Write the equation of the parabola in standard form, and find the vertex of its graph. y = x$^{2}$ - 8x + 3

Write each expression using a positive exponent. $m^{-4}$

Fill in the blanks.

$$\begin{matrix} \text{Key signature} & \text{Name of Key}\\ \text{\_\_\_\_\_\_\_} & e\flat minor\\ \end{matrix}$$

Write the prime factorization of each number. Use exponents for repeated factors. 117

Why do we sometimes multiply a row of a Routh table by a positive constant?

Use the ideas in the proof of Property 1 of the theorem to prove Property 3 of the theorem.

In order to self-balance a bicycle, its open-loop transfer function is found to be:

$$\begin{aligned} G(s) &=\frac{\theta(s)}{U(s)} \\ &=\frac{334019}{s^{4}+5126.16 s^{3}+2470.7 s^{2}+428419 s-34040} \end{aligned}$$

where $\theta(s)$ is the angle of the bicycle with respect to the vertical, and U(s) is the voltage applied to the motor that drives a flywheel used to stabilize the bicycle. Note that the bicycle is open-loop unstable with one open-loop pole in the right half-plane. a. Draw the Nyquist diagram of the system. b. Find the system's gain and phase margins. c. Assuming a unit feedback system, find the range of K for closed-loop stability if the forward path transfer function is KG(s). d. Assuming a second-order approximation, what is the expected %OS if K = 0.141? e. Use a computer program to simulate your system for a unit-step response using the value of K in Part d.

Using the information thus far in this chapter, explain why battery-powered electronics perform poorly in low temperatures.

Some television tubes are CRTs. They use an approximately 30-kV accelerating potential to send electrons to the screen, where the electrons stimulate phosphors to emit the light that forms the pictures we watch. Would you expect x rays also to be created?

Describe one type of evidence for the particle nature of EM radiation.

When (R)-2-chloro-3-methylbutane is treated with potassium tert-butoxide, a monosubstituted alkene is obtained. When this alkene is treated with HBr, a mixture of products is obtained. Draw all of the expected products.

The functions $f(x)=(x-1)^{2}$ and $g(x)=x^{2}-1$ both have a root at x = 1. Apply Newton's method to both functions with an initial approximation $x_{0}=2$. Compare the rates at which the method converges in these cases, and give an explanation.

What is the molar solubility of $\mathrm{Tl}(\mathrm{OH})_{3}$ in a 0.10-M solution of $\mathrm{NH}_{3}$?

If

$$f(x)=\left\{\begin{array}{ccc} \frac{x^{2}-25}{x-5} & \mathrm { if } & x \neq 5 \\ 5 & \mathrm { if } & x=5 \end{array}\right.$$

, which of the following statements about f are true? I. $\lim _{x \rightarrow 5} f$ exists. II. f is continuous at x=5. III. f is differentiable at x=5. (A) I only, (B) I and II only, (C) I and III only, (D) I, II, and III.