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r F P s P p .002 w .38616 .80797 m .36592 .81559 L .3696 .85034 L p .873 .706 .672 r F P s P p .002 w .45371 .57862 m .42742 .60617 L .45354 .64662 L p .848 .838 .836 r F P s P p .002 w .42742 .66908 m .45354 .64662 L .42742 .60617 L p .861 .84 .824 r F P s P p .002 w .43235 .96283 m .40732 .94695 L .39549 .9811 L p .855 .573 .509 r F P s P p .002 w .39549 .9811 m .41888 1.0028 L .43235 .96283 L p .855 .573 .509 r F P s P p .002 w .39026 .8935 m .36917 .88437 L .36464 .91425 L p .879 .646 .582 r F P s P p .002 w .36464 .91425 m .38475 .93076 L .39026 .8935 L p .879 .646 .582 r F P s P p .002 w .42742 .60617 m .40378 .63347 L .42742 .66908 L p .861 .84 .824 r F P s P p .002 w .4038 .6914 m .42742 .66908 L .40378 .63347 L p .875 .842 .809 r F P s P p .002 w .38268 .71359 m .36408 .73565 L .377 .76813 L p .88 .783 .75 r F P s P p .002 w .35848 .78359 m .377 .76813 L .36408 .73565 L p .898 .788 .731 r F P s P p .002 w .377 .76813 m .35848 .78359 L .36592 .81559 L p .882 .744 .705 r F P s P 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1.22861 L .81765 1.29929 L p .722 .324 .294 r F P s P p .002 w .76486 1.2746 m .81765 1.29929 L .84929 1.22861 L p .73 .333 .298 r F P s P p .002 w .33452 .848 m .35085 .84928 L .34806 .82307 L p .921 .739 .638 r F P s P p .002 w .35085 .84928 m .33452 .848 L .33426 .8652 L p .921 .716 .609 r F P s P p .002 w .33426 .8652 m .3505 .87494 L .35085 .84928 L p .921 .716 .609 r F P s P p .002 w .47339 1.0455 m .44484 1.02427 L .42405 1.05151 L p .84 .477 .367 r F P s P p .002 w .42405 1.05151 m .45053 1.07659 L .47339 1.0455 L p .84 .477 .367 r F P s P p .002 w .33264 .83041 m .34806 .82307 L .34241 .79897 L p .928 .765 .66 r F P s P p .002 w .34806 .82307 m .33264 .83041 L .33452 .848 L p .921 .739 .638 r F P s P p .002 w .3644 .68736 m .34864 .714 L .36408 .73565 L p .906 .843 .771 r F P s P p .002 w .348 .75762 m .36408 .73565 L .34864 .714 L p .922 .84 .746 r F P s P p .002 w .81765 1.29929 m .87362 1.32401 L .9048 1.24832 L p .722 .324 .294 r F P s P p .002 w .36464 .91425 m .34701 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.31928 .86266 L p .953 .728 .562 r F P s P p .002 w .31928 .86266 m .33189 .88022 L .33426 .8652 L p .953 .728 .562 r F P s P p .002 w .33551 .74044 m .32499 .76672 L .33445 .77949 L p .939 .836 .714 r F P s P p .002 w .32346 .80129 m .33445 .77949 L .32499 .76672 L p .956 .827 .675 r F P s P p .002 w .33445 .77949 m .32346 .80129 L .32883 .81428 L p .94 .795 .673 r F P s P p .002 w .44952 .52834 m .42299 .5589 L .45371 .57862 L p .859 .937 .872 r F P s P p .002 w .45371 .57862 m .48266 .55078 L .44952 .52834 L p .859 .937 .872 r F P s P p .002 w .42742 .60617 m .45371 .57862 L .42299 .5589 L p .874 .935 .857 r F P s P p .002 w .47893 .49734 m .44952 .52834 L .48266 .55078 L p .845 .938 .885 r F P s P p .002 w .48266 .55078 m .51431 .52265 L .47893 .49734 L p .845 .938 .885 r F P s P p .002 w .42299 .5589 m .3993 .58902 L .42742 .60617 L p .874 .935 .857 r F P s P p .002 w .40378 .63347 m .42742 .60617 L .3993 .58902 L p .889 .932 .84 r F P s P p .002 w .51125 .46586 m .47893 .49734 L .51431 .52265 L p .832 .938 .896 r F P s P p .002 w .51431 .52265 m .54867 .4942 L .51125 .46586 L p .832 .938 .896 r F P s P p .002 w .3993 .58902 m .3784 .61875 L .40378 .63347 L p .889 .932 .84 r F P s P p .002 w .38277 .66053 m .40378 .63347 L .3784 .61875 L p .905 .927 .82 r F P s P p .002 w .31775 .82952 m .32883 .81428 L .32346 .80129 L p .961 .794 .629 r F P s P p .002 w .32883 .81428 m .31775 .82952 L .31968 .83763 L p .954 .775 .623 r F P s P p .002 w .54653 .43388 m .51125 .46586 L .54867 .4942 L p .819 .937 .906 r F P s P p .002 w .54867 .4942 m .58577 .46542 L .54653 .43388 L p .819 .937 .906 r F P s P p .002 w .35641 .93687 m .34073 .91432 L .33227 .92381 L p .933 .633 .45 r F P s P p .002 w .33227 .92381 m .34526 .94971 L .35641 .93687 L p .933 .633 .45 r F P s P p .002 w .3784 .61875 m .36028 .64809 L .38277 .66053 L p .905 .927 .82 r F P s P p .002 w .3644 .68736 m .38277 .66053 L .36028 .64809 L p .92 .92 .797 r F P s P p .002 w .58484 .40137 m .54653 .43388 L .58577 .46542 L p .808 .936 .914 r F P s P p .002 w .58577 .46542 m .62564 .43628 L .58484 .40137 L p .808 .936 .914 r F P s P p .002 w .36028 .64809 m .34489 .67708 L .3644 .68736 L p .92 .92 .797 r F P s P p .002 w .34864 .714 m .3644 .68736 L .34489 .67708 L p .936 .91 .769 r F P s P p .002 w .33189 .88022 m .31928 .86266 L .31713 .86826 L p .959 .719 .531 r F P s P p .002 w .31713 .86826 m .32763 .89146 L .33189 .88022 L p .959 .719 .531 r F P s P p .002 w .62622 .3683 m .58484 .40137 L .62564 .43628 L p .797 .935 .922 r F P s P p .002 w .62564 .43628 m .66832 .40676 L .62622 .3683 L p .797 .935 .922 r F P s P p .002 w .34489 .67708 m .33223 .70574 L .34864 .714 L p .936 .91 .769 r F P s P p .002 w .33551 .74044 m .34864 .714 L .33223 .70574 L p .95 .897 .738 r F P s P p .002 w .34073 .91432 m .32763 .89146 L .32193 .89769 L p .951 .672 .472 r F P s P p .002 w .32193 .89769 m .33227 .92381 L .34073 .91432 L p .951 .672 .472 r F P s P p .002 w .32499 .76672 m .3171 .79284 L .32346 .80129 L p .956 .827 .675 r F P s P p .002 w .31504 .82302 m .32346 .80129 L .3171 .79284 L p .972 .814 .627 r F P s P p .002 w .32346 .80129 m .31504 .82302 L .31775 .82952 L p .961 .794 .629 r F P s P p .002 w .67073 .33464 m .62622 .3683 L .66832 .40676 L p .786 .933 .928 r F P s P p .002 w .66832 .40676 m .71385 .37683 L .67073 .33464 L p .786 .933 .928 r F P s P p .002 w .33223 .70574 m .32227 .73408 L .33551 .74044 L p .95 .897 .738 r F P s P p .002 w .32499 .76672 m .33551 .74044 L .32227 .73408 L p .964 .879 .702 r F P s P p .002 w .30923 .84471 m .32063 .84648 L .31968 .83763 L closepath p .977 .773 .563 r F P s P p .002 w .30923 .84471 m .32049 .85513 L .32063 .84648 L closepath p .977 .767 .555 r F P s P p .002 w .30923 .84471 m .31968 .83763 L .31775 .82952 L closepath p .978 .78 .568 r F P s P p .002 w .71846 .30035 m .67073 .33464 L .71385 .37683 L p .777 .931 .934 r F P s P p .002 w .71385 .37683 m .76227 .34649 L .71846 .30035 L p .777 .931 .934 r F P s P p .002 w .30923 .84471 m .31928 .86266 L .32049 .85513 L closepath p .978 .762 .544 r F P s P p .002 w .32227 .73408 m .315 .76213 L .32499 .76672 L p .964 .879 .702 r F P s P p .002 w .3171 .79284 m .32499 .76672 L .315 .76213 L p .975 .857 .66 r F P s P p .002 w .32763 .89146 m .31713 .86826 L .31425 .87133 L p .969 .714 .495 r F P s P p .002 w .31425 .87133 m .32193 .89769 L .32763 .89146 L p .969 .714 .495 r F P s P p .002 w .30923 .84471 m .31775 .82952 L .31504 .82302 L closepath p .981 .787 .569 r F P s P p .002 w .30923 .84471 m .31713 .86826 L .31928 .86266 L closepath p .98 .758 .532 