Find the simplified form for the reciprocal of $\frac{2}{x-1}-\frac{1}{3 x-2}$.

Calculate $1 \frac{7}{15} \div 1 \frac{11}{25}$ by multiplying by the reciprocal.

At launch a rocket ship weighs $4.5$ million pounds. When it is launched from rest, it takes $8.00$ s to reach $161$ km/h; at the end of the first $1.00$ min, its speed is $1610$ km/h.
(b) Assuming the acceleration is constant during each time inter- val (but not necessarily the same in both intervals), what distance does the rocket travel (i) during the first $8.00$ s and (ii) during the interval from $8.00$ s to $1.00$ min?

Mariana: Mira, aqu^i hay liquidaci^on de camisetas de colores vivos. Tatiana: Viene el invierno. Yo quiero ropa m^as grande de colores oscuros. Mariana: Entonces no vas a encontrar ropa en liquidaci^on. Tampoco vas a encontrar ropa de moda. Tatiana: Est^a bien. No tiene que ser una ganga, s^olo un precio no demasiado exagerado. Mariana: ¿Te gusta esta blusa? Es de algod^on. Y tambi^en es de una marca popular. Tatiana: S^i. Tambi^en me gusta aquella falda. ¿Sabes de qu^e est^a hecha? Mariana: Parece de cuero. Tatiana: En realidad no me importa. Se ve bien con la blusa. Me las voy a probar. Mariana: ¿C^omo te quedan? Tatiana: Bastante bien. La blusa est^a un poco floja y la falda est^a un poco apretada. Mariana: Te ves muy bien. ¿Quieres buscar algo m^as? Tatiana: ¿Por qu^e no miramos esas camisetas en liquidaci^on? Mariana: Vamos!

¿Qu^e busca Tatiana?

What lessons do you now draw about reciprocal loyalty between companies and their workers?

Write as a natural logarithmic equation: a. $N=50 e^{2 t}$ b. $P=8.69 e^{-0.0541 t}$ c. $S=a^{2} e^{-k t}$

Find the stationary points and use the method illustrated in earlier examples to determine the local extreme values.

$$f(x, y)=2 x+2 y-x^2+y^2+5$$

Answer the items below:

(a) What natural events happen in the first stanza?

(b) What specific words suggest the speaker's feelings about the scene she observes?

Winston Corporation purchased 40 percent of the stock of Fullbright Company on January 1, 20X2, at underlying book value. During the period of January 1, 20X2, through December 31, 20X4, the market value of Winston's investment in Fullbright's stock increased by $20,000 each year. The companies reported the following operating results and dividend payments during the first three years of inter-corporate ownership:

$$\begin{array}{l} \hspace{50pt}\textbf{Winston Corporation} \hspace{30pt} \textbf{Fullbright Company}\\ \end{array}$$

$$\begin{array}{lrrrr} \textbf{Year} & \textbf{Operating Income} &\textbf{ Dividends} & \textbf{Net Income} & \textbf{Dividends} \\ \\ \text{20X2} & \$100,000 & \$\hspace{7pt}40,000 & \$70,000 & \$30,000\\ \text{20X3} & 60,000 & 80,000 & 40,000 & 60,000 \\ \text{20X4} & 250,000 & 120,000 & 25,000 & 50,000 \\ \end{array}$$

Required

Compute the net income reported by Winston for each of the three years, assuming it accounts for its investment in Fullbright by using the equity method.

If the sun expanded to a radius 100 times its present radius, what would its density be? (Hint: The volume of a sphere is $\frac{4}{3} \pi R^3.)$

A car is traveling at 80 feet per second (approximately 55 miles per hour) and slows down as it passes through a busy inter section. The car's velocity is shown in the following table.

$$\begin{array}{c|c|c|c|c|c|} \hline \text { Time since brakes applied (seconds) } & {0} & {3} & {6} & {9} & {12} \\ \hline \text { velocity (ft/sec) } & {80} & {62} & {47} & {32} & {22} \\ \hline \end{array}$$

Use a left sum to approximate the total distance the car has traveled over the 12 second interval.

Sketch a graph of the equation $y=\frac{\sqrt[3]{6 \pi^2 x}}{2 \pi}$, where $y$ is the radius of a sphere and $x$ is the volume of the sphere. Use the graph to estimate the volume of a sphere with a radius of $2 \mathrm{~cm}$. Use the graph to estimate the radius of a cube with a volume of $14 \mathrm{~cm}^3$.

At what points, if any, does f assume local maximum or minimum values?

$$f^{\prime}(x)=1-\frac{4}{x^2}, \quad x \neq 0$$

Lee las frases y complétalas con el antónimo de la palabra señalada. Escoge el antónimo del recuadro y escríbelo en la forma correcta según la frase. Recuadro: comenzar; de prisa; dormido; muerto; se murieron; subir.

Sus peces no están vivos, están ____.

¿Qué vas a hacer, ____ o bajar la escalera?

No puede terminar el trabajo porque primero tiene que ____ el trabajo.

Los gatos no están despiertos. Están ___.

La señorita no está caminando lentamente. Está caminando ____.

En el artículo dice que tres personas nacieron y tres personas ___ en el hospital ayer.