Use integration to compute the volume of a right circular cone generated by revolving the ordinate set of a linear function f(x)=cx over the interval $0 \leq x \leq b$. Show that the result is one-third the area of the base times the altitude of the cone.

In exercises below, compute the average A(f) for the given function f over the specified interval.

$$f(x)=x^2, \quad a \leq x \leq b$$

Evaluate the integral in Exercise below.

$$\int_0^x\left(1+t+t^2\right) d t$$

Fort Bliss, a U.S. Army military base, contributed $3.3 million of the$87 million capital cost for a desalting plant constructed and operated by El Paso Water Utilities (EPWU). In return, EPWU agreed to sell water to Fort Bliss at $0.85 per 1000 gallons for 20 years. If the army base uses 200 million gallons of water per month, what is the Army’s cost per month for water? The$3.3 million capital cost is amortized at an interest rate of 6% per year, compounded monthly.

Determine the constant speed of satellite S so that it circles the earth with an orbit of radius r = 15 Mm.

What were the motivations behind European exploration of distant lands?

A two-step mechanism has been proposed for the decomposition of nitryl chloride $\left(\mathrm{NO}_{2} \mathrm{Cl}\right)$.

$$\begin{array}{l}{\text { Step } 1: \mathrm{NO}_{2} \mathrm{Cl}(\mathrm{g}) \rightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{Cl}(\mathrm{g})} \\ {\text { Step } 2: \mathrm{NO}_{2} \mathrm{Cl}(\mathrm{g})+\mathrm{Clg} \rightarrow\mathrm{NO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})}\end{array}$$

What is the overall reaction? Identify any intermediates in the reaction sequence, and explain why they euro called intermediates.

Why did European exploration expand dramatically in the fifteenth century?

Two equations are given. Find the intersection point(s) of its graphs by solving the system.

$$\left\{\begin{array}{r}2 x+3 y=7 \\ x-2 y=0\end{array}\right.$$

The average lifespan of American women has been tracked, and the model for the data is

$$y = 0.2t + 73,$$

where t = 0 corresponds to 1960. What is the meaning of the y-intercept? F. In 2007, the average lifespan was 60. G. In 1960, the average lifespan was 58. H. In 1960, the average lifespan was 73. J. The lifespan is increasing 0.2 years every year.

Suppose you drop a care package from an airplane traveling at constant velocity, and further suppose that air resistance doesn't affect the falling package. What will be its falling path as observed by someone at rest on the ground, not directly below but off to the side where there's a clear view? What will be the falling path as observed by you looking downward from the airplane? Where will the package strike the ground, relative to you in the airplane? Where will it strike in the more realistic case in which air resistance does affect the fall?

Quand il sera en Europe

aller a Bruxelles

When possible, compute the truth values of the simple components in the following compound propositions. If no truth value can be computed, write a question mark (?) under the letter or letters with unknown truth value. $\sim L \supset M \\ TF$

To test if the graph of a polar equation may be symmetric with respect to the polar axis, replace $\theta$ by _____.