r F P s P p .002 w .76947 .26542 m .71846 .30035 L .76227 .34649 L p .768 .928 .939 r F P s P p .002 w .76227 .34649 m .81364 .3157 L .76947 .26542 L p .768 .928 .939 r F P s P p .002 w .315 .76213 m .31041 .7899 L .3171 .79284 L p .975 .857 .66 r F P s P p .002 w .31184 .81884 m .3171 .79284 L .31041 .7899 L p .983 .83 .613 r F P s P p .002 w .3171 .79284 m .31184 .81884 L .31504 .82302 L p .972 .814 .627 r F P s P p .002 w .30923 .84471 m .31504 .82302 L .31184 .81884 L closepath p .984 .793 .566 r F P s P p .002 w .30923 .84471 m .31425 .87133 L .31713 .86826 L closepath p .983 .757 .519 r F P s P p .002 w .31041 .7899 m .30848 .81742 L .31184 .81884 L p .983 .83 .613 r F P s P p .002 w .30923 .84471 m .31184 .81884 L .30848 .81742 L closepath p .988 .797 .559 r F P s P p .002 w .36093 .97542 m .34526 .94971 L .33232 .95116 L p .93 .565 .304 r F P s P p .002 w .34526 .94971 m .33227 .92381 L .32249 .92471 L p .949 .615 .354 r F P s P p .002 w .32249 .92471 m .33232 .95116 L .34526 .94971 L p .949 .615 .354 r F P s P p .002 w .37927 1.00094 m .36093 .97542 L .34489 .97752 L p .907 .515 .255 r F P s P p .002 w .33232 .95116 m .34489 .97752 L .36093 .97542 L p .93 .565 .304 r F P s P p .002 w .33227 .92381 m .32193 .89769 L .31538 .89817 L p .966 .664 .405 r F P s P p .002 w .31538 .89817 m .32249 .92471 L .33227 .92381 L p .966 .664 .405 r F P s P p .002 w .40031 1.0263 m .37927 1.00094 L .36023 1.00383 L p .884 .467 .209 r F P s P p .002 w .34489 .97752 m .36023 1.00383 L .37927 1.00094 L p .907 .515 .255 r F P s P p .002 w .32193 .89769 m .31425 .87133 L .31096 .87151 L p .978 .712 .456 r F P s P p .002 w .31096 .87151 m .31538 .89817 L .32193 .89769 L p .978 .712 .456 r F P s P p .002 w .42405 1.05151 m .40031 1.0263 L .37837 1.03008 L p .859 .42 .166 r F P s P p .002 w .36023 1.00383 m .37837 1.03008 L .40031 1.0263 L p .884 .467 .209 r F P s P p .002 w .30923 .84471 m .31096 .87151 L .31425 .87133 L closepath p .986 .757 .506 r F P s P p .002 w .45053 1.07659 m .42405 1.05151 L .39935 1.05631 L p .833 .376 .126 r F P s P p .002 w .37837 1.03008 m .39935 1.05631 L .42405 1.05151 L p .859 .42 .166 r F P s P p .002 w .30411 .79285 m .30534 .81896 L .30848 .81742 L p .993 .84 .585 r F P s P p .002 w .30848 .81742 m .31041 .7899 L .30411 .79285 L p .993 .84 .585 r F P s P p .002 w .30923 .84471 m .30848 .81742 L .30534 .81896 L closepath p .991 .8 .549 r F P s P p .002 w .30923 .84471 m .30099 .82996 L .30028 .83824 L closepath p .997 .791 .506 r F P s P p .002 w .30923 .84471 m .30274 .82329 L .30099 .82996 L closepath p .996 .797 .521 r F P s P p .002 w .30923 .84471 m .30534 .81896 L .30274 .82329 L closepath p .994 .8 .535 r F P s P p .002 w .30923 .84471 m .30762 .86877 L .31096 .87151 L closepath p .989 .76 .495 r F P s P p .002 w .30923 .84471 m .30458 .86338 L .30762 .86877 L closepath p .992 .764 .488 r F P s P p .002 w .30923 .84471 m .30218 .85593 L .30458 .86338 L closepath p .994 .77 .485 r F P s P p .002 w .30923 .84471 m .30069 .84723 L .30218 .85593 L closepath p .996 .777 .487 r F P s P p .002 w .30923 .84471 m .30028 .83824 L .30069 .84723 L closepath p .997 .784 .494 r F P s P p .002 w .30556 .76637 m .30411 .79285 L .31041 .7899 L p .99 .878 .619 r F P s P p .002 w .31041 .7899 m .315 .76213 L .30556 .76637 L p .99 .878 .619 r F P s P p .002 w .47978 1.10155 m .45053 1.07659 L .42321 