This problem refers to the two-person tent shown in the figure below. Assume the tent has a floor and is closed at both ends. Give your answers in exact form and also approximate to the nearest tenth of a unit.

If the height h at the center of the tent is to be 3 feet and 162 square feet of material are available to make the tent, how long should the tent be?

exact form                        _________  

approximate form              _________ 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

An Ancient Chinese Problem This problem is taken from a Chinese mathematics textbook called Chui-chang suan-shu, or Nine Chapters on the Mathematical Art, which was written about 250 B.C. A 10-ft.-long stem of bamboo is broken in such a way that its tip touches the ground 3 ft. from the base of the stem, as shown in the figure. What is the height of the break? [Hint: Use the Pythagorean Theorem.]

Maxima and Minima Use the formulas of this section to give an alternative solution to the indicated problem in Focus on Modeling: Modeling with Functions on pages 237–244.

Problem 24: Maximizing Area A wire 10 cm long is cut into two pieces, one of length and the
other of length 10, as shown in the figure. Each piece is bent into the shape of a square.
Find a function that models the total area enclosed by the two squares.

Orbit of a Satellite: Scientists and engineers often use polar equation to model the motion of satellite whose orbit is modeled by the equation , where is the distance in miles between the satellite and the center of the earth and is the angle shown in the following figure.

For what angle is the satellite closest to the earth? Find the height of the satellite above the earth’s surface for this value of .