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Difference between revisions of "2005 CEMC Gauss (Grade 7) Problems/Problem 3"

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==Problem==
 
==Problem==
  
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--|----------|----------|----------|----------|----------|
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<asy>
−
 
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//make the picture small and square
−
9.0.........9.2..........9.4.........9.6..^...9.8........10.0
+
size(80,80);
 +
//draw an arc from 0 to 75 degrees of radius 1 centered at the origin
 +
draw(arc((0,0),1,0,75));
 +
//draw a line with an arrow on the end pointing to 25 degrees (scale it down by .95 so that it stays inside the arc)
 +
//dir(25) is a unit vector pointing 25 degrees
 +
draw((0,0)--scale(.95)*dir(25),Arrow);
 +
//put a label at the end of the 75 degree unit vector (and position it out 75 degrees)
 +
MarkPoint("9",dir(75),dir(75));
 +
//put a label at the end of the 75 degree unit vector (rotate label 75 degrees to create a tick)
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MarkPoint(75,"-",scale(.85)*dir(75),dir(75));
 +
MarkPoint("9.2",dir(60),dir(60));
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MarkPoint(60,"-",scale(.85)*dir(60),dir(60));
 +
MarkPoint("9.4",dir(45),dir(45));
 +
//put a label at the end of the 45 degree unit vector - use NE to move it slightly NorthEast of this point (or use dir(45))
 +
MarkPoint(45,"-",scale(.85)*dir(45),NE);
 +
MarkPoint("9.6",dir(30),dir(30));
 +
MarkPoint(30,"-",scale(.85)*dir(30),dir(30));
 +
MarkPoint("9.8",dir(15),dir(15));
 +
MarkPoint(15,"-",scale(.85)*dir(15),dir(15));
 +
//put a label at the end of the 0 degree unit vector - use E to move it slightly East of this point (or use dir(0))
 +
MarkPoint("10",dir(0),E);
 +
MarkPoint(0,"-",scale(.85)*dir(0),dir(0));</asy>
  
 
Contestants on "Gauss Reality TV" are rated by an applause metre.  In the diagram, the arrow for one of the contestants is pointing to a rating closest to:
 
Contestants on "Gauss Reality TV" are rated by an applause metre.  In the diagram, the arrow for one of the contestants is pointing to a rating closest to:
Line 17: Line 38:
 
==See Also==
 
==See Also==
  
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[[2005 CEMC Gauss (Grade 7)]]
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{{CEMC box|year=2005|competition=Gauss (Grade 7)|num-b=2|num-a=4}}

Latest revision as of 00:43, 23 October 2014

Problem

[asy] //make the picture small and square size(80,80); //draw an arc from 0 to 75 degrees of radius 1 centered at the origin draw(arc((0,0),1,0,75)); //draw a line with an arrow on the end pointing to 25 degrees (scale it down by .95 so that it stays inside the arc) //dir(25) is a unit vector pointing 25 degrees draw((0,0)--scale(.95)*dir(25),Arrow); //put a label at the end of the 75 degree unit vector (and position it out 75 degrees) MarkPoint("9",dir(75),dir(75)); //put a label at the end of the 75 degree unit vector (rotate label 75 degrees to create a tick) MarkPoint(75,"-",scale(.85)*dir(75),dir(75)); MarkPoint("9.2",dir(60),dir(60)); MarkPoint(60,"-",scale(.85)*dir(60),dir(60)); MarkPoint("9.4",dir(45),dir(45)); //put a label at the end of the 45 degree unit vector - use NE to move it slightly NorthEast of this point (or use dir(45)) MarkPoint(45,"-",scale(.85)*dir(45),NE); MarkPoint("9.6",dir(30),dir(30)); MarkPoint(30,"-",scale(.85)*dir(30),dir(30)); MarkPoint("9.8",dir(15),dir(15)); MarkPoint(15,"-",scale(.85)*dir(15),dir(15)); //put a label at the end of the 0 degree unit vector - use E to move it slightly East of this point (or use dir(0)) MarkPoint("10",dir(0),E); MarkPoint(0,"-",scale(.85)*dir(0),dir(0));[/asy]

Contestants on "Gauss Reality TV" are rated by an applause metre. In the diagram, the arrow for one of the contestants is pointing to a rating closest to:

$\text{(A)}\ 9.4 \qquad \text{(B)}\ 9.3 \qquad \text{(C)}\ 9.7 \qquad \text{(D)}\ 9.9 \qquad \text{(E)}\ 9.5$

Solution

Since the arrow is pointing between $9.6$ and $9.8$, it is pointing to a rating closest to $9.7$.

The answer is $C$.

See Also

2005 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources)
Preceded by
Problem 2 		Followed by
Problem 4
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
CEMC Gauss (Grade 7)
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