A tűkísérlet valószínűsége

[size=200]Legyen a vonalak távolsága [i]d[/i]=1,[i] l[/i] a tű hossza ([i]l[/i][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAXCAYAAAALHW+jAAAAr0lEQVRIid2UXQ0EIQyE4XIG0IAFPICVWsBQ8QECMIADPMy97g/cHkkfdm8SHkibL9NCRgOAEtRLEvbnwJSSCiGoUsq+gAW11hBjhDEGRISc86nnEth7BzPDOQfnHJgZvfdp/xRYawURwVoLIkKt9acpdsCtG+/9pZuvwNYarLVQSg13swwUd3iUyA5HEnvlkUT+4UzMDO/9CaqBJ8WX1nr5HMPhvb1ITH+fPHwu8AMUXOuiMDqwKwAAAABJRU5ErkJggg==[/img][i]d[/i]).[br][/size][size=200]Milyen feltételekkel fogalmazható meg az, hogy metszi-e a tű a vonalakat? [br]Jellemeznünk kell a tű "helyét" és a tű "irányát" is.[br][/size][size=200]Mozgasd a tűt a felezőpontjánál megfogva, forgasd el a csúszka segítségével, változtasd a tű hosszát. Figyeld meg, mitől függ, hogy metszi-e a tű a vonalakat?[/size]
[size=200]Egy adott hosszúságú tűt megadhatunk a tűnek az egyenesekkel bezárt [img]data:image/png;base64,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[/img] szögével és a tű felezőpontjának a hozzá közelebb eső egyenestől mért [i]y[/i] távolságával. Ha a tűt a vonalakkal párhuzamosan eltoljuk, az nem fogja a vonalakkal való metszést befolyásolni, ezért az így kapott ([img]data:image/png;base64,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[/img];y) számpárt használhatjuk a tű helyzetének egyértelmű jellemzésére, ahol [img]data:image/png;base64,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[/img], [img]data:image/png;base64,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[/img].[br]Az alábbi ablakban a felezőpontot és az [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACUAAAAYCAYAAAB9ejRwAAAB1UlEQVRIie2WMY7CMBBFv/cASIYLIExJhSwq+qSi9RmSA1Bwg9wgdHQ5gSPR0AAdSGloU1A74gizVSzIJiFmtdrVii9ZGsU/npex5QkjIsIf08dvA9TpDdVVb6iu+p9QRVFgvV7D930wxsAYQ7/fRxiGKIrC+vI8t/OMMeR53rwofUNaa+KcEwCKooiMMUREFMcxASAppX2mlCIABIBWq1Xrui9DJUlik2RZ9mU+CAICQHEc036/t14p5dO1X4LSWtskcRzXespqKaVISkkAiHNe+wHfhjLG2C0TQjT67qtTjiRJOuVwhoqiqFOSKpRSqnMOZ6iySgDsIa7T/ZkTQrR6q3K6EtI0xe12AwAopTAYDBq91+vVxpvNptVblRPU8Xi08XQ6bfXudjsAgJQS8/ncJY0b1Pl8tvFkMmn05XmO7XYLAE4Vegnq/obu9XqNvjAMbTwajX4W6nQ6PfUcDgdbJQAYDoc/CyWEaJ0vigKLxQJRFDmDvAw1Ho9tfLlcvgD5vo/ZbIblcln7fpqmD1vbKJc7qmwdqLQMrTVJKR8acOnzPM96OOcUBMHTPE5Qxhjbx6rD87yHC7LO1wXIGaoEu/8NkVLWtpssy0gIYT1a6845PgGG5Z7Agrwd4AAAAABJRU5ErkJggg==[/img] szöget változtatva írj fel összefüggést, mely a metszés feltételét fogalmazza meg![br] [/size]
[size=200]A helyes összefüggés:[br][img]data:image/png;base64,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[/img][br]Az ([img]data:image/png;base64,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[/img];y) számpároknak megfelelő pontok a [img]data:image/png;base64,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[/img] és d/2 oldalhosszúságú téglalap P pontjai. Mozgasd a tűt a felezőpontja valamint a csúszkán az [img]data:image/png;base64,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[/img] segítségével, és figyeld meg az ([img]data:image/png;base64,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[/img] ;y) pontok elhelyezkedését a téglalapban![br][br][/size]
[size=200]Számold ki a kérdéses valószínűséget, azaz a zölddel jelölt terület és a téglalap területének hányadosát![br][/size][size=200]A zöld területet az [br][img]data:image/png;base64,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[/img][br][/size][size=200]integrállal számolhatod.[/size]

Information: A tűkísérlet valószínűsége