1.08254 L p .808 .334 .089 r F P s P p .002 w .39935 1.05631 m .42321 1.08254 L .45053 1.07659 L p .833 .376 .126 r F P s P p .002 w .30971 .7395 m .30556 .76637 L .315 .76213 L p .98 .91 .65 r F P s P p .002 w .315 .76213 m .32227 .73408 L .30971 .7395 L p .98 .91 .65 r F P s P p .002 w .31538 .89817 m .31096 .87151 L .30762 .86877 L p .985 .714 .417 r F P s P p .002 w .31659 .71221 m .30971 .7395 L .32227 .73408 L p .966 .938 .679 r F P s P p .002 w .32227 .73408 m .33223 .70574 L .31659 .71221 L p .966 .938 .679 r F P s P p .002 w .51181 1.12642 m .47978 1.10155 L .44999 1.10877 L p .783 .294 .056 r F P s P p .002 w .42321 1.08254 m .44999 1.10877 L .47978 1.10155 L p .808 .334 .089 r F P s P p .002 w .29889 .80144 m .30274 .82329 L .30534 .81896 L p .999 .84 .542 r F P s P p .002 w .30534 .81896 m .30411 .79285 L .29889 .80144 L p .999 .84 .542 r F P s P p .002 w .32623 .68448 m .31659 .71221 L .33223 .70574 L p .946 .96 .704 r F P s P p .002 w .33223 .70574 m .34489 .67708 L .32623 .68448 L p .946 .96 .704 r F P s P p .002 w .54667 1.15122 m .51181 1.12642 L .47974 1.13504 L p .759 .258 .026 r F P s P p .002 w .44999 1.10877 m .47974 1.13504 L .51181 1.12642 L p .783 .294 .056 r F P s P p .002 w .32249 .92471 m .31538 .89817 L .30868 .89278 L p .972 .658 .327 r F P s P p .002 w .30762 .86877 m .30868 .89278 L .31538 .89817 L p .985 .714 .417 r F P s P p .002 w .33867 .65629 m .32623 .68448 L .34489 .67708 L p .922 .976 .725 r F P s P p .002 w .34489 .67708 m .36028 .64809 L .33867 .65629 L p .922 .976 .725 r F P s P p .002 w .30868 .89278 m .30762 .86877 L .30458 .86338 L p .989 .721 .383 r F P s P p .002 w .29536 .81479 m .30099 .82996 L .30274 .82329 L p .999 .828 .489 r F P s P p .002 w .30274 .82329 m .29889 .80144 L .29536 .81479 L p .999 .828 .489 r F P s P p .002 w .58439 1.17595 m .54667 1.15122 L .51253 1.16135 L p .736 .225 0 r F P s P p .002 w .47974 1.13504 m .51253 1.16135 L .54667 1.15122 L p .759 .258 .026 r F P s P p .002 w .29771 .77916 m .29889 .80144 L .30411 .79285 L p .991 .876 .544 r F P s P p .002 w .30411 .79285 m .30556 .76637 L .29771 .77916 L p .991 .876 .544 r F P s P p .002 w .33232 .95116 m .32249 .92471 L .31245 .91676 L p .948 .592 .229 r F P s P p .002 w .30868 .89278 m .31245 .91676 L .32249 .92471 L p .972 .658 .327 r F P s P p .002 w .35395 .62761 m .33867 .65629 L .36028 .64809 L p .895 .987 .742 r F P s P p .002 w .36028 .64809 m .3784 .61875 L .35395 .62761 L p .895 .987 .742 r F P s P p .002 w .30458 .86338 m .30257 .88203 L .30868 .89278 L p .989 .721 .383 r F P s P p .002 w .30257 .88203 m .30458 .86338 L .30218 .85593 L p .988 .733 .363 r F P s P p .002 w .29392 .83145 m .30028 .83824 L .30099 .82996 L p .994 .805 .434 r F P s P p .002 w .30099 .82996 m .29536 .81479 L .29392 .83145 L p .994 .805 .434 r F P s P p .002 w .62503 1.20063 m .58439 1.17595 L .54841 1.18774 L p .714 .194 0 r F P s P p .002 w .51253 1.16135 m .54841 1.18774 L .58439 1.17595 L p .736 .225 0 r F P s P p .002 w .37211 .59842 m .35395 .62761 L .3784 .61875 L p .865 .994 .756 r F P s P p .002 w .3784 .61875 m .3993 .58902 L .37211 .59842 L p .865 .994 .756 r F P s P p .002 w .30218 .85593 m .29774 .86707 L .30257 .88203 L p .988 .733 .363 r F P s P p .002 w .29774 .86707 m .30218 .85593 L .30069 .84723 L p .988 .752 .365 r F P s P p .002 w .29474 .84955 m .30069 .84723 L .30028 .83824 L