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Category: Algebra

Question-147272

Question Number 147272 by mathdanisur last updated on 19/Jul/21 Answered by puissant last updated on 19/Jul/21 $${y}={arctan}\left({a}\right)\:\Rightarrow\:{cos}\left({arctan}\left({a}\right)\right)={cos}\left({y}\right) \\ $$$$\mathrm{1}+{tan}^{\mathrm{2}} {y}=\frac{\mathrm{1}}{{cos}^{\mathrm{2}} {y}}\:\Rightarrow\:{cos}^{\mathrm{2}} {y}=\frac{\mathrm{1}}{\mathrm{1}+{tan}^{\mathrm{2}} {y}} \\ $$$$\Rightarrow{cos}^{\mathrm{2}}…

Question-147260

Question Number 147260 by mathdanisur last updated on 19/Jul/21 Answered by Rasheed.Sindhi last updated on 19/Jul/21 $${AM}={MB}={x} \\ $$$${MD}={y}\Rightarrow{DC}=\mathrm{2}{y}\Rightarrow{MC}=\mathrm{3}{y} \\ $$$$\bigtriangleup{BDM}:\:{BD}=\sqrt{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \\ $$$$\bigtriangleup{BDC}:\:{BC}=\sqrt{\left(\sqrt{{x}^{\mathrm{2}}…

Question-147259

Question Number 147259 by mathdanisur last updated on 19/Jul/21 Answered by Rasheed.Sindhi last updated on 19/Jul/21 $$\bigtriangleup{AED}: \\ $$$$\because{AD}\:{is}\:{diameter} \\ $$$$\therefore\angle{AED}=\mathrm{90} \\ $$$${tan}\angle{A}=\frac{\mathrm{1}}{\mathrm{3}}\:\Rightarrow\angle{A}=\mathrm{19}.\mathrm{47} \\ $$$${AC}=\sqrt{{AE}^{\mathrm{2}}…

Soient-a-0-1-et-b-R-Soit-f-une-application-de-R-dans-lui-me-me-de-classe-C-1-telle-que-pour-tout-re-el-x-f-f-x-ax-b-1-Montrer-que-pour-tout-re-el-x-f-ax-b-af-x-b-En-de-duire-

Question Number 147254 by Ar Brandon last updated on 19/Jul/21 $$\left.\mathrm{Soient}\:\mathrm{a}\in\right]\mathrm{0},\:\mathrm{1}\left[\:\mathrm{et}\:\mathrm{b}\in\mathbb{R}.\:\mathrm{Soit}\:\mathrm{f}\:\mathrm{une}\:\mathrm{application}\:\mathrm{de}\:\mathbb{R}\:\mathrm{dans}\:\mathrm{lui}-\mathrm{m}\hat {\mathrm{e}me},\:\mathrm{de}\:\mathrm{classe}\:\mathrm{C}^{\mathrm{1}} ,\:\mathrm{telle}\:\mathrm{que}\:\mathrm{pour}\:\mathrm{tout}\:\mathrm{r}\acute {\mathrm{e}el}\right. \\ $$$$\mathrm{x},\:\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{ax}+\mathrm{b}. \\ $$$$ \\ $$$$\mathrm{1}.\:\:\mathrm{Montrer}\:\mathrm{que}\:\mathrm{pour}\:\mathrm{tout}\:\mathrm{r}\acute {\mathrm{e}el}\:\mathrm{x},\:\mathrm{f}\left(\mathrm{ax}+\mathrm{b}\right)=\mathrm{af}\left(\mathrm{x}\right)+\mathrm{b}.\:\mathrm{En}\:\mathrm{d}\acute {\mathrm{e}duire}\:\mathrm{que}\:\mathrm{pour}\:\mathrm{tout}\:\mathrm{r}\acute {\mathrm{e}el}\:\mathrm{x}, \\ $$$$\:\:\mathrm{f}\:'\left(\mathrm{ax}+\mathrm{b}\right)=\mathrm{f}\:'\left(\mathrm{x}\right).…

if-3-a-2-5-3b-1-7-3-2c-find-a-b-c-

Question Number 147231 by mathdanisur last updated on 19/Jul/21 $${if}\:\:\:\mathrm{3}^{\boldsymbol{{a}}+\mathrm{2}} \:=\:\mathrm{5}^{\mathrm{3}\boldsymbol{{b}}−\mathrm{1}} \:=\:\mathrm{7}^{\mathrm{3}−\mathrm{2}\boldsymbol{{c}}} \\ $$$${find}\:\:\:\boldsymbol{{a}}\centerdot\boldsymbol{{b}}\centerdot\boldsymbol{{c}}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 19/Jul/21 $$\mathrm{3}^{{a}+\mathrm{2}} \:=\:\mathrm{5}^{\mathrm{3}{b}−\mathrm{1}}…