This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Huu hapa ni ufumbuzi wa maswali yako: 2. Ni nini unaweza kusema kuhusu kila jozi ya pembe ulizotaja katika Swali la 2(a) hapo juu? Pembe zilizoundwa na arc moja kwenye mzingo wa duara ni sawa. 3. Katika mchoro hapa chini, ECD = 25^, EAF = 30^ na CFD = 35^. Tafuta: Kutokana na mchoro, F ni makutano ya kodi AC na ED. Tunachukulia EAF kama EAC. Hatua ya 1: Tafuta vipimo vya arc kutokana na pembe zilizotolewa. • Pembe ECD = 25^ inaunda arc ED. Hivyo, arc(ED) = 2 × ECD = 2 × 25^ = 50^. • Pembe EAC = 30^ (kutoka EAF) inaunda arc EC. Hivyo, arc(EC) = 2 × EAC = 2 × 30^ = 60^. • Tunajua arc(EC) = arc(ED) + arc(DC). 60^ = 50^ + arc(DC) arc(DC) = 60^ - 50^ = 10^. • Pembe CFD = 35^ ni pembe iliyoundwa na kodi zinazokatana AC na ED. CFD = (1)/(2) (arc(CD) + arc(AE)). 35^ = (1)/(2) (10^ + arc(AE)). 70^ = 10^ + arc(AE). arc(AE) = 70^ - 10^ = 60^. Kwa hivyo, vipimo vya arc ni: arc(CD) = 10^ arc(DE) = 50^ arc(EA) = 60^ Hatua ya 2: Tafuta pembe zinazohitajika kwa kutumia vipimo vya arc. a) CAD Pembe CAD inaunda arc CD. CAD = (1)/(2) arc(CD) = (1)/(2) × 10^ = 5^ CAD = 5^ b) CDF Pembe CDF ni sawa na CDE. Pembe CDE inaunda arc CE. arc(CE) = arc(CD) + arc(DE) = 10^ + 50^ = 60^. CDE = (1)/(2) arc(CE) = (1)/(2) × 60^ = 30^ CDF = 30^ c) DCF Pembe DCF ni sawa na DCA. Pembe DCA inaunda arc DA. arc(DA) = arc(DE) + arc(EA) = 50^ + 60^ = 110^. DCA = (1)/(2) arc(DA) = (1)/(2) × 110^ = 55^ DCF = 55^ d) DFE Pembe DFE na CFD ni pembe za ziada (ziko kwenye mstari ulionyooka). DFE = 180^ - CFD = 180^ - 35^ = 145^ DFE = 145^ That's 2 down. 3 left today — send the next one.