Question Number 134469 by SEKRET last updated on 04/Mar/21 $$\:\:\:\int\:\:\frac{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{m}}} +\mathrm{1}}{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}} +\mathrm{1}}\:\boldsymbol{\mathrm{dx}}\:\:=?\:\:\:\:\:\boldsymbol{\mathrm{n}}>\boldsymbol{\mathrm{m}}\:\:\:\:\:\:\boldsymbol{\mathrm{m}};\boldsymbol{\mathrm{n}}\in\boldsymbol{\mathrm{Z}}^{+} \\ $$ Answered by Olaf last updated on 04/Mar/21 $${x}^{{n}} +\mathrm{1}\:=\:\mathrm{0}\:\Leftrightarrow\:{x}\:=\:{e}^{{i}\frac{\pi}{{n}}\left(\mathrm{1}+\mathrm{2}{k}\right)} ,\:{k}\in\left\{\mathrm{0},\:\mathrm{1},…,\:{n}−\mathrm{1}\right\} \\…
Question Number 68935 by Maclaurin Stickker last updated on 17/Sep/19 $${Find}\:{all}\:{values}\:{for}\:\boldsymbol{{x}}: \\ $$$$\left({x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{11}\right)^{{x}^{\mathrm{2}} −\mathrm{13}{x}+\mathrm{42}} =\mathrm{1} \\ $$$$\left({Easy}\right) \\ $$ Answered by $@ty@m123 last updated…
Question Number 68930 by Maclaurin Stickker last updated on 17/Sep/19 $$\mathrm{In}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{we}\:\mathrm{have}\:\mathrm{7}\:\mathrm{circles}\:\mathrm{having} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{radius}.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{circle}\:\mathrm{and}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{gray}\:\mathrm{region}. \\ $$ Commented by Maclaurin Stickker last updated…
Question Number 134464 by bramlexs22 last updated on 04/Mar/21 $$\:\:\:\:\:\:\:\begin{array}{|c|c|}{\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{Equation}}\\{\:\:\mathrm{81}^{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}} \:+\:\mathrm{81}^{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}} \:=\:\mathrm{30}\:}\\\hline\end{array} \\ $$ Commented by harckinwunmy last updated on 04/Mar/21 $${ff} \\…
Question Number 134467 by bramlexs22 last updated on 04/Mar/21 $$\begin{array}{|c|c|}{\mathrm{If}\:\mathrm{x}^{\mathrm{2}} =\mathrm{2y}+\mathrm{5}\:\mathrm{and}\:\mathrm{y}^{\mathrm{2}} =\mathrm{2x}+\mathrm{5}\:}\\{\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} −\mathrm{2x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} .}\\\hline\end{array} \\ $$ Answered by benjo_mathlover last updated on 04/Mar/21…
Question Number 134461 by pticantor last updated on 04/Mar/21 $${soit}\:\left(\boldsymbol{{E}}\right)\:{l}'{equation}\:{complex}: \\ $$$$\boldsymbol{{z}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{pz}}−\boldsymbol{{q}}=\mathrm{0} \\ $$$$\boldsymbol{{p}},\boldsymbol{{q}}\in\mathbb{C} \\ $$$$\boldsymbol{{let}}\:\boldsymbol{{u}}\in\mathbb{C}\backslash\:\boldsymbol{{u}}^{\mathrm{2}} =\boldsymbol{{q}} \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{if}}\:\boldsymbol{{z}}_{\mathrm{1}} ,\boldsymbol{{z}}_{\mathrm{2}} \boldsymbol{{are}}\:\boldsymbol{{solutions}}\:\boldsymbol{{of}}\:\left(\boldsymbol{{E}}\right), \\ $$$$\mid\boldsymbol{{z}}_{\mathrm{1}} \mid+\mid\boldsymbol{{z}}_{\mathrm{2}}…
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Question Number 134460 by bramlexs22 last updated on 04/Mar/21 $$ \\ $$2. When the cost of a bag of potatoes is $5 a supermarket sells…
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Question Number 68925 by ramirez105 last updated on 16/Sep/19 Commented by kaivan.ahmadi last updated on 16/Sep/19 $$\frac{\partial{u}}{\partial{x}}=\left({x}+\mathrm{3}\right)^{−\mathrm{1}} {cosy}\Rightarrow{u}\left({x},{y}\right)={cosyln}\left({x}+\mathrm{3}\right)+{h}\left({y}\right) \\ $$$$\frac{\partial{u}}{\partial{y}}={y}^{−\mathrm{1}} −{sinyln}\left(\mathrm{5}{x}+\mathrm{15}\right)=−{sinyln}\left({x}+\mathrm{3}\right)+\frac{{dh}}{{dy}}\Rightarrow \\ $$$${y}^{−\mathrm{1}} −{ln}\mathrm{5}=\frac{{dh}}{{dy}}\Rightarrow{h}={lny}−{yln}\mathrm{5} \\…