p .989 .777 .39 r F P s P p .002 w .30028 .83824 m .29392 .83145 L .29474 .84955 L p .989 .777 .39 r F P s P p .002 w .34489 .97752 m .33232 .95116 L .31896 .94074 L p .912 .515 .124 r F P s P p .002 w .31245 .91676 m .31896 .94074 L .33232 .95116 L p .948 .592 .229 r F P s P p .002 w .30069 .84723 m .29474 .84955 L .29774 .86707 L p .988 .752 .365 r F P s P p .002 w .31245 .91676 m .30868 .89278 L .30257 .88203 L p .964 .654 .251 r F P s P p .002 w .29923 .75641 m .29771 .77916 L .30556 .76637 L p .967 .901 .538 r F P s P p .002 w .30556 .76637 m .30971 .7395 L .29923 .75641 L p .967 .901 .538 r F P s P p .002 w .3932 .56868 m .37211 .59842 L .3993 .58902 L p .835 .997 .767 r F P s P p .002 w .3993 .58902 m .42299 .5589 L .3932 .56868 L p .835 .997 .767 r F P s P p .002 w .66861 1.22529 m .62503 1.20063 L .58745 1.21421 L p .694 .166 0 r F P s P p .002 w .54841 1.18774 m .58745 1.21421 L .62503 1.20063 L p .714 .194 0 r F P s P p .002 w .29237 .7992 m .29536 .81479 L .29889 .80144 L p .973 .842 .438 r F P s P p .002 w .29889 .80144 m .29771 .77916 L .29237 .7992 L p .973 .842 .438 r F P s P p .002 w .36023 1.00383 m .34489 .97752 L .32825 .96473 L p .865 .432 .016 r F P s P p .002 w .31896 .94074 m .32825 .96473 L .34489 .97752 L p .912 .515 .124 r F P s P p .002 w .30349 .73318 m .29923 .75641 L .30971 .7395 L p .925 .912 .522 r F P s P p .002 w .30971 .7395 m .31659 .71221 L .30349 .73318 L p .925 .912 .522 r F P s P p .002 w .41727 .53837 m .3932 .56868 L .42299 .5589 L p .804 .996 .776 r F P s P p .002 w .42299 .5589 m .44952 .52834 L .41727 .53837 L p .804 .996 .776 r F P s P p .002 w .30257 .88203 m .30325 .90067 L .31245 .91676 L p .964 .654 .251 r F P s P p .002 w .30325 .90067 m .30257 .88203 L .29774 .86707 L p .941 .657 .196 r F P s P p .002 w .71521 1.24994 m .66861 1.22529 L .62971 1.24079 L p .675 .14 0 r F P s P p .002 w .58745 1.21421 m .62971 1.24079 L .66861 1.22529 L p .694 .166 0 r F P s P p .002 w .31896 .94074 m .31245 .91676 L .30325 .90067 L p .908 .559 .092 r F P s P p .002 w .37837 1.03008 m .36023 1.00383 L .34037 .98875 L p .808 .343 0 r F P s P p .002 w .32825 .96473 m .34037 .98875 L .36023 1.00383 L p .865 .432 .016 r F P s P p .002 w .29018 .82433 m .29392 .83145 L .29536 .81479 L p .943 .783 .322 r F P s P p .002 w .29536 .81479 m .29237 .7992 L .29018 .82433 L p .943 .783 .322 r F P s P p .002 w .4444 .50746 m .41727 .53837 L .44952 .52834 L p .773 .993 .782 r F P s P p .002 w .44952 .52834 m .47893 .49734 L .4444 .50746 L p .773 .993 .782 r F P s P p .002 w .29774 .86707 m .29596 .87815 L .30325 .90067 L p .941 .657 .196 r F P s P p .002 w .29596 .87815 m .29774 .86707 L .29474 .84955 L p .921 .677 .185 r F P s P p .002 w .76486 1.2746 m .71521 1.24994 L .67529 1.26751 L p .657 .117 0 r F P s P p .002 w .62971 1.24079 m .67529 1.26751 L .71521 1.24994 L p .675 .14 0 r F P s P p .002 w .29207 .78317 m .29237 .7992 L .29771 .77916 L p .906 .827 .362 r F P s P p .002 w .29771 .77916 m .29923 .75641 L .29207 .78317 L p .906 .827 .362 r F P s P p .002 w .31054 .70945 m .30349 .73318 L .31659 .71221 L p .863 .907 .497 r F P s P p .002 w .31659 .71221 m .32623 .68448 L .31054 .70945 L p .863 .907 .497 r F P s P p .002 w .29142 .85169 m .29474 .84955 L .29392 .83145 L p .921 .721 .23 r F P s P p .002 w .29392 .83145 m .29018 .82433 L .29142 .85169 L p .921 .721 .23 r F P s P p .002 w .29474 .84955 m .29142 .85169 L .29596 .87815 L p .921 .677 .185 r F P s P p .002 w .39935 1.05631 m .37837 1.03008 L .35536 1.01281 L p .745 .254 0 r F P s P p .002 w .34037 .98875 m .35536 1.01281 L .37837 1.03008 L p .808 .343 0 r F P s P p .002 w .47464 .47591 m .4444 .50746 L .47893 .49734 L p .743 .988 .786 r F P s P p .002 w .47893 .49734 m .51125 .46586 L .47464 .47591 L p .743 .988 .786 r F P s P p .002 w .32825 .96473 m .31896 .94074 L .30667 .91933 L p .816 .437 0 r F P s P p .002 w .30325 .90067 m .30667 .91933 L .31896 .94074 L p .908 .559 .092 r F P s P p .002 w .81765 1.29929 m .76486 1.2746 L .72426 1.29437 L p .641 .096 0 r F P s P p .002 w .67529 1.26751 m .72426 1.29437 L .76486 1.2746 L p .657 .117 0 r F P s P p .002 w .30667 .91933 m .30325 .90067 L .29596 .87815 L p .832 .53 0 r F P s P p .002 w .32044 .68517 m .31054 .70945 L .32623 .68448 L p .786 .884 .464 r F P s P p .002 w .32623 .68448 m .33867 .65629 L .32044 .68517 L p .786 .884 .464 r F P s P p .002 w .42321 1.08254 m .39935 1.05631 L .37328 1.03693 L p .678 .167 0 r F P s P p .002 w .35536 1.01281 m .37328 1.03693 L .39935 1.05631 L p .745 .254 0 r F P s P p .002 w .50806 .4437 m .47464 .47591 L .51125 .46586 L p .715 .982 .789 r F P s P p .002 w .51125 .46586 m .54653 .43388 L .50806 .4437 L p .715 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.002 w .4773 .70777 m .44318 .7201 L .45208 .59331 L p .329 .177 .518 r F P s P p .002 w .45208 .59331 m .48638 .57073 L .4773 .70777 L p .329 .177 .518 r F P s P p .002 w .58648 1.14963 m .54429 1.12961 L .50859 1.00866 L p .343 .451 .826 r F P s P p .002 w .47222 .99779 m .50859 1.00866 L .54429 1.12961 L p .318 .433 .821 r F P s P p .002 w .61274 .498 m .56655 .52312 L .59169 .40623 L p .263 .009 .327 r F P s P p .002 w .59169 .40623 m .63813 .37389 L .61274 .498 L p .263 .009 .327 r F P s P p .002 w .45017 .8616 m .41916 .86183 L .41284 .73188 L p .356 .286 .639 r F P s P p .002 w .41284 .73188 m .44318 .7201 L .45017 .8616 L p .356 .286 .639 r F P s P p .002 w .68293 1.19039 m .73752 1.21118 L .7856 1.31223 L p .249 .514 .908 r F P s P p .002 w .41916 .86183 m .45017 .8616 L .47222 .99779 L p .354 .365 .734 r F P s P p .002 w .51535 .69485 m .4773 .70777 L .48638 .57073 L p .351 .196 .525 r F P s P p .002 w .48638 .57073 m .52449 .54734 L .51535 .69485 L p .351 .196 .525 r F P s P p .002 w .50859 1.00866 m .47222 .99779 L .45017 .8616 L p .378 .384 .739 r F P s P p .002 w .66323 .47194 m .61274 .498 L .63813 .37389 L p .283 .025 .334 r F P s P p .002 w .63813 .37389 m .68857 .34056 L .66323 .47194 L p .283 .025 .334 r F P s P p .002 w .63265 1.16988 m .58648 1.14963 L .54891 1.01957 L p .364 .466 .831 r F P s P p .002 w .50859 1.00866 m .54891 1.01957 L .58648 1.14963 L p .343 .451 .826 r F P s P p .002 w .48501 .86112 m .45017 .8616 L .44318 .7201 L p .38 .304 .645 r F P s P p .002 w .44318 .7201 m .4773 .70777 L .48501 .86112 L p .38 .304 .645 r F P s P p .002 w .45017 .8616 m .48501 .86112 L .50859 1.00866 L p .378 .384 .739 r F P s P p .002 w .55753 .68132 m .51535 .69485 L .52449 .54734 L p .371 .211 .531 r F P s P p .002 w .52449 .54734 m .56655 .52312 L .55753 .68132 L p .371 .211 .531 r F P s P p .002 w .68293 1.19039 m .63265 1.16988 L .59336 1.03053 L p .382 .479 .834 r F P s P p .002 w .54891 1.01957 m .59336 1.03053 L .63265 1.16988 L p .364 .466 .831 r F