As an avid biker, you’ve come to realize that your top speed is really an air speed, not a ground speed, because air resistance is very noticeable when you ride fast. You like to ride at top speed for exactly an hour every day, and you know that on a calm day, you can ride 20 km before having to turn around and come back the same way. Today, though, you have a 20-km/h head wind for the first leg of the trip (which of course is a tailwind on the way back). You must be back home in an hour, so you look at your map.

All members of the junior class at a local high school took the PSAT exam. The distribution of the results of the mathematics section was found to be approximately normal, with a mean score of 52 and a standard deviation of 6.8. Stephan claimed that he scored better than 90% of the students in the junior class. Use z-sore and your z-table to determine what score Stephan must have earned to be correct.

Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $\int \frac { d x } { \sqrt { 4 - x ^ { 2 } } }$

A historian discovers a nineteenth-century notebook in which some observations, dated 1822, were recorded on a substance thought to be a new element. Here are some of the data recorded in the notebook: "Ductile, silver-white, metallic looking. Softer than lead. Unaffected by water. Stable in air. Melting point:

$$153 ^ { \circ } \mathrm { C }$$

Den sity:

$$7.3 \ g/cm^3$$

Electrical conductivity: 20% that of copper. Hardness: About 1 % as hard as iron. When 4.20 g of the unknown is h eated in an excess of oxygen, 5.08 g of a white solid is formed. The solid could be sublimed by heating to over

$$800 ^ { \circ } \mathrm { C }$$

" Using information in the text and the CRC Handbook of Chemistry and Physics, and making allowances for possible variations in numbers from current values, identify the element reported.

Find the limit by interpreting the expression as an appropriate derivative. (a)

$$\lim _ { x \rightarrow 0 } \frac { \ln ( 1 + 3 x ) } { x }$$

, (b)

$$\lim _ { x \rightarrow 0 } \frac { \ln ( 1 - 5 x ) } { x }$$

For the characteristic function

$$\begin{gather*} s^3 + 5s^2 + 9s + 5 \end{gather*}$$

, use Routh’s stability criterion to determine the number of roots with positive real parts. Confirm your answers by using a computer to find the roots.

Show that the inverse of

$$A=\left[\begin{array}{rr} a&b \\ c&d \end{array}\right]$$

is given by the formula

$$A^{-1}=\left[\begin{array}{rr} \dfrac d{\Delta}& \dfrac {-b}{\Delta} \\\\ \dfrac {-c}{\Delta}&\dfrac {a}{\Delta} \end{array}\right]$$

where $\Delta =ad-bc \neq 0$. The number $\Delta$ is called the determinant of A.

The maintenance cost for furnaces at a copper smelting plant have been constant at $140,000 per year for the past 5 years. If the interest rate was 8% per year for the first 3 years and then it increased to 10% in years 4 and 5, what is the equivalent future worth (in year 5) of the maintenance cost? Show hand and spreadsheet solutions.

Independence of events is not always obvious. Toss two balanced coins independently. The four possible combinations of heads and tails in order each have probability 0.25. The events A = head on the first toss B = both tosses have the same outcome may seem intuitively related. Show that P(B|A) = P(B), so that A and B are in fact independent.

Vocabulary Types of stores Words to talk about jewelry Other gifts Words to talk about the past

At a certain depth in an incompressible liquid, the absolute pressure is p. At twice this depth, will the absolute pressure be equal to 2p, greater than 2p, or less than 2p? Justify your answer.

Concurso de diseno. Una compania de coches quiere incorporar las ideas de los jovenes en una serie nueva de coches. Patrocinan un concurso en el que grupos de dos o tres estudiantes disenan un coche nuevo. El grupo que gane tendra la oportunidad de trabajar con la compania para crear un prototipo real. En grupos de tres, disenen un coche para el concurso. Deben explicar os rasgos mas importantes e indicar que tipo de persona va a querer comprarlo y por que. Consideren los siguientes aspectos: -el diseno exterior: apariencia, tamano y forma -el diseno interior: comodidad, rasgos para atraer al tipo de persona al que se le vendera -el rendimiento: las habilidades del coche, como se desplaza -la eficiencia energetica: que combustble se usa y cuanto se requiere para accionar el motor

Graph the linear system. Then use the graph to tell whether the linear system has one solution, no solution, or infinitely many solutions.

$$\begin{array} { l } { x - y = 1 } \\ { x - y = 6 } \end{array}$$

Explain the significance of: James K. Polk, manifest destiny, Zachary Taylor, Bear Flag Revolt, Winfield Scott, Treaty of Guadalupe Hidalgo, Mexican Cession.