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?

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

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

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

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

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

What can you conclude by using the given statement together with each additional statement? If no conclusion is possible, say so.

Given: If two angles are vertical angles, then they are congruent.

$$\angle 1 \cong \angle 2$$

What is the state of matter of beryllium at room temperature?

Express the following quantities using an SI prefix and a base unit. For instance, $1.6 \times 10^{-6} \mathrm{~m}=$ $1.6 \mu \mathrm{m}$. A quantity such as $0.000168 \mathrm{~g}$ could be written $0.168 \mathrm{mg}$ or $168 \mu \mathrm{g}$. a $1.84 \times 10^{-9} \mathrm{~m}$ b $5.67 \times 10^{-12} \mathrm{~s}$ c) $7.85 \times 10^{-3} \mathrm{~g}$ d) $9.7 \times 10^3 \mathrm{~m}$ e) $0.000732 \mathrm{~s}$ f) $0.000000000154 \mathrm{~m}$

In the following exercise,

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

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

State how library catalogs list information.

Determine whether the following is true or false.

Every finite extension of every field F is separable over F.

If cos A+cos B= 0, then A and B are supplementary angles. Justify your answer..

Use triangle ABC with vertices A(1,-2), B(-3,-5), and C(-5,6) Classify $\triangle A B C$ by its sides and by its angles.

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.)