Consider a rectangular wave guide with dimensions $2.28\mathrm{~cm}\times1.01\mathrm{~cm}$. What TE modes will propagate in this wave guide, if the driving frequency is $1.70\times10^{10}\mathrm{~Hz}$? Suppose you wanted to excite only one TE mode; what range of frequencies could you use? What are the corresponding wavelenghts (in open space)?

Choose the letter of the correct term or concept below to complete the sentence. a. personality b. contingencies of reinforcement c. trait d. defense mechanism e. inferiority complex f. self-actualization g. positive regard h. conditions of worth i. extravert j. introvert. When a person deceives herself into thinking nothing is wrong instead of facing intense conflict, she is using a(n)__________.

The trade balance includes which of the following? I. import s and exports of goods II. imports and exports of services III. net capital flows A. I only B. II only C. III only D. I and II only E. I, II, and III

Work out the theory of TM modes for a rectangular wave guide. In particular, find the longitudinal electric field, the cutoff, and the wave and group velocities. Find the ratio of the lowest TM cutoff frequency to the lowest TE cutoff frequency, for a given wave guide. [Caution: What is the lowest TM mode?]

Prove each identity. State any restrictions on the variables. a)

$$\frac { \sin x } { \tan x } = \cos x$$

b)

$$\frac { \tan \theta } { \cos \theta } = \frac { \sin \theta } { 1 - \sin ^ { 2 } \theta }$$

c)

$$\frac { 1 } { \cos \alpha } + \tan \alpha = \frac { 1 + \sin \alpha } { \cos \alpha }$$

d)

$$1 - \cos ^ { 2 } \theta = \sin \theta \cos \theta \tan \theta$$

A(n) ____ reverses the inputs and outputs of a function. square root function, inverse of a function, cube root function

Determine whether the Mean Value Theorem applies to the following functions on the given interval [a, b]. f(x)=ln 2x; [1, e]

Suppose that an observational study showed that students who got at least 7 hours of sleep performed better on exams than students who got less than 7 hours of sleep. Which of the following are possible confounding variables, and which are not? Explain why in each case.

Number of courses the student took that term.

Simplify the expression. Write answers using positive exponents.

$$\left( \frac { y ^ { 8 } } { z ^ { 6 } } \right) ^ { - 2 }$$

Find the product. (-7/12)(-4/21)

Suppose that you wanted to know whether the mean arm span is different for U.S. Census at School seventh-grade girls and U.S. Census at School seventh-grade boys. A random sample of 10 students from the population of U.S. Census at School seventh-grade girls was selected using the random sampler on the Census at School website. The arm spans (in cm) for these 10 students were as follows: 171 152 176 147 167 165 152 161 152 147 A random sample of 10 students from the population of U.S. Census at School seventh-grade boys was also selected. The arm spans for these 10 students were as follows: 176 168 176 155 154 160 170 172 179 190. Do the dot plots suggest that there is about the same amount of variability in the arm span data for U.S. seventh-grade girls and the arm span data for U.S. seventh-grade boys?

Decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem. If false, provide an example, illustration, or brief explanation of why the statement is false. For any matrices A and B of the same dimensions, rank(A + B) = rank(A) + rank(B).

A proud legislator claims that your state's new law banning texting and hand-held phones while driving reduced occurrences of infractions to less than 10% of all drivers. While on a long drive home from your college, you notice a few people seemingly texting. You decide to count everyone using their smartphones illegally who pass you on the expressway for the next 20 minutes. It turns out that 5 out of the 20 drivers were actually using their phones illegally. Does this cast doubt on the legislator's figure of 10%? Use a simulation to estimate the likelihood of seeing at least 5 out of 20 drivers using their phones illegally if the actual usage rate is only 10%. Explain your conclusion clearly.

Solve.

$$x ^ { 4 } + x ^ { 2 } - 12 = 0$$