Homework 2

due Monday, Jan. 22

1. Do the following problems from the handout Exploring Linear Equations (Investigating Linear Equations Using Graphing Calculator):

a. Page 8, numbers 2-8.

2. Write an equation that, together with the equation

,

Makes a pair of simultaneous equations with graphs

a. that are parallel.

b. that coincide.

c. that intersect in the point (0,2).

3. The bouncing ball. A ball is dropped from various heights and the height to which it bounces back is measured. Here is some data from the web.

Dr. DeTurck collected the following data in his garage:

Height of Drop (in.)	Height of Bounce (in.)
36	25
40	29
40	28.5
44	31.5
44	32
48	35
52	38
56	42
60	46

a) Enter this data into your calculator and use the following program PR –proportional regression- to estimate the coefficient if the bounce height is proportional to the drop height.

b) What (if any) are the units of the coefficients? What does the coefficient represent?

c) Estimate the bounce height if the ball is dropped from 58 inches; from 75 inches? How confident are you of the estimate?

4. For overnight delivery, UPS charges a base price of $13.05 plus a charge of $2.45 for each pound the package weighs. Fedex charges a base price of $18.25 plus $1.95 for each pound.

a. Write an equation for the cost U (in dollars) of mailing a package weighing x pounds using UPS.

b. Write an equation for the cost F (in dollars) of mailing a package weighing x pounds using Fedex.

c. A friend does a lot of shipping. He needs to know when it is cheaper to use UPS and when it is cheaper to use Fedex. Make a graph to find approximate value s for the coordinates of the point at which the cost would be the same. Then find the exact answer algebraically. Use that point to give your friend advice on which company to use if he does a lot of shipping.