A planning engineer for a new alum plant must present some estimates to his company regarding the capacity of a silo designed to store bauxite ore until it is processed into alum. The ore resembles pink talcum powder and is poured from a conveyor at the top of the silo. The silo is a cylinder 100 ft high with a radius of 200 ft. The conveyor carries ore at a rate of 60,000 $\pi \mathrm{ft}^{3} / \mathrm{h}$ and the ore maintains a conical shape whose radius is 1.5 times its height. If, at a certain time t, the pile is 60 ft high, how long will it take for the pile to reach the top of the silo?

Solve the inequality in terms of intervals and illustrate the solution set on the real number line. $x^{3}>x$

Escucha a Ana y toma notas. Luego, lee cada oración y contesta Cierto o Falso. Es importante que todos puedan decir su punto de vista.

Write the equation in spherical coordinates. $z=x^{2}+y^{2}$

¿Qué opiniones tienes sobre la vida escolar? Completa las siguientes oraciones según lo que piensas, usando el vocabulario de esta lección. Es malo que no

Calculate the double integral.

$$\iint_{R} \frac{1}{1+x+y} d A, \quad R=[1,3] \times[1,2]$$

Graciela tiene muchas cosas que hacer para el periódico escolar. Completa las siguientes oraciones con el vocabulario de la lección. Graciela no sólo escribe los artículos

Change the following sentences, using direct object pronouns instead of stating the direct objects. Ud. ve la pelicula en el cine. __________________________________

Completa con la forma apropiada del verbo. 1. Necesitamos hacer algo que nos _____ bien. (pagar) 2. Josefina tiene un puesto que _____ muy interesante. (ser) 3. Yo conozco a una joven que _____ todos los requisitos necesarios para el puesto. (tener) 4. Quieren un empleo que les _____ tener a lo menos dos días libres a la semana. (permitir)

Find the area of triangle PQR. P(2, -3, 4), Q(-1, -2, 2), R(3, 1, -3)

Find a power series representation for f, and graph f and several partial sums s$_{n}(x)$ on the same screen. What happens as n increases?

$$f(x)=\ln \left(1+x^{4}\right)$$

Suppose a stone is thrown vertically upward from the edge of a cliff on Earth with an initial velocity of 32 ft/s from a height of 48 ft above the ground. The height (in feet) of the stone above the ground t seconds after it is thrown is $s(t)=-16 t^{2}+32 t+48$. a. Determine the velocity v of the stone after t seconds. b. When does the stone reach its highest point? c. What is the height of the stone at the highest point? d. When does the stone strike the ground? e. With what velocity does the strike strike the ground? f. On what intervals is the speed increasing?

Combine items from each column in order to write eight logical sentences. Remember that a + el = al.

$$\begin{matrix} \text{yo} & \quad & \text{la clase }\\ \text{tú} & \quad & \text{la oficina}\\ \text{Ud.} & \quad & \text{el parque}\\ \text{Felipe} & \text{ir + a} & \text{el restaurante}\\ \text{Elena} & \quad & \text{la fiesta}\\ \text{nosotros} & \quad & \text{la escuela}\\ \text{los estudiantes} & \quad & \text{el banco}\\ \text{los profesores} & \quad & \text{el hotel}\\ \end{matrix}$$

Prove or disprove: There exists an infinite abelian subgroup of O(n).