Describe the sets of points in 3-space that satisfy the equations. Here, $r , \theta , R$ , and $\phi$ denote the appropriate cylindrical or spherical coordinates. $\phi = \pi / 2$

Find an equation of the cubic polynomial f(x)=ax$^3$+bx$^2$+cx+d that passes through the given points.

P(0,-6), Q(1,-11), R(-1,-5), S(2,-14)

Sketch the graph. $\rho=2 \sec \phi$

Solve. Where appropriate, include approximations to four decimal places.

$3^{2 x}=\frac{1}{9}$.

use the given values to evaluate (if possible) all six trigonometric functions.

$$\newline\sec \phi=\frac{3}{2},\csc \phi=-\frac{3\sqrt{5}}{5}$$

Use the given diagram.

$$\begin{array}{llllllll} r &~~~~~& s &~~~~~~& t ~~~~~~~\\ \end{array} \\ \begin{array}{c|cc|cc|c} \\ \qquad \quad & ~~~~ & ~~~~ & ~~~~ &~~~~ & \qquad \quad \\ \\ \hline \\ \\ \\ \hline \\ \\ \\ \end{array} \begin{array}{} m \\ \\ \\ n \end{array}$$

Is $s \| t$?

find (f - g)(x). What is the domain of f g?. f(x) = x^2 + 6, g(x) = √1-x

Find the product.

$$\begin{bmatrix}-2&-4\\5&1\end{bmatrix} \begin{bmatrix}6&-1\\3&-3\end{bmatrix}$$

Sunspots appear dark because (a) they are patches of the photosphere that occasionally burn up, creating soot; (b) the changing magnetic polarity of the Sun causes gas in the sunspot to cool down substantially; (c) they are regions in which strong magnetic fields make it difficult for fresh supplies of hot, ionized gas to reach the photosphere; (d) they are much hotter than the surrounding area, so their emission peaks at ultraviolet wavelengths, which our eyes cannot see; or (e) they are holes in the photosphere through which the cooler interior of the Sun is visible.

Fais des phrases en utilisant les elements donnes. N'oublie pas de faire tous les changements necessaires.

1. il / etre / triste / que / son chien / etre / mort

2. nous / etre / ravi / que / aline / etre / fiance

3. c' / etre dommage / que / vous / devoir / partir

4. je / etre / desole / que / tu / avoir / un gros rhume

5. vous / souhaiter / que / Jeanne et Marc / avoir beaucoup d'enfants

6. il / etre essentiel / que / nous / etre / a l'heure / au boulot

What are the mean and standard deviation of the difference Y - X between the readings? (The readings X and Y are independent.)

Use trigonometric identities to write each expression in terms of a single trigonometric function or as a constant.

$$\frac{\tan \phi+1}{\cot \phi+1}$$

Write each function in slope-intercept form. Then graph the function.

$$8 x-6 y=-12$$

Fill in the blanks.

veins $\quad$ varicosities $\quad$ varix $\quad$ vein $\quad$ varicose $\quad$ varices $\quad$ venogram

The $\rule{3cm}{0.15mm}$ performed on this patient's left saphenous and popliteal $\rule{3cm}{0.15mm}$ shows the following:

One slightly engorged and dilated $\rule{3cm}{0.15mm}$ at the midpoint of the saphenous $\rule{3cm}{0.15mm}$ and several $\rule{3cm}{0.15mm}$ at the terminal end of the popliteal. Diagnosis: $\rule{3cm}{0.15mm}$ veins.

These $\rule{3cm}{0.15mm}$ need immediate attention by a vascular surgeon.