P s P p .002 w .54891 1.01957 m .50859 1.00866 L .48501 .86112 L p .399 .399 .743 r F P s P p .002 w .52384 .86037 m .48501 .86112 L .4773 .70777 L p .399 .32 .65 r F P s P p .002 w .4773 .70777 m .51535 .69485 L .52384 .86037 L p .399 .32 .65 r F P s P p .002 w .48501 .86112 m .52384 .86037 L .54891 1.01957 L p .399 .399 .743 r F P s P p .002 w .73752 1.21118 m .68293 1.19039 L .64212 1.04155 L p .398 .49 .837 r F P s P p .002 w .59336 1.03053 m .64212 1.04155 L .68293 1.19039 L p .382 .479 .834 r F P s P p .002 w .604 .66714 m .55753 .68132 L .56655 .52312 L p .387 .225 .536 r F P s P p .002 w .56655 .52312 m .61274 .498 L .604 .66714 L p .387 .225 .536 r F P s P p .002 w .59336 1.03053 m .54891 1.01957 L .52384 .86037 L p .416 .412 .747 r F P s P p .002 w .56685 .85935 m .52384 .86037 L .51535 .69485 L p .416 .333 .654 r F P s P p .002 w .51535 .69485 m .55753 .68132 L .56685 .85935 L p .416 .333 .654 r F P s P p .002 w .52384 .86037 m .56685 .85935 L .59336 1.03053 L p .416 .412 .747 r F P s P p .002 w .64212 1.04155 m .69539 1.05264 L .73752 1.21118 L p .398 .49 .837 r F P s P p .002 w .65498 .65228 m .604 .66714 L .61274 .498 L p .401 .236 .54 r F P s P p .002 w .61274 .498 m .66323 .47194 L .65498 .65228 L p .401 .236 .54 r F P s P p .002 w .64212 1.04155 m .59336 1.03053 L .56685 .85935 L p .431 .423 .749 r F P s P p .002 w .61423 .85805 m .56685 .85935 L .55753 .68132 L p .431 .344 .657 r F P s P p .002 w .55753 .68132 m .604 .66714 L .61423 .85805 L p .431 .344 .657 r F P s P p .002 w .56685 .85935 m .61423 .85805 L .64212 1.04155 L p .431 .423 .749 r F P s P p .002 w .69539 1.05264 m .64212 1.04155 L .61423 .85805 L p .443 .432 .752 r F P s P p .002 w .66619 .85644 m .61423 .85805 L .604 .66714 L p .443 .354 .66 r F P s P p .002 w .604 .66714 m .65498 .65228 L .66619 .85644 L p .443 .354 .66 r F P s P p .002 w .61423 .85805 m .66619 .85644 L .69539 1.05264 L p .443 .432 .752 r F P s P p .002 w .08032 .12484 m .65649 .03922 L s .65649 .03922 m .66589 1.30027 L s .66589 1.30027 m .03922 1.32632 L s .03922 1.32632 m .08032 .12484 L s .93467 .45164 m .65649 .03922 L s .65649 .03922 m .66589 1.30027 L s .66589 1.30027 m .96078 1.42367 L s .96078 1.42367 m .93467 .45164 L s P p p .002 w .93467 .45164 m .65649 .03922 L s P p .002 w .93098 .44617 m .92124 .44726 L s P [(-1)] .95047 .444 -1 .11149 Mshowa p .002 w .87649 .36538 m .86675 .36654 L s P [(-0.5)] .89596 .36307 -1 .11873 Mshowa p .002 w .81503 .27427 m .80531 .2755 L s P [(0)] .83448 .2718 -1 .12697 Mshowa p .002 w .74518 .17071 m .73547 .17203 L s P [(0.5)] .76461 .16806 -1 .13643 Mshowa p .002 w .66509 .05197 m .65539 .0534 L s P [(1)] .68449 .04911 -1 .14743 Mshowa p .001 w .92058 .43075 m .91474 .43141 L s P p .001 w .90994 .41498 m .9041 .41565 L s P p .001 w .89905 .39884 m .89321 .39951 L s P p .001 w .8879 .38231 m .88206 .38299 L s P p .001 w .86479 .34805 m .85895 .34875 L s P p .001 w .85281 .33028 m .84697 .331 L s P p .001 w .84053 .31208 m .8347 .3128 L s P p .001 w .82794 .29341 m .82211 .29414 L s P p .001 w .80178 .25463 m .79595 .25538 L s P p .001 w .78819 .23447 m .78236 .23524 L s P p .001 w .77423 .21378 m .7684 .21456 L s P p .001 w .7599 .19254 m .75407 .19332 L s P p .001 w .73005 .14827 m .72422 .14908 L s P p .001 w .71449 .12521 m .70867 .12603 L s P p .001 w .69849 .10149 m .69267 .10232 L s P p .001 w .68203 .07709 