As used in line 25 of the second passage, harbinger most nearly means A. an attack. B. an omen. C. a result. D. a deletion. E. a message.

Find the quotient $\frac{z_1}{z_2}$ and express it in rectangular form.

$$z_1 = 8\left[ \cos \left(\frac{5\pi}{8}\right) + i \sin \left({\frac{5\pi}{8}}\right)\right] \text{ and } z_2 = 4\left[ \cos \left(\frac{3\pi}{8}\right) + i \sin \left({\frac{3\pi}{8}}\right)\right]$$

Solve the following exercise.

The region bounded by the curves $y=\sqrt[3]{1+x^3}, y=0, x=0$, and $x=2$ is rotated about the $x$-axis. Use Simpson's Rule given below with $n=10$ to estimate the volume of the resulting solid.

$$\begin{gathered} \int_a^b f(x) d x \approx S_n=\frac{\Delta x}{3}\left[f\left(x_0\right)+4 f\left(x_1\right)+2 f\left(x_2\right)+4 f\left(x_3\right)+\cdots\right. \\ \left.+2 f\left(x_{n-2}\right)+4 f\left(x_{n-1}\right)+f\left(x_n\right)\right] \end{gathered}$$

where $n$ is even and $\Delta x=(b-a) / n$.

Find whether $\mathbf{u}$ and $\mathbf{v}$ make an acute angle, make an obtuse angle, or are orthogonal.

$$\mathbf{u}=(-6,0,4), \mathbf{v}=(3,1,6)$$

For which acute angle measure $\theta$, is $\tan \theta$ less than 1 ? equal to 1 ? greater than 1 ?

A 32.4-cm-OD pipe, 145-cm long, is buried with its centerline 1.2 m below the surface of the ground. The ground surface is at 280 K and the mean thermal conductivity of the soil is 0.66W/m? K. If the pipe surface is at 370K, what is the heat loss per day from the pipe?

For each of the following complexes, give the oxidation state of the metal and its $d^n$ configuration: (a) $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{4-}$; (b) $\left[\mathrm{FeCl}_4\right]^{2-}$; (c) $\left[\mathrm{CoCl}_3(\mathrm{py})_3\right]$; (d) $\left[\mathrm{ReO}_4\right]^{-} ;$(e) $\left[\mathrm{Ni}(\mathrm{en})_3\right]^{2+} ;$ (f) $\left[\mathrm{Ti}\left(\mathrm{OH}_2\right)_6\right]^{3+}$; (g) $\left[\mathrm{VCl}_6\right]^{3-}$; (h) $\left[\mathrm{Cr}(\mathrm{acac})_3\right]$.

Let $\theta$ be an acute angle of a right triangle for which $\tan \theta=\frac{4}{3}$. Find $\\$$\sin \theta$

If the measure of one of the acute angles and the hypotenuse of a right triangle are known, describe how to find the measure of the remaining parts of the triangle.

Let $\theta$ be an acute angle of a right triangle for which $\sin \theta=\frac{3}{5}$. Find $\\$$\cos \theta$

Suppose f(x)=

$$\frac { x } { 2 }$$

, g(x)=x-3, and

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

. Find a real-number value or an expression in x for each of the following. If no real value can be found say so. f(g(-5))

The overall tone of passage 2 is A. severely critical. B. speculative. C. mildly ironic. D. apathetic. E. condemning.

A "moving sidewalk" in an airport runs at a constant $1.0 \mathrm{~m} / \mathrm{s}$. From opposite ends of the 50-m-long sidewalk, two old friends begin running toward one another, each with a speed of $4.0 \mathrm{~m} / \mathrm{s}$ relative to the moving sidewalk. Where do they meet, relative to the fixed ends of the sidewalk?

What is the LCM of $\left(4 x^4-14 x^3\right)$ and $\left(6 x^2-21 x\right)$?

A $6 x^3(2 x-7)$

B $6 x^4(2 x-7)$

C $6\left(2 x^4-7 x^3\right)\left(2 x^2-7 x\right)$

D $\left(4 x^4-14 x^3\right)\left(6 x^2-21 x\right)$