Question Number 224848 by Abdulazim last updated on 07/Oct/25 Commented by fantastic last updated on 07/Oct/25 $${Same}\:{Q}\:\mathrm{222958} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 224833 by fantastic last updated on 06/Oct/25 $$\int\mathrm{sec}\:\theta\:{d}\theta \\ $$ Answered by taha3738 last updated on 06/Oct/25 $$\int\:\mathrm{sec}\:\theta\:{d}\theta\:=\:\int\:\frac{\mathrm{sec}\:\theta\:\left(\mathrm{sec}\:\theta\:+\:\mathrm{tan}\:\theta\right)}{\mathrm{sec}\:\theta\:+\:\mathrm{tan}\:\theta}\:{d}\theta \\ $$$$=\:\int\:\:\frac{\mathrm{sec}^{\mathrm{2}} \theta+\:\mathrm{sec}\:\theta\:\mathrm{tan}\:\theta}{\mathrm{sec}\:\theta\:+\:\mathrm{tan}\:\theta\:}\:{d}\theta\:=\:\mathrm{ln}\:\mid\:\mathrm{sec}\:{x}\:+\:\mathrm{tan}\:{x}\:\mid\:+\:{C} \\ $$$${Because}\:\frac{{d}}{{d}\theta}\:\left(\:\mathrm{sec}\:\theta\:+\:\mathrm{tan}\:\theta\:\right)\:=\:\frac{{d}}{{d}\theta}\:\mathrm{sec}\:\theta\:+\:\frac{{d}}{{d}\theta}\:\mathrm{tan}\:\theta…
Question Number 224814 by fantastic last updated on 05/Oct/25 Answered by mr W last updated on 05/Oct/25 $${v}_{{D}} =\frac{{v}_{{A}} +{v}_{{E}} }{\mathrm{2}}=\frac{\mathrm{4}+\mathrm{0}}{\mathrm{2}}=\mathrm{2}\:{m}/{s} \\ $$$${v}_{{C}} =\frac{{v}_{{B}} +{v}_{{D}}…
Question Number 224806 by fkwow344 last updated on 05/Oct/25 $$\mathrm{Use}\:\mathrm{the}\:\mathrm{Gauss}\:\mathrm{Bonnet}\:\mathrm{Theorem}\:\mathrm{to}\:\mathrm{show}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{holes}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straw}\:\mathrm{is}\:\mathrm{1}. \\ $$$$\mathrm{Then}\:\mathrm{associate}\:\mathrm{it}\:\mathrm{and}\: \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{Genus}\:\mathrm{on}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{is}\:\mathrm{1}. \\ $$ Answered by MrAjder last updated on 18/Oct/25…
Question Number 224807 by fantastic last updated on 05/Oct/25 Commented by fantastic last updated on 05/Oct/25 $${It}\:{took}\:{me}\:\mathrm{10}\:{to}\:\mathrm{15}\:{minutes}\:{to}\:{solve} \\ $$$${this}\:{question}.{It}\:{was}\:{not}\:{too}\:{hard} \\ $$$${but}\:{the}\:{question}\:{is}\:{very}\:{interesting} \\ $$$${Here}\:{is}\:{the}\:{question}: \\ $$$${A}\:{bottle}\:{of}\:{syllendrical}\:{shape}…
Question Number 224819 by Abdulazim last updated on 05/Oct/25 Answered by fantastic last updated on 05/Oct/25 Answered by Ghisom_ last updated on 06/Oct/25 $$\left(\mathrm{2}{x}^{\mathrm{3}} +{x}−{a}\right)^{\mathrm{3}}…
Question Number 224798 by Tawa11 last updated on 04/Oct/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{arctan}^{\mathrm{2}} \left(\mathrm{x}\right)\:\mathrm{ln}\left(\mathrm{1}\:\:\:−\:\:\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 224789 by fkwow344 last updated on 04/Oct/25 $$\mathrm{prove}\:\mathrm{Sphere}\:\mathcal{S};\mathbb{R}^{\mathrm{3}} \rightarrow\mathbb{R} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={R}^{\mathrm{2}} \:,\:\mathrm{Euler}\:\mathrm{characteristic}\:\boldsymbol{\chi}=\mathrm{2} \\ $$$$\mathrm{by}\:\mathrm{gauss}-\mathrm{Bonnet}\:\mathrm{theorem} \\ $$$$\mathrm{2}\pi\boldsymbol{\chi}\left(\boldsymbol{\Omega}\right)=\int_{\:\boldsymbol{\Omega}} \:\mathrm{d}{A}\:{K} \\ $$$$\mathrm{Gauss}\:\mathrm{curvature}\:\mathrm{defined}\:\mathrm{as}\:{K}=\frac{\mathrm{det}\:\Pi}{\mathrm{det}\:\mathrm{I}}=\frac{{LN}−{M}^{\mathrm{2}} }{{EG}−{F}^{\mathrm{2}}…
Question Number 224790 by Tawa11 last updated on 04/Oct/25 Commented by Tawa11 last updated on 04/Oct/25 Commented by Tawa11 last updated on 04/Oct/25 $$\mathrm{Am}\:\mathrm{not}\:\mathrm{sure}\:\mathrm{sir} \\…
Question Number 224777 by mr W last updated on 03/Oct/25 Terms of Service Privacy Policy Contact: info@tinkutara.com