Question Number 203905 by sniper237 last updated on 01/Feb/24 $${let}\:{ABC}\:{a}\:{given}\:{triangle}.\:{Can}\:{we}\:{find} \\ $$$${three}\:{positions}\:{I},{J},{K}\:{on}\:{the}\:{side}\:{AB},{AC},{BC} \\ $$$${Such}\:{that}\:{IJK}\:{is}\:{equilateral}? \\ $$ Commented by mr W last updated on 01/Feb/24 $${yes},\:{we}\:{can}\:{find}\:{infinite}\:{many}\:{such}…
Question Number 203884 by Mathspace last updated on 31/Jan/24 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{3}} }{\left(\mathrm{1}+{x}\right)^{\mathrm{4}} \left({x}+\mathrm{2}\right)^{\mathrm{5}} }{dx} \\ $$ Answered by Frix last updated on 01/Feb/24 $$\mathrm{Use}\:\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}\:\mathrm{to}\:\mathrm{get}…
Question Number 203881 by mr W last updated on 31/Jan/24 Commented by mr W last updated on 31/Jan/24 $${find}\:{the}\:{hatched}\:{area}\:{between}\:{curve} \\ $$$${and}\:{its}\:{tangent}\:{line}. \\ $$ Answered by…
Question Number 203877 by Spillover last updated on 31/Jan/24 $$\mathrm{Write}\:\mathrm{a}\:\mathrm{balanced}\:\mathrm{Ionic}\:\mathrm{chemical}\:\mathrm{equation} \\ $$$$\:\mathrm{for}\:\mathrm{the}\:\mathrm{following}\:\mathrm{reaction} \\ $$$$\left(\mathrm{a}\right){HCl}+{C}\mathrm{aCO}_{\mathrm{3}} \rightarrow\mathrm{Ca}{Cl}_{\mathrm{2}} +{C}\mathrm{O}_{\mathrm{2}\left(\mathrm{g}\right)} +\mathrm{H}_{\mathrm{2}} \mathrm{O}_{\left({l}\right)} \\ $$$$\left({b}\right){NH}_{\mathrm{4}} {OH}_{\:\left({aq}\right)} +{HCl}_{\left({aq}\right)} \:\rightarrow{NH}_{\mathrm{4}} \mathrm{C}{l}_{\left({aq}\right)} +{H}_{\mathrm{2}}…
Question Number 203878 by Spillover last updated on 31/Jan/24 $$\mathrm{A}\:\mathrm{compound}\:\mathrm{M}\:\mathrm{is}\:\mathrm{composed}\:\mathrm{of}\:\mathrm{52}.\mathrm{2\%}\: \\ $$$$\mathrm{carbon}\:,\mathrm{13\%}\:\mathrm{hydrogenand}\:\mathrm{the}\:\mathrm{rest}\: \\ $$$$\mathrm{is}\:\mathrm{oxygen}.\mathrm{if}\:\mathrm{the}\:\mathrm{molecuar}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{M}\:\mathrm{is}\:\mathrm{138} \\ $$$$\left(\mathrm{a}\right)\mathrm{The}\:\mathrm{empirical}\:\mathrm{formular} \\ $$$$\left(\mathrm{b}\right)\mathrm{The}\:\mathrm{molecular}\:\mathrm{formular} \\ $$$$\mathrm{31}/\mathrm{1}/\mathrm{2024} \\ $$ Answered by Calculusboy…
Question Number 203879 by Spillover last updated on 31/Jan/24 $$\mathrm{Complete}\:\mathrm{and}\:\mathrm{balance}\:\mathrm{the}\:\mathrm{following}\:\mathrm{chemical}\:\mathrm{reaction}\: \\ $$$$\mathrm{equation} \\ $$$$\left(\mathrm{a}\right)\mathrm{Ca}\:+\:\mathrm{H}_{\mathrm{2}} \mathrm{O}\:\:\rightarrow\:\: \\ $$$$\left(\mathrm{b}\right)\mathrm{BaC}{l}\:+\:\mathrm{H}_{\mathrm{2}} \mathrm{SO}_{\mathrm{4}} \:\:\rightarrow \\ $$$$\left(\mathrm{c}\right)\mathrm{CuSO}_{\mathrm{4}} .\mathrm{5H}_{\mathrm{2}} \mathrm{O}\:\:\:\overset{\mathrm{Heat}\:\mathrm{strongly}} {\rightarrow} \\…
Question Number 203875 by MathedUp last updated on 31/Jan/24 $$\mathrm{Hmmm}…..\:\mathrm{I}\:\mathrm{have}\:\mathrm{one}\:\mathrm{Question}. \\ $$$${f}\left({t}\right)\in{C}^{\infty} \:,\:\left\{{C}_{\:} ^{\boldsymbol{\alpha}} \:\mathrm{mean}\:\mathrm{can}\:\mathrm{derivate}\:\boldsymbol{\alpha}\:\mathrm{times}.\right\} \\ $$$$\mathrm{where}\:{t}\in\mathbb{R}\:,\:\mathrm{Can}\:{f}\left({t}\right)\:\:\mathrm{integrable}\:\mathrm{when}\:{S}\in\mathbb{R}\backslash\left\{\mathbb{Q}\right\}?? \\ $$$$\mathrm{Ex}.\:\mathrm{integral}\:\int_{\mathrm{1}} ^{\:{e}} \:\mathrm{ln}\left({z}\right)\mathrm{d}{z}\:{S}\in\left[\mathrm{1},{e}\right]\: \\ $$$$\mathrm{But}\:\mathrm{Except}\:\mathbb{Q}\:\mathrm{in}\:\mathrm{set}\:{S}\:\mathrm{like}..\:{S}^{'} ={S}\backslash\left\{\mathbb{Q}\right\}\: \\…
Question Number 203867 by Mathspace last updated on 30/Jan/24 $${find}\:\int\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{3}} }}{dx} \\ $$ Answered by MathematicalUser2357 last updated on 06/Feb/24 $$\frac{\mathrm{8}{x}\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{3}} }{{x}^{\mathrm{3}} +\mathrm{1}}}{F}_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}};−\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\frac{\mathrm{4}}{\mathrm{3}};{x}^{\mathrm{3}}…
Question Number 203858 by Mastermind last updated on 30/Jan/24 $$\mathrm{Classsify}\:\mathrm{the}\:\mathrm{critical}\:\mathrm{points}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{x}^{\mathrm{2}} \mathrm{y}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{y}^{\mathrm{3}} \:−\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{2} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{in}\:\mathrm{advance}! \\ $$ Commented…
Question Number 203859 by Mastermind last updated on 30/Jan/24 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{surface}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{z}\:=\:\mathrm{xy} \\ $$$$\mathrm{has}\:\mathrm{neither}\:\mathrm{a}\:\mathrm{maximum}\:\mathrm{nor}\:\mathrm{a}\:\mathrm{minimum}\:\mathrm{point} \\ $$ Commented by AST last updated on 30/Jan/24 $${For}\:{x},{y}\rightarrow\infty;\:{z}\rightarrow\infty \\…