Find the arc length of the curve over the given interval. $r=6 \cos \theta, 0 \leq \theta \leq 2 \pi.$ Check your answer by geometry.

Metabolic activity in the human body releases approximately $1.0\times10^4\;\mathrm{kJ}$ of heat per day. Assume that a 55-kg body has the same specific heat as water; how much would the body temperature rise if it were an isolated system? How much water must the body eliminate as perspiration to maintain the normal body temperature (98.6 °F)? Comment on your results. (The heat of vaporization of water is 2.41 kJ/g.)

An epidemic hits a city. Each person is classified by the Health Department as either well, sick, or a carrier. The proportion of people in each category by age groups is given by the matrix

$$\begin{array}{lll}{0-15} & {16-35} & {\text { Over } 35} \\ {\text { Sick }} & {0.25} & {0.60} & {0.70} \\ {\text { Sick }} & {0.25} & {0.35} & {0.20} \\ {\text { Carrier }} & {0.10} & {0.05} & {0.10}\end{array} ]=A$$

The population of the city by age and gender is

$$\begin{array}{lll}{0-15} & {35,000} & {30,000} \\ {16-35} & {55,000} & {50,000} \\ {\text { Over } 35} & {70,000} & {75,000}\end{array} ]=B$$

(a) Compute AB. Interpret the meaning of the entries in AB. (b) How many sick males are there? (c) How many females are well?

(A) Identify the type of equation or inequality (some may fit more than one category). (B) Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible.

$$(2p+1)(p+5)=2p+40$$

How would you say 'tools' in Spanish?

A basketball team scored 43, 55, 41, and 37 points in their first four matches. Find the mean number of points scored for the first four matches.

A and B are events for which P(A) = 0.3 + x, P(B) = 0.2 + x, and $P(A \cap B)=x$. Find x if A and B are mutually exclusive events.

When a guitar string is sounded along with a 440-Hz tuning fork, a beat frequency of 5 Hz is heard. When the same string is sounded along with a 436-Hz tuning fork, the beat frequency is 9 Hz. What is the frequency of the string?

Show that each sequence is geometric. Then find the common ratio and write out the first four terms. $\left\{ t_{n}\right\}=\left\{\frac{3^{n-1}}{2^{n}}\right\}$

C.F. Jordon Construction Services has operated for the last 26 years in a northern U.S. state where the state income tax on corporate revenue is 6% per year. C.F. Jordon pays an average federal tax of 23% and reports taxable income of $7 million. Because of pressing labor cost increases, the president wants to move to another state to reduce the total tax burden. The new state may have to be willing to offer tax allowances or an interest-free grant for the first couple of years in order to attract the company. You are an engineer with the company and are asked to do the following. (a) Determine the effective tax rate for C.F. Jordon. (b) Estimate the state tax rate that would be necessary to reduce the overall effective tax rate by 10% per year. (c) Determine what the new state would have to do financially for C.F. Jordon to move there and to reduce its effective tax rate to 22% per year.

$$16 - 2 t = 5 t + 9$$

Find the vertices and foci of each ellipse. Graph each equation. $x^{2}+y^{2}=16$

How are rates and ratios related?

How does the human body illustrate levels of organization?