6
Part of 2003 AMC 10
Problems(2)
Heart Function
Source:
2/16/2008
Define to be |x\minus{}y| for all real numbers and . Which of the following statements is not true?(A)\ x \heartsuit y \equal{} y \heartsuit x \text{ for all } x \text{ and } y
(B)\ 2(x \heartsuit y) \equal{} (2x) \heartsuit (2y) \text{ for all } x \text{ and } y
(C)\ x \heartsuit 0 \equal{} x \text{ for all } x
(D)\ x \heartsuit x \equal{} 0 \text{ for all } x
function
Big TV Screen
Source:
1/4/2009
Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is . The horizontal length of a “-inch” television screen is closest, in inches, to which of the following?
[asy]import math;
unitsize(7mm);
defaultpen(linewidth(.8pt)+fontsize(8pt));draw((0,0)--(4,0)--(4,3)--(0,3)--(0,0)--(4,3));
fill((0,0)--(4,0)--(4,3)--cycle,mediumgray);
label(rotate(aTan(3.0/4.0))*"Diagonal",(2,1.5),NW);
label(rotate(90)*"Height",(4,1.5),E);
label("Length",(2,0),S);[/asy]
geometryrectangleratio