Euclides, jaargang 90 // 2014-2015, nummer 5 PDF
2014·0.03 MB·Dutch
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Preview Euclides, jaargang 90 // 2014-2015, nummer 5
r = straal grasveld hoek OCA =x, Dus hoek ACB = 2x E =straal touw/ lengte touw dus hoek OCB =x C = paal geit = midden (/2RA2*2 x =RA2*X —> ACH? wkn AD + BO= 2((1/2}r*2{pt-2xH1/2)rn2sin(pi-2a0) =rA2(pi- 2x - sinf2x0}} K = 2rcos{a} Dus RA2*y = ArA2 cost 2} Oplossen met de methode van Newton-Raphson Arart*cosA2fe} + ra2lpi- 2t- sin{2x)} ={1/2}pi*rA2 ofwel. An*cosh2{x} + (pì-2 x sinf2al} =(4/2)pt _AxtcosA2[i} + (1/2)pi - 2 - sinf2x} =0 Verhauding tussen —> lengte touw : straal grasveld Dus (R/r 2eas{x} ) ä Uiteindelijk —> x=0,95284786466 —> coslx}=0,579364236509 DUSSS55E R/r=2eosix}=2 0573364236509 = 1,15872847
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