Menu Close

Author: Tinku Tara

Question-226386

Question Number 226386 by fantastic2 last updated on 26/Nov/25 Commented by fantastic2 last updated on 27/Nov/25 $${l}=\mathrm{5}\pi{R} \\ $$$${a}\:{force}\:{F}\:{is}\:{given}\:{horizontally} \\ $$$${for}\:\mathrm{1}{sec}\:{such}\:{that}\:{the}\:{speed}\:{of}\:{the}\:{ball} \\ $$$${becomes}\:\mathrm{0}\:{just}\:{before}\:{touching}\:{the}\:{cylinder} \\ $$$${find}\:{the}\:{time}\:{taken}\:{to}\:{touch}\:{and}\:{the}\:{force}…

Prove-Mo-bious-String-is-Not-a-Orientated-Surface-u-1-u-sin-1-2-cos-1-u-sin-1-2-sin-u-cos-1-2-1-2-u-1-2-0-2pi-

Question Number 226351 by Lara2440 last updated on 26/Nov/25 $$\mathrm{Prove}\:\mathrm{M}\ddot {\mathrm{o}bious}\:\mathrm{String}\:\mathrm{is}\:\mathrm{Not}\:\mathrm{a}\:\mathrm{Orientated}\:\mathrm{Surface}. \\ $$$$\sigma\left({u},\theta\right)=\begin{cases}{\left(\mathrm{1}−{u}\centerdot\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\theta\right)\right)\mathrm{cos}\left(\theta\right)}\\{\left(\mathrm{1}−{u}\centerdot\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\theta\right)\right)\mathrm{sin}\left(\theta\right)}\\{{u}\centerdot\mathrm{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}\theta\right)}\end{cases}\:\:,\:−\frac{\mathrm{1}}{\mathrm{2}}\leq{u}\leq\frac{\mathrm{1}}{\mathrm{2}}\:,\:\mathrm{0}\leq\theta\leq\mathrm{2}\pi \\ $$ Answered by Lara2440 last updated on 26/Nov/25 $$\: \\ $$$$\mathrm{To}\:\mathrm{show}\:\mathrm{that}\:\mathrm{this}\:\mathrm{Surface}\:\mathrm{is}\:\mathrm{Oriented},…

Question-226292

Question Number 226292 by Spillover last updated on 25/Nov/25 Answered by Frix last updated on 25/Nov/25 $$=\int\frac{\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}}{dx}\:\overset{\left[{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\right]} {=} \\ $$$$=\mathrm{4}\int\frac{{t}\left({t}^{\mathrm{2}} −\mathrm{1}\right)}{\left({t}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} \left({t}^{\mathrm{2}} −\mathrm{2}{t}−\mathrm{1}\right)}{dt}\:\overset{\left[\mathrm{decompose}\:\mathrm{etc}.\right]} {=}…

A-hemispherical-bowl-of-radius-R-with-maimum-water-in-it-without-needing-to-spill-is-spinning-with-the-content-at-constant-Find-volume-of-water-in-bowl-

Question Number 226293 by ajfour last updated on 25/Nov/25 $${A}\:{hemispherical}\:{bowl}\:{of}\:{radius}\:{R} \\ $$$$\:{with}\:{maimum}\:{water}\:{in}\:{it}\:{without} \\ $$$${needing}\:{to}\:{spill}\:{is}\:{spinning}\:{with}\:{the} \\ $$$${content}\:{at}\:{constant}\:\omega.\:{Find}\:{volume} \\ $$$${of}\:{water}\:{in}\:{bowl}. \\ $$$$ \\ $$ Commented by fantastic2…