document.write( "Question 1162452: Find the number of pairs of integers, x and y, such that (x^2 + y^2) < 100. \r
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Algebra.Com's Answer #786267 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "Let's count the integer points in the first quadrant area  0 <  < 100,  0 < argument <= 90 degrees.\r\n" );
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document.write( "    y = 1;  x from 0 to 9  (10 points);\r\n" );
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document.write( "    y = 2;  x from 0 to 9  (10 points);\r\n" );
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document.write( "    y = 3;  x from 0 to 9  (10 points);\r\n" );
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document.write( "    y = 4;  x from 0 to 9  (10 points);\r\n" );
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document.write( "    y = 5;  x from 0 to 8  (9 points);\r\n" );
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document.write( "    y = 6;  x from 0 to 7  (8 points);\r\n" );
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document.write( "    y = 7;  x from 0 to 7  (8 points);\r\n" );
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document.write( "    y = 8;  x from 0 to 5  (6 points);\r\n" );
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document.write( "    y = 9;  x from 0 to 4  (5 points);\r\n" );
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document.write( "    y = 10;  no points     (0 points).\r\n" );
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document.write( "So, in the first quadrant we have \r\n" );
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document.write( "    10 + 10 + 10 + 10 + 9 + 8 + 8 + 6 + 5 = 76 points.\r\n" );
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document.write( "We take this amount 4 times and add the point (0,0).\r\n" );
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document.write( "In all, we have 4*76 + 1 = 305 points.      ANSWER\r\n" );
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document.write( "    Notice that in my count for QI, I include the points on the vertical axis x= 0 (0 < y < 10),\r\n" );
document.write( "    but do not include the points on the horizontal axis y= 0 (0 < x < 10).\r\n" );
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document.write( "    Thus, I can multiply 76 by 4 without doubling counted points. \r\n" );
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