1.
1/64974 (approx. 0.000015)
2.(a)
(Note: Just as 
, not just x, we really should say 
. This is a subtlety that occurs when we take an even root.)
(b)
(c)
(d)
67, or 67 + 0i
3.(a)
(parabola opening to the right, vertex at (17/8, 3/4), x-intercept at (1, 0), y-intercepts at (0, Ό(3 + Ö
17) ) and (0, Ό(3 Ö
17) ), and y = Ύ as the axis of symmetry)
(b-e)
4.
5.(a)
You should sketch a hyperbola opening left and right, with labeled vertices at (16Ö 2, 0) and (16Ö 2, 0), center at (0, 0), x-intercepts at the vertices, and no y-intercepts.
(b)
You should sketch a circle with labeled center at (0, 0), radius Ö 6, x-intercepts at (± Ö 6, 0), and y-intercepts at (0, ± Ö 6).
6.
{(0, 2), (Ö 2, 4), (Ö 2, 4)}
7.(a)
{3/2} (Note: We must discard the extraneous solution x = 1.)
(b)
Æ (no solution)
(c)
{15 + 6Ö 6} (Note: We must discard the extraneous solution x = 15 6Ö 6.)
8.(a)
A
= 10(50/L)0.2, where A = average cost per km ($millions) and L = length of expressway (km). Note: If you stop after writing A = k/L0.2 or A = kL0.2, you will earn only partial credit, since those equations are general equations involving an unspecified constant k. Because part (a) gives you enough information to solve for k, you should find the particular equation for A.(b)
$500,000,000
(c)
cost per km = $9,641,925; total cost = $578,515,502
(d)
32.0 km
9.(a)
86,400
(b)
60
10.(a)
1/171
(b)
91/285
(c)
170/171
11.(a)
1/81
(b)
8/27
(c)
80/81
12.
1152
13.(a)
45/8
(b)
3
14.
0.1312
15.
361,708.5 (or 502,505.0 if you did the simpler alternative problem)
16.
17.(a)
Note:
The following answers for part (a) are not the only ones possible. Write out a few terms of your sigma expression to make sure that it works correctly. For the arithmetic series,
, and for the geometric series, 
.(b)
For the arithmetic series, S400 = 240,600. For the geometric series, S400 » 1.093 ´ 1071.
18.
n
= 71 or n = 138 (both values work)19.
Two values for r are possible: 
20.(a)
155 feet, 0 inches
21.
x
7 14x6y + 84x5y2 280x4y3 + 560x3y4 672x2y5 + 448xy6 128y7