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Author: Tinku Tara

Question-153203

Question Number 153203 by mathdanisur last updated on 05/Sep/21 Answered by Kamel last updated on 05/Sep/21 $${f}\left({x}\right)=\frac{\mathrm{1}−\sqrt{\mathrm{1}−\mathrm{2}{x}}}{\mathrm{2}},{f}_{{n}} ^{−\mathrm{1}} =\underset{…………… {n}\:{times} ………} {{f}^{−\mathrm{1}} \circ{f}^{−\mathrm{1}} \circ{f}^{−\mathrm{1}} \circ…\circ{f}^{−\mathrm{1}}…

1-sin-1-8-pi-i-cos-1-8-pi-1-sin-1-8-pi-i-cos-1-8-pi-

Question Number 87656 by M±th+et£s last updated on 05/Apr/20 $$\frac{\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi+{i}\:{cos}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi}{\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi−{i}\:{cos}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi}=? \\ $$ Commented by Tony Lin last updated on 05/Apr/20 $${let}\:{sin}\frac{\pi}{\mathrm{8}}+{icos}\frac{\pi}{\mathrm{8}}={z}\:,\mid{z}\mid=\mathrm{1} \\ $$$$\frac{\mathrm{1}+{z}}{\mathrm{1}+\bar {{z}}} \\…

Question-153189

Question Number 153189 by liberty last updated on 05/Sep/21 Answered by EDWIN88 last updated on 05/Sep/21 $$\:{eq}\:{of}\:{circle}\:\mathrm{16}{x}^{\mathrm{2}} +\mathrm{16}{y}^{\mathrm{2}} +\mathrm{48}{x}−\mathrm{8}{y}−\mathrm{43}= \\ $$$${with}\:{center}\:{point}\:\begin{cases}{{x}=−\frac{\mathrm{48}}{\mathrm{32}}=−\frac{\mathrm{3}}{\mathrm{2}}}\\{{y}=\frac{\mathrm{8}}{\mathrm{32}}=\frac{\mathrm{1}}{\mathrm{4}}}\end{cases} \\ $$$${with}\:{radius}\:=\sqrt{\frac{\mathrm{9}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{6}}−\left(\frac{−\mathrm{43}}{\mathrm{16}}\right)} \\ $$$$\Rightarrow{r}=\sqrt{\frac{\mathrm{36}+\mathrm{1}+\mathrm{43}}{\mathrm{16}}}\:=\frac{\mathrm{4}\sqrt{\mathrm{5}}}{\mathrm{4}}=\sqrt{\mathrm{5}}\:…

the-sequence-a-1-a-2-a-3-satisfies-the-relation-a-n-1-a-n-a-n-1-for-n-gt-1-given-that-a-20-6765-and-a-18-2584-what-is-a-16-

Question Number 87648 by john santu last updated on 05/Apr/20 $$\mathrm{the}\:\mathrm{sequence}\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,\mathrm{a}_{\mathrm{3}} ,\:…\:\mathrm{satisfies} \\ $$$$\mathrm{the}\:\mathrm{relation}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\mathrm{a}_{\mathrm{n}} +\mathrm{a}_{\mathrm{n}−\mathrm{1}} \:,\:\mathrm{for} \\ $$$$\mathrm{n}>\mathrm{1}.\:\mathrm{given}\:\mathrm{that}\:\mathrm{a}_{\mathrm{20}} \:=\:\mathrm{6765}\:\mathrm{and} \\ $$$$\mathrm{a}_{\mathrm{18}} \:=\:\mathrm{2584}\:\mathrm{what}\:\mathrm{is}\:\mathrm{a}_{\mathrm{16}}…