Question Number 227054 by Spillover last updated on 28/Dec/25 $${A}\:{Segment}\:{of}\:{a}\:{sphere}\:{has}\:{radius}\:{r} \\ $$$${and}\:{maximum}\:{height}\:{h}.{Prove}\:{that} \\ $$$${its}\:{volume}\:\frac{\boldsymbol{\pi{h}}}{\mathrm{6}}\left(\boldsymbol{{h}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{{r}}^{\mathrm{2}} \right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 227055 by Spillover last updated on 28/Dec/25 $${A}\:{parabolic}\:{refector}\:{is}\:{formed}\:{by} \\ $$$${revolving}\:{the}\:{arc}\:{of}\:{the}\:{parabala} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{ax}\:\:{from}\:{x}=\mathrm{0}\:\:\:\:{to}\:\:{x}={h} \\ $$$${about}\:{the}\:{axis}.{If}\:{the}\:\:{diameter} \\ $$$${of}\:{the}\:{reflector}\:{is}\:\mathrm{2}{l}.{Show}\:{that} \\ $$$${the}\:{area}\:{of}\:{the}\:{reflecting}\:{surface}\:{is} \\ $$$$\frac{\pi{l}}{\mathrm{6}{h}^{\mathrm{2}} }\left\{\left({l}^{\mathrm{2}} +\mathrm{4}{h}^{\mathrm{2}}…
Question Number 227051 by mnjuly1970 last updated on 28/Dec/25 $$ \\ $$$$\:\:\:\:\:\underset{{n}\in\mathbb{N}\cup\left\{\mathrm{0}\right\}} {\sum}{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{3}{n}\:+\:\mathrm{2}}\:\right)=?\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$ Commented by Spillover last updated on…
Question Number 227047 by Spillover last updated on 28/Dec/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 227043 by Spillover last updated on 28/Dec/25 Answered by Spillover last updated on 28/Dec/25 Answered by Spillover last updated on 28/Dec/25 Answered by…
Question Number 227032 by mr W last updated on 27/Dec/25 Commented by mr W last updated on 27/Dec/25 $${draw}\:{a}\:{straight}\:{line}\:{only}\:{with}\:{ruler} \\ $$$${and}\:{compass},\:{which}\:{divides}\:{the}\: \\ $$$${yellow}\:{figure}\:{into}\:{two}\:{parts}\:{with}\: \\ $$$${equal}\:{area}.…
Question Number 227034 by AgniMath last updated on 27/Dec/25 $$\mathrm{Velocity}\:\left({v}\right),\:\mathrm{time}\:\left({t}\right)\:\mathrm{and}\:\mathrm{displacement} \\ $$$$\left({x}\right)\:\mathrm{of}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{relation} \\ $$$$\left(\mathrm{1}\:+\:{t}^{\mathrm{3}} \right){v}\:+\:\mathrm{3}{t}^{\mathrm{2}} {x}\:=\:\mathrm{4}{t}.\:\mathrm{If}\:\mathrm{at}\:{t}\:=\:\mathrm{0},\:{x}\:=\:\mathrm{1}\:\mathrm{m} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{displacement}\:\mathrm{at}\:{t}\:=\:\mathrm{1}\:\mathrm{s}. \\ $$ Commented by fantastic2 last updated…
Question Number 227024 by mr W last updated on 26/Dec/25 Commented by mr W last updated on 26/Dec/25 $${the}\:{floor}\:{is}\:{smooth}.\:{the}\:{small}\:{ball} \\ $$$${is}\:{released}\:{from}\:{rest}\:{at}\:{the}\:{position} \\ $$$${as}\:{shown}.\:{find}\:{the}\:{locus}\:{of}\:{the}\: \\ $$$${small}\:{ball}\:{in}\:{given}\:{coordinate}…
Question Number 227026 by Mohammedqasim last updated on 26/Dec/25 Answered by Kassista last updated on 26/Dec/25 $$ \\ $$$${Numerator}: \\ $$$$\frac{{d}}{{dx}}\left(\pi{x}+\sqrt[{\mathrm{5}}]{\mathrm{99}}\right)=\pi \\ $$$$ \\ $$$${Denominator}:…
Question Number 227016 by Spillover last updated on 25/Dec/25 $${If}\:\alpha\:{and}\:.\beta\:\:{are}\:{root}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}=\mathrm{0}\:{and}\:{for}\:{n}\in\mathbb{N} \\ $$$${Show}\:{that}\: \\ $$$$\alpha^{{n}} +\beta^{{n}} =\mathrm{2}^{{n}+\mathrm{1}} \mathrm{cos}\:\left(\frac{{n}\pi}{\mathrm{3}}\right) \\ $$ Answered by Frix…