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Question-199174

Question Number 199174 by tri26112004 last updated on 29/Oct/23 Answered by ajfour last updated on 29/Oct/23 $${If}\:{i}\:{take}\:\angle{ACI}\:=\theta\:\:{then} \\ $$$$\frac{{CI}}{{HI}}=\frac{\mathrm{sin}\:\theta}{\mathrm{2}−\mathrm{sin}\:\theta} \\ $$ Commented by tri26112004 last…

Question-199175

Question Number 199175 by SANOGO last updated on 29/Oct/23 Answered by a.lgnaoui last updated on 29/Oct/23 $$\mathrm{g}_{\mathrm{m}} \left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{2x}}{\mathrm{m}}+\frac{\mathrm{1}}{\mathrm{m}^{\mathrm{2}} }\:\:\:\:\left(\mathrm{m}\neq\mathrm{0}\:\:\:\:\mathrm{x}\geqslant\mathrm{0}\right) \\ $$$$\:\:\:\:\mathrm{n}\:\mathrm{est}\:\mathrm{pas}\:\mathrm{une}\:\mathrm{suite}\:\mathrm{convergente} \\ $$$$\:\mathrm{preuve}: \\…

Question-199165

Question Number 199165 by hardmath last updated on 28/Oct/23 Answered by Frix last updated on 28/Oct/23 $$−\mathrm{1}=\mathrm{e}^{\mathrm{i}\pi} \\ $$$$\left(−\mathrm{1}\right)^{\pi} =\mathrm{e}^{\mathrm{i}\pi^{\mathrm{2}} } = \\ $$$$=\mathrm{cos}\:\pi^{\mathrm{2}} \:+\mathrm{i}\:\mathrm{sin}\:\pi^{\mathrm{2}}…

a-2-b-1-1999-how-many-natural-solutions-of-the-equation-a-b-have-

Question Number 199133 by hardmath last updated on 28/Oct/23 $$\mathrm{a}^{\mathrm{2}} \mathrm{b}\:−\:\mathrm{1}\:=\:\mathrm{1999} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{natural}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{have}? \\ $$ Answered by Rasheed.Sindhi last updated on 28/Oct/23 $$\mathrm{a}^{\mathrm{2}}…

Give-a-function-f-R-0-continous-on-R-and-such-that-f-x-y-f-x-f-y-a-Prove-f-0-1-b-Let-h-x-ln-f-x-Prove-that-h-x-y-h-x-h-y-c-Find-all-the-function-f-such-that-problem-re

Question Number 199167 by tri26112004 last updated on 28/Oct/23 $${Give}\:{a}\:{function}\: \\ $$$${f}:\:{R}\rightarrow\left(\mathrm{0};+\infty\right)\:{continous}\:{on}\:{R}\:{and}\:{such}\:{that} \\ $$$${f}\left({x}+{y}\right)\:=\:{f}\left({x}\right).{f}\left({y}\right) \\ $$$${a}.\:{Prove}\:{f}\left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$$${b}.\:{Let}\:{h}\left({x}\right)\:=\:{ln}\left[{f}\left({x}\right)\right].\:{Prove}\:{that}: \\ $$$$\:{h}\left({x}+{y}\right)\:=\:{h}\left({x}\right)\:+\:{h}\left({y}\right) \\ $$$${c}.\:{Find}\:{all}\:{the}\:{function}\:{f}\:{such}\:{that}\:{problem}\:{request} \\ $$$$\:\:\: \\…