Test 3 Math 159
Place your name in the upper right hand corner. Place your answers in the blanks
at the left. Show your work on a separate sheet. Have fun.
____________________ 1) Find the center and radius of the following circle,
x 2 + y 2 + 4x ! 8y ! 6 = 0 .
____________________ 2) Find the center of the following ellipse,
9x 2 + 4 y 2 + 54x ! 8y ! 50 = 0
3) On your work sheet derive the formula for the sum of a geometric series.
N
"a r
k= 0
k!1
=
a(1 ! r N )
1 ! r
! 1 $ k )1
____________________4) Sum the infinite geometric series (#" &% .
k= 0 a
'
10
____________________ 5) Sum the geometric series
! 8 (1.09)
k
k= 1
6) On your work sheet prove the following statement,
1 + 2 + 3 + . .. + n =
n (n + 1)
2
________________ 7) How many times do the following curves intersect each other on
the range 0 ! " ! # /2 .
r = 5sin( 2! )
r = 2 + cos(! )
________________ 8) Compute 8 P4 .
________________ 9) Compute 1 2C3 .
________________ 10) How many 5 digit numbers can be formed using 2, 4, 6, 8, and 9
using each digit only once.
11) Cartesian coordinates are related to polar coordinates by
x = r cos(! ) and y = r sin(!) .
Derive the equations relating polar coordinates to Cartesian coordinates.
12) Find the heading and the ground speed of an airplane whose air speed is 250 mph in
the direction of 60 degrees with a wind of speed 40 mph from the direction of 330
degrees.