High-speed elevators function under two limitations: (1) the maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about $1.2 \mathrm{~m} / \mathrm{s}^2$, and (2) the typical maximum speed attainable is about $9.0 \mathrm{~m} / \mathrm{s}$. You board an elevator on a skyscraper's ground floor and are transported $180 \mathrm{~m}$ above the ground level in three steps: acceleration of magnitude $1.2 \mathrm{~m} / \mathrm{s}^2$ from rest to $9.0 \mathrm{~m} / \mathrm{s}$, followed by constant upward velocity of $9.0 \mathrm{~m} / \mathrm{s}$, then deceleration of magnitude $1.2 \mathrm{~m} / \mathrm{s}^2$ from $9.0 \mathrm{~m} / \mathrm{s}$ to rest. Find the elapsed time for each of these $3$ stages.

State two reasons why listening is difficult.

Show that if G is a locally compact topological group and H is a subgroup, then G/H is locally compact.

What were some of the differences between the Aryans and the dasas in India?

The running event known as the $100 \mathrm{~m}$ dash consists of three stages. In the first, the runner accelerates to the maximum speed, which usually occurs at the $50 \mathrm{~m}$ to $70 \mathrm{~m}$ mark. That speed is then maintained until the last $10 \mathrm{~m}$, when the runner slows. Consider three parts of the record-setting run by Usain Bolt in the 2008 Olympics: (a) from $10 \mathrm{~m}$ to $20 \mathrm{~m}$, elapsed time of $1.02 \mathrm{~s}$, (b) from $50 \mathrm{~m}$ to $60 \mathrm{~m}$, elapsed time of $0.82 \mathrm{~s}$, and (c) from $90 \mathrm{~m}$ to $100 \mathrm{~m}$, elapsed time of $0.90 \mathrm{~s}$. What was the average velocity for each part?

State five guidelines to follow in a speech of acceptance.

In any triangle ABC with AB = 23 cm and AC = 17 cm., what are the minimum and maximum limits of the length of side $\overline{BC}$?

Identify the graph of the equation as a parabola (with vertical or horizontal axis), circle, ellipse, or hyperbola.

9x$^2$-y$^2$=10-2y

State three rules concerning parallel circuits.

Use slopes to show that the points are vertices of the specified polygon.

$A(2,3), B(5,-1), C(0,-6), D(-6,2) ; \quad$ trapezoid

Reasoning Sketch a triangle and two exterior angles that have a side of the triangle in common. For what type of triangle, if any, is each statement true? Justify each answer.

The bisectors of the two exterior angles are parallel.

In the following exercise,

$$r(t)=\left(t^2+t\right) i+\left(t^2-t\right) j$$

find $r^{\prime \prime}(t)$

Suppose that you are aboard a spaceship. The Earth is at the origin of a Cartesian coordinate system, and the path of your spaceship is the graph of

$$9 x^2+25 y^2-72 x=81 .$$

a. Which conic section is this path, and how do you tell?
b. Sketch the graph of this path.
c. Show that the Earth is at the focus of this conic section.
d. To determine your position at a particular time, you tune in to the LORAN station and find that you are also on the graph of

$$9 x^2-15 y^2=9 .$$

Which conic section is this graph, and how do you tell?
e. By solving the system formed by the equations of the two conic sections above, find the three possible points at which your spaceship could be located.
f. Draw the graph of the conic section in part $\mathbf{d}$ on the same Cartesian coordinate system as in part b, and thus show that your answer to part e is correct.
g. To ascertain at which one of the three points you are located, you find that you are also on the graph of

$$3 x-5 y=27 .$$

At which of the points are you located? (There is a clever way to do this, as well as the long way.)

Express the following using metric prefixes: (a) $3 \times 10^{-6} \mathrm{~F}$ (b) $3.3 \times 10^6 \Omega$ (c) $350 \times 10^{-9} \mathrm{~A}$