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. How much room will be left in the floor area of the silo when the pile is 60 ft high? How fast is the floor area of the pile growing at the height?

Write the words from your vocabulary that you associate with each of the following definitions. Lo que haces si quieres aprender más _______

Evaluate the double integral.

$$\iint_{D} \frac{y}{x^{2}+1} d A, \quad D=\{(x, y) \mid 0 \leqslant x \leqslant 4,0 \leqslant y \leqslant \sqrt{x}\}$$

Find the area of the surface. The part of the plane 6x + 4y + 2z = 1 that lies inside the cylinder x$^{2}$ + y$^{2}$ = 25

Find the absolute maximum and minimum values of f on the set D.

$$\begin{array}{l} f(x, y)=x^{2}+x y+y^{2}-6 y \\ D=\{(x, y) \mid-3 \leq x \leq 3,0 \leq y \leq 5\} \end{array}$$

Write a ll names that apply to each number. Then place the numbers in the correct location on the Venn diagram. 257

Escribe un párrafo en que explicas todo lo que tienen que hacer los pasajeros internacionales en el aeropuerto de llegada.

Let W be the subset of continuous functions on [0, 1] such that f(0)=0. Prove that W is a subspace of C[0, 1].

Evaluate the integral. $\int \frac{\sinh x}{1+\cosh x} d x$

Use the information provided to form complete sentences, adding any necessary words. yo / tener / reproductor de DVDs _____________________

Let F be a ring and $f(x)=a_{0}+a_{1} x+\cdots+a_{n} x^{n}$ be in F[x]. Define $f^{\prime}(x)=a_{1}+2 a_{2} x+\cdots+n a_{n} x^{n-1}$ to be the derivative of f(x). (a) Prove that $(f+g)^{\prime}(x)=f^{\prime}(x)+g^{\prime}(x)$. Conclude that we can define a homomorphism of abelian groups $D : F[x] \rightarrow F[x]$ by (D(f(x))=f'(x). (b) Calculate the kernel of D if charF=0. (c) Calculate the kernel of D if charF=p. (d) Prove that $(f g)^{\prime}(x)=f^{\prime}(x) g(x)+f(x) g^{\prime}(x)$. (e) Suppose that we can factor a polynomial $f(x) \in F[x]$ into linear factors, say $f(x)=a\left(x-a_{1}\right)\left(x-a_{2}\right) \cdots\left(x-a_{n}\right)$. Prove that f(x) has no repeated factors if and only if f(x) and f'(x) are relatively prime.

Assume that the carrying capacity for the US population is 800 million. Use it and the fact that the population was 282 million in 2000 to formulate a logistic model for the US population.

For the following composite function, find an inner function u = g(x) and an outer function y = f(u) such that y = f(g(x)). Then calculate dy/dx. $y=\sqrt{7 x-1}$

Use Newton's method to find all the solutions of the equation correct to eight decimal places. Start by looking at a graph to find initial approximations.

$$\ln \left(x^{2}+2\right)=\frac{3 x}{\sqrt{x^{2}+1}}$$