Math 142

Exam 3

Summer 1999

1. (10 pt) Verify the formula: and find (exactly).

2. (10 pt) Show that

(Hint:

and

3. (32 pt) Solve the following equations:

a) b) c)

d)

4. (24 pt) Find the exact values for the following, show your work.

a) b) c)

5. (10 pt) Find the equation for the line that makes a 30° angle with the x-axis and passes through the point (2,3).

6. (8 pt) I forgot the formula for , but I remember that it is one of the following two:

a) or

b)

Figure out which one is correct and justify your answer (the answer “I memorized it” is not a justification).

7. (16 pt) A camera on a 5 foot tripod is placed in front of a 6 foot high picture that is mounted 3 feet above the floor (see picture).

a) Express as a function of x (the distance from the wall).

b) If the lens has angle , how far from the wall should you put the camera to make sure that the entire picture is in the photograph?

q 6

5

3

x