Difference between revisions of "2005 CEMC Gauss (Grade 7) Problems/Problem 3"
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| − | Since the arrow is pointing between <math>9.6</math> and <math>9.8</math>, it is pointing to a rating closest to <math>9.7</math>. | + | ==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: | ||
| + | |||
| + | <math>\text{(A)}\ 9.4 \qquad \text{(B)}\ 9.3 \qquad \text{(C)}\ 9.7 \qquad \text{(D)}\ 9.9 \qquad \text{(E)}\ 9.5</math> | ||
| + | |||
| + | ==Solution== | ||
| + | |||
| + | Since the arrow is pointing between <math>9.6</math> and <math>9.8</math>, it is pointing to a rating closest to <math>9.7</math>. | ||
| + | |||
| + | The answer is <math>C</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{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]](http://latex.artofproblemsolving.com/b/4/4/b44ab17351a8899b2ae3fa1e4726895b488deaa0.png)
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:
Solution
Since the arrow is pointing between 
and 
, it is pointing to a rating closest to 
.
The answer is 
.
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) | ||
