How is Congress structured and organized?

Using the graph of

$$f ( x ) = \sqrt { x }$$

as a guide, describe the transformation and graph the function.

$$h ( x ) = \sqrt { 4 x }$$

A meter stick lies along the optical axis of a convex mirror of focal length $40 \ \mathrm{cm}$, with its nearer end $60 \ \mathrm{cm}$ from the mirror surface. How long is the image of the meter stick?

Find the radius of the sphere with the given volume.

$$\text { Volume } = \frac { 32 } { 3 } \pi f t ^ { 3 }$$

The autonomous differential equations represent models for population growth. For each exercise, use a phase line analysis to sketch solution curves for P(t), selecting different starting values P(0). Which equilibria are stable, and which are unstable?

$$\frac { d P } { d t } = 1 - 2 P$$

Simplify.

$$( \sqrt { 6 } - \sqrt { 15 } ) ^ { 2 }$$

How many calories are needed to melt 1 gram of ice at

$$0^\circ C?$$

The pressure that a column of air exerts on the area below it is called _____.

Use division to write the rational function in the form q(x)+r(x)/d(x), where the degree of r(x) is less then the degree of d(x). Then find the partial fraction decomposition of r(x)/d(x). Compare the graphs of the rational function with the graphs of its terms in the partial fraction decomposition.

$$\dfrac{x^3+2}{x^2-x}$$

$$\begin{array} { l } { \text { Suppose that } H \text { and } K \text { are subgroups of a group and that } | H | \text { and } | K | } \\ { \text { are relatively prime. Show that } H \cap K = \{ e \} } \end{array}$$

Graph each equation. Select integers for x from - 3 to 3, inclusive.

$$y=x^3-1$$

Give parametric equations and parameter intervals for the motion of a particle in the xy-plane. Identify the particle’s path by finding a Cartesian equation for it. Graph the Cartesian equation. (The graphs will vary with the equation used.) Indicate the portion of the graph traced by the particle and the direction of motion. x = sin t, y = cos 2t,

$$- \frac { \pi } { 2 } \leq t \leq \frac { \pi } { 2 }$$

Find the sum of each series.

$$\sum _ { n = 1 } ^ { \infty } \frac { 2 n + 1 } { n ^ { 2 } ( n + 1 ) ^ { 2 } }$$

Use synthetic substitution to evaluate the polynomial for the given value.

$$P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 5 x + 6 \text { for } x = - 1$$