best matches given definition below.
One of a number of points along the main artery supplying blood to an affected limb.

After 7 months, none of 238 angioplasty patients who received a drug-coated stent to keep their arteries open had experienced restenosis (re-blocking of the arteries). (a) Use MINITAB to construct a 95 percent binomial confidence interval for the proportion of all angioplasty patients who experience restenosis. (b) Why is it necessary to use a binomial in this case? (c) If the goal is to reduce the occurrence of restenosis to 5 percent or less, does this sample show that the goal is being achieved?

In the myogenic response, ________. a. muscle contraction promotes venous return to the heart b. ventricular contraction strength is decreased c. vascular smooth muscle responds to stretch d. endothelins dilate muscular arteries

Choose the appropriate infinitive and then write the correct present-tense verb form to complete each sentence.

$$\begin{matrix} \text{estudiar} & \text{hablar} & \text{necesitar} & \text{terminar}\\ \end{matrix}$$

Clara _________________ arte y matemáticas.

An arriving plane carries r families. A total of

$$n_j$$

of these families have checked in a total of j pieces of luggage,

$$\sum _ { j } n _ { j } = r$$

. Suppose that when the plane lands, the

$$N = \sum _ { j } j n _ { j }$$

pieces of luggage come out of the plane in a random order. As soon as a family collects all of its luggage, it immediately departs the airport. If the Sanchez family checked in j pieces of luggage, find the expected number of families that depart after they do.

Ensayo de reflexion y sintesis. Con base en lo que has estudiado en este contexto, escribe un ensayo sobre este tema: ¿Como contribuyen las actividades extraescolares, como la artes y los deportes, al bienes de la comunidad en general?

(Some questions have more than one correct answer. Select the best answer or answers from the choices given.) Peripheral resistance (a) is inversely proportional to the length of the vascular bed, (b) increases in anemia, (c) decreases in polycythemia, (d) is inversely related to the diameter of the arterioles.

Graph the family of polynomials in the same viewing rectangle, using the given values of c. Explain how changing the value of c affects the graph.

$$P ( x ) = x ^ { 4 } + c ; \quad c = - 1,0,1,2$$