Find $\alpha$ and $Z_{0}$ of a distortionless line whose $R^{\prime}=2 \Omega / \mathrm{m}$ and $G^{\prime}=2 \times 10^{-4} \mathrm{S} / \mathrm{m}$.

Draw angles in standard position such that the terminal side passes through the given point. (-4, -2)

Find the volume of a spherical beach ball wit h a diameter of

Use the root test to show that $\Sigma k^{p} e^{-k}$ converges for any fixed positive real number p. What does this imply about the following improper integral?

$$\int_{1}^{\infty} x^{p} e^{-x} d x$$

If a system is described by transfer function $h(t)=2u(t)+2n(t-1)$, use the convolution to calculate the output (time domain) if the input is $(a)2u(t); \; (b)2te^{-2t}u(t)$.

How does the textbook's discussion of Anglo-American settlers in the Ohio Valley support or challenge each of the historians' arguments regarding British policy?

The expansion of $(a+b)^3$ has 4 terms. a. How many terms are in the expansion of $(a+b+c)^3$? b. How many terms are in the expansion of $(a+b+c+d)^3$? c. Generalize these results.

Fill in the blank in the sentence with the correct form of the passive tense of the verb using the infinitive in parentheses, then translate the sentence: Dico vos esse felices, qui a Hunis non _____. (capere)

Explain when it is necessary to use a table showing z-scores and percentiles rather than the 68–95–99.7 Rule to determine the percentage of data items less than a given data item.

Sketch the enclosed region and use the Shell Method to calculate the volume of rotation about the x-axis. x = y(4 - y),

$$x = ( y - 2 ) ^ { 2 }$$

In addition to not dissipating power, a lossless line has two important features: (1) it is dispersionless ($u_{\mathrm{p}}$ is independent of frequency); and (2) its characteristic impedance $Z_{0}$ is purely real. Sometimes, it is not possible to design a transmission line such that $R^{\prime} \ll \omega L^{\prime}$ and $G^{\prime} \ll \omega C^{\prime}$, but it is possible to choose the dimensions of the line and its material properties so as to satisfy the condition $R^{\prime} C^{\prime}=L^{\prime} G^{\prime}$ (distortionless line) Such a line is called a distortionless line, because despite the fact that it is not lossless, it nonetheless possesses the previously mentioned features of the lossless line. Show that for a distortionless line, $\alpha=R^{\prime} \sqrt{\frac{C^{\prime}}{L^{\prime}}}=\sqrt{R^{\prime} G^{\prime}}$, $\beta=\omega \sqrt{L^{\prime} C^{\prime}}$, $Z_{0}=\sqrt{\frac{L^{\prime}}{C^{\prime}}}$.

Write two or three sentences to add more details to one of Walter Mitty's adventures in the story. Underline each complete subject once and each complete predicate twice.

State the meaning of each sentence if "or" is interpreted as the inclusive-or; then, state the meaning of each sentence if "o" is interpreted as the exclusive-or. In each case, which meaning do you think is intended.

To enter Utopia, you must possess a driver's license or a passport.

Use Separation of Variables to find the general solution.

$$\frac { d x } { d t } = ( t + 1 ) \left( x ^ { 2 } + 1 \right)$$