m .67621 .07793 L s P P p p .002 w .08032 .12484 m .03922 1.32632 L s P p .002 w .07948 .14941 m .08918 .14798 L s P [(-1)] .06008 .15225 1 -0.14644 Mshowa p .002 w .07024 .41963 m .07997 .41844 L s P [(-0.5)] .05078 .42201 1 -0.12243 Mshowa p .002 w .06062 .7006 m .07038 .69965 L s P [(0)] .04111 .7025 1 -0.09742 Mshowa p .002 w .05062 .99296 m .0604 .99226 L s P [(0.5)] .03106 .99435 1 -0.07136 Mshowa p .002 w .0402 1.29742 m .05 1.29699 L s P [(1)] .02062 1.29829 1 -0.04417 Mshowa p .001 w .07766 .20262 m .08349 .2018 L s P p .001 w .07583 .25625 m .08166 .25545 L s P p .001 w .07398 .31029 m .07981 .30952 L s P p .001 w .07212 .36475 m .07795 .364 L s P p .001 w .06835 .47494 m .07419 .47426 L s P p .001 w .06644 .53069 m .07228 .53004 L s P p .001 w .06452 .58688 m .07036 .58625 L s P p .001 w .06258 .64351 m .06843 .64291 L s P p .001 w .05866 .75814 m .06451 .7576 L s P p .001 w .05667 .81614 m .06253 .81563 L s P p .001 w .05467 .8746 m .06053 .87412 L s P p .001 w .05265 .93354 m .05852 .93309 L s P p .001 w .04857 1.05286 m .05444 1.05247 L s P p .001 w .04651 1.11325 m .05238 1.11289 L s P p .001 w .04442 1.17414 m .0503 1.17381 L s P p .001 w .04232 1.23552 m .0482 1.23523 L s P P p P % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup] Graphics3D["<<>>"] ;[o] -Graphics3D- :[font = text; inactive; preserveAspect] The cylinder cuts off the paraboloid in the plane y = 1. The surface projects to the disk x^2 + z^2 <= 1 in the xz-plane. We use the formula for surface integrals, integrating the constant 1 to get area. The surface integral equals the integral of Norm[Grad[f]]/Abs[Grad[f].p] over the unit disk in the xz-plane. Here, f comes from the equations that defines the surface (f == 0): ;[s] 17:0,0;50,1;55,0;90,1;104,0;112,1;114,0;189,1;190,0;248,1;276,0;303,1;305,0;319,1;320,0;372,1;378,0;381,-1; 2:9,13,9,Times,0,12,0,0,0;8,13,10,Courier,1,12,0,0,0; :[font = input; preserveAspect; startGroup] f = x^2 - y + z^2 :[font = output; output; inactive; preserveAspect; endGroup] x^2 - y + z^2 ;[o] 2 2 x - y + z :[font = text; inactive; preserveAspect] The vector p is the unit vector perpendicular to the plane to which we are projecting, so in this case: ;[s] 3:0,0;11,1;12,0;104,-1; 2:2,13,9,Times,0,12,0,0,0;1,13,10,Courier,1,12,0,0,0; :[font = input; preserveAspect; startGroup] p = j :[font = output; output; inactive; preserveAspect; endGroup] {0, 1, 0} ;[o] {0, 1, 0} :[font = input; preserveAspect; startGroup] Grad[f] :[font = output; output; inactive; preserveAspect; endGroup] {2*x, -1, 2*z} ;[o] {2 x, -1, 2 z} :[font = input; preserveAspect; startGroup] Grad[f].p :[font = output; output; inactive; preserveAspect; endGroup] -1 ;[o] -1 :[font = input; preserveAspect; startGroup] Norm[Grad[f]]/Abs[Grad[f].p] :[font = output; output; inactive; preserveAspect; endGroup] (1 + 4*x^2 + 4*z^2)^(1/2) ;[o] 2 2 Sqrt[1 + 4 x + 4 z ] :[font = text; inactive; preserveAspect] We use polar coordinates in the xz-plane so this function becomes Sqrt[1 + 4r^2] and its integral over the unit disk is: ;[s] 5:0,0;32,1;34,0;66,1;80,0;121,-1; 2:3,13,9,Times,0,12,0,0,0;2,13,10,Courier,1,12,0,0,0; :[font = input; preserveAspect; startGroup] Integrate[Sqrt[1 + 4r^2] r, {r,0,1},{theta,0,2Pi}] :[font = output; output; inactive; preserveAspect; endGroup] -Pi/6 + (5*5^(1/2)*Pi)/6 ;[o] -Pi 5 Sqrt[5] Pi --- + ------------ 6 6 ^*)