The main meeting room of the Glen Oaks Community Center measures 46 feet by 34 feet and has a 12-foot ceiling. It is well insulated and faces the east side of his house. The manager wants to purchase an air conditioner. How large an air conditioner should he purchase? Round up to the next thousand BTUs.

Kim is building a large gazebo for her backyard. It is in the shape of a regular hexagon. Each side of the gazebo is 12 feet long. The apothem is 10.4 feet. She needs to purchase stones for the floor. It costs $9.50 per square foot for a special type of interlocking stone. Find the cost of the gazebo's floor. Round to the nearest ten dollars.

A regular heptagon (7 sides) has perimeter 126 and area A. Express the apothem a of the heptagon algebraically in terms of the area A.

The length of a room is $19 \frac{1}{2}$ feet. When using $\frac{1}{4}$ inch = 1 foot scale, what would be the length of the wall on a floor plan?

A rectangular room has length L and width W. Its volume is 2,455 cubic feet Express the height of the ceiling algebraically in terms of x.

A rectangular room has length L, width W, and height H, where L, W, and H are measured in feet. a. Express the volume in cubic feet algebraically. b. If carpeting costs $72 per square yard, write an expression for the cost of carpeting the floor of this room.

A rectangular room measures 16 feet by 18 feet. The ceiling is 9 feet high. a. Find the total area of the four walls in the room. b. If a gallon of paint costs $37.99 and it covers 400 square feet on average, what is the cost of painting the room, including the ceiling, with two coats of paint? Explain your answer. c. This room is well insulated and is on the north side of the house. How large of an air conditioner would this room require? Round to the next highest thousand BTUs. d. A scale drawing is made of this room using the scale 1 sq$$\mathrm{ft}$=$\frac{1}{4}$ $$\mathrm{sq}$ in. What are the dimensions of this room on the drawing?

An irregular plane figure drawn on graph paper is framed inside of a 15 by 40 rectangle. To find its area, 10,000 random points are generated, and 5,710 of them land inside the irregular region. What is the area of the irregular region, to the nearest integer?

A rectangular room has length L and width W, where L and W are measured in feet. If carpeting costs x dollars per square yard, express the cost of carpeting this room algebraically.

Elizabeth is a landscape designer. She created a small pond with a fountain that her company plans to manufacture and market. It is a free-form shape and the company wants to include the area of the pond on the packaging. What is the area of the pond, to the nearest square foot?

Kim is building a large gazebo for her backyard. It is in the shape of a regular hexagon. Each side of the gazebo is 12 feet long. The apothem is 10.4 feet. She needs to purchase stones for the floor. It costs $9.50 per square foot for a special type of interlocking stone. Find the cost of the gazebo's floor. Round to the nearest ten dollars.

A community of hares on an island has a population of 50 when observations begin at t=0. The population for

$$t \geq 0$$

is modeled by the initial value problem

$$\frac { d P } { d t } = 0.08 P \left( 1 - \frac { P } { 200 } \right)$$

, P(0)=50. a. Find and graph the solution of the initial value problem. b. What is the steady-state population?

A small, isolated mountain community with a population of 700 is visited by an outsider who carries influenza. After 6 weeks, 300 people are uninfected. a. Write an equation for the number of people who remain uninfected at time t (in weeks). b.Find the number still uninfected after 7 weeks. c. When will the maximum infection rate occur?

The Tojolobal Mayan Indian community in southem Mexico has available a fived amount of land. The proportion, $P$, of land in use for farming $t$ years after $1935$ is modeled with the logistic function in Figure $11.72$:

$$P=\frac{1}{1+2.968 e^{-0.027 5t}}.$$

(d) When is the proportion of land used for farming increasing most rapidly?