Difference between revisions of "2004 AMC 12B Problems"
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== Problem 16 == | == Problem 16 == | ||
| + | |||
| + | A [[function]] <math>f</math> is defined by <math>f(z) = i\overline{z}</math>, where <math>i=\sqrt{-1}</math> and <math>\overline{z}</math> is the [[complex conjugate]] of <math>z</math>. How many values of <math>z</math> satisfy both <math>|z| = 5</math> and <math>f(z) = z</math>? | ||
| + | |||
| + | <math>\mathrm{(A)}\ 0 | ||
| + | \qquad\mathrm{(B)}\ 1 | ||
| + | \qquad\mathrm{(C)}\ 2 | ||
| + | \qquad\mathrm{(D)}\ 4 | ||
| + | \qquad\mathrm{(E)}\ 8</math> | ||
| + | |||
[[2004 AMC 12B Problems/Problem 16|Solution]] | [[2004 AMC 12B Problems/Problem 16|Solution]] | ||
Revision as of 20:12, 16 September 2008
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
At each basketball practice last week, Jenny made twice as many free throws as she made at the previous practice. At her fifth practice she made 48 free throws. How many free throws did she make at the first practice?
Problem 2
In the expression 
, the values of 
, 
, 
, and 
are 0, 1, 2, and 3, although not necessarily in that order. What is the maximum possible value of the result?
Problem 3
If 
and 
are positive integers for which 
, what is the value of 
?
Problem 4
An integer , with 
, is to be chosen. If all choices are equally likely, what is the probability that at least one digit of is a 7?
Problem 5
On a trip from the United States to Canada, Isabella took U.S. dollars. At the border she exchanged them all, receiving 10 Canadian dollars for every 7 U.S. dollars. After spending 60 Canadian dollars, she had Canadian dollars left. What is the sum of the digits of ?
Problem 6
Minneapolis-St. Paul International Airport is 8 miles southwest of downtown St. Paul and 10 miles southeast of downtown Minneapolis. Which of the follow- ing is closest to the number of miles between downtown St. Paul and downtown Minneapolis?
Problem 7
A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the circle?
Problem 8
A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows does it contain?
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
If 
and 
with and real, what is the value of 
?
Problem 14
Problem 15
Problem 16
A function 
is defined by 
, where 
and 
is the complex conjugate of 
. How many values of satisfy both 
and 
?
