Difference between revisions of "2006 Cyprus MO/Lyceum/Problems"
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+ | In the figure, <math>ABC</math> is an equilateral triangle and <math>AD\perp BC</math>, <math>DE\perp AC</math>, <math>EZ\perp BC</math>. If <math>EZ=\sqrt{3}</math>, then the length of the side os the triangle ABC is | ||
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+ | A. <math>\frac{3\sqrt{3}}{2}</math> | ||
+ | |||
+ | B. <math>8</math> | ||
+ | |||
+ | C. <math>4</math> | ||
+ | |||
+ | D. <math>3</math> | ||
+ | |||
+ | E. <math>9</math> | ||
[[2006 Cyprus MO/Lyceum/Problem 7|Solution]] | [[2006 Cyprus MO/Lyceum/Problem 7|Solution]] |
Revision as of 10:41, 30 June 2007
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 Problem 26
- 27 Problem 27
- 28 Problem 28
- 29 Problem 29
- 30 Problem 30
- 31 See also
Problem 1
A diary industry, in a quantity of milk with $4%$ (Error compiling LaTeX. Unknown error_msg) fat adds a quantity of milk with $1%$ (Error compiling LaTeX. Unknown error_msg) fat and produces kg of milk with $2%$ (Error compiling LaTeX. Unknown error_msg) fat.
The quantity of milk with $1%$ (Error compiling LaTeX. Unknown error_msg) fat, that was added is (in kg)
A.
B.
C.
D.
E.
Problem 2
The operation is defined by
.
The value of the expression
is
A.
B.
C.
D.
E.
Problem 3
The domain of the function is
A.
B.
C.
D.
E.
Problem 4
Given the function ,
Which of the following is correct, about the graph of
?
A. intersects x-axis
B. touches y-axis
C. touches x-axis
D. has minimum point
E. has maximum point
Problem 5
If both integers are bigger than 1 and satisfy
, then the minimum value of
is
A.
B.
C.
D.
E.
Problem 6
The value of the expression is
A.
B.
C.
D.
E.
Problem 7
In the figure, is an equilateral triangle and
,
,
. If
, then the length of the side os the triangle ABC is
A.
B.
C.
D.
E.