Question Number 104099 by mohammad17 last updated on 19/Jul/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 38557 by kunal1234523 last updated on 27/Jun/18 $${prove}\:{that} \\ $$$$\frac{\mathrm{2}\:\mathrm{cos}\:\mathrm{2}^{{n}} \theta\:+\:\mathrm{1}}{\mathrm{2}\:\mathrm{cos}\:\theta\:+\:\mathrm{1}}\:=\:\left(\mathrm{2}\:\mathrm{cos}\:\theta\:−\:\mathrm{1}\right)\left(\mathrm{2}\:\mathrm{cos}\:\mathrm{2}\theta\:−\:\mathrm{1}\right)\left(\mathrm{2}\:\mathrm{cos}\:\mathrm{2}^{\mathrm{2}} \theta−\:\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\left(\mathrm{2}\:\mathrm{cos}\:\mathrm{2}^{{n}\:−\:\mathrm{1}} \theta\:\:−\:\mathrm{1}\right) \\ $$ Answered by kunal1234523 last updated on…
Question Number 104092 by naka3546 last updated on 19/Jul/20 $${Prove}\:\:{that}\:\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:\centerdot\:\frac{\mathrm{3}}{\mathrm{4}}\:\centerdot\:\frac{\mathrm{5}}{\mathrm{6}}\:\centerdot\:\ldots\centerdot\:\frac{\mathrm{2005}}{\mathrm{2006}}\:\centerdot\:\frac{\mathrm{2007}}{\mathrm{2008}}\:\:<\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2009}}} \\ $$ Commented by JDamian last updated on 19/Jul/20 $${I}\:{guess}\:\frac{\mathrm{2007}}{\mathrm{2009}}\:{should}\:{actually}\:{be}\:\frac{\mathrm{2007}}{\mathrm{2008}} \\ $$ Answered…
Question Number 104071 by DGmichael last updated on 19/Jul/20 Answered by Dwaipayan Shikari last updated on 19/Jul/20 $$\int\mathrm{6}\sqrt{{t}^{\mathrm{2}} +{t}+\frac{\mathrm{1}}{\mathrm{4}}}{dt} \\ $$$$\mathrm{6}\int\sqrt{\left({t}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{dt} \\ $$$$\mathrm{6}\int\left({t}^{\mathrm{2}}…
Question Number 169600 by bounhome last updated on 04/May/22 $${give}\::\:{x},{y},{z}\in\mathbb{R}\: \\ $$$${x}+{y}+{xy}=\mathrm{8} \\ $$$${y}+{z}+{yz}=\mathrm{15} \\ $$$${z}+{x}+{zx}=\mathrm{35} \\ $$$$\Rightarrow{x}+{y}+{z}+{xyz}=? \\ $$ Commented by infinityaction last updated…
Question Number 104046 by mathocean1 last updated on 19/Jul/20 $$\mathrm{To}\:\mathrm{do}\:\mathrm{normally}\:\mathrm{his}\:\mathrm{commercial} \\ $$$$\mathrm{activities}\:\mathrm{in}\:\mathrm{some}\:\mathrm{place}\:\mathrm{situated}\:\mathrm{at}\:\mathrm{150km} \\ $$$$\mathrm{from}\:\mathrm{him},\:\mathrm{a}\:\mathrm{driver}\:\mathrm{use}\:\mathrm{a}\:\mathrm{car}.\:\mathrm{the}\:\mathrm{consumption} \\ $$$$\mathrm{of}\:\mathrm{gazoil}\:\mathrm{in}\:\mathrm{liters}\:\mathrm{for}\:\mathrm{10}\:\mathrm{km}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by}: \\ $$$$\mathrm{C}\left(\mathrm{v}\right)=\frac{\mathrm{20}}{\mathrm{v}}+\frac{\mathrm{v}}{\mathrm{45}}\:\mathrm{where}\:\mathrm{v}\:\mathrm{is}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{car}. \\ $$$$\mathrm{How}\:\mathrm{should}\:\mathrm{be}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{car}\:\mathrm{to}\:\mathrm{reduce} \\ $$$$\mathrm{minimally}\:\mathrm{the}\:\mathrm{consumption}\:\mathrm{of}\:\mathrm{gazoil}? \\ $$ Commented…
Question Number 169573 by mathocean1 last updated on 03/May/22 $${find}\:{real}\:{matrix}\:{A}\:{such}\:{that}: \\ $$$${t}_{{A}} ×{A}={O}\:,\:{where}\:{O}\:{is}\:{null}\:{marix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 104034 by mohammad17 last updated on 19/Jul/20 $${Solve}:\:{y}^{''} +\mathrm{2}{y}^{'} +\mathrm{2}{y}={secax} \\ $$ Answered by bramlex last updated on 19/Jul/20 $${HE}\::\:\ell^{\mathrm{2}} +\mathrm{2}\ell+\mathrm{2}=\mathrm{0} \\ $$$$\left(\ell+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 169497 by Huy last updated on 01/May/22 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{functions}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{a}{f}\left(\mathrm{b}\right)+\mathrm{b}{f}\left(\mathrm{a}\right)=\left(\mathrm{a}+\mathrm{b}\right){f}\left(\sqrt{\mathrm{ab}}\right)\:\forall\mathrm{ab}>\mathrm{0} \\ $$ Answered by aleks041103 last updated on 02/May/22 $${let}\:{a}={x},\:{b}={x}+\mathrm{2}{dx} \\ $$$$\sqrt{{ab}}=\sqrt{{x}\left({x}+\mathrm{2}{dx}\right)}={x}\left(\mathrm{1}+\mathrm{2}\frac{{dx}}{{x}}\right)^{\mathrm{1}/\mathrm{2}} ={x}+{dx}…
Question Number 169466 by BHOOPENDRA last updated on 30/Apr/22 Answered by mr W last updated on 01/May/22 $${deflection}\:{at}\:{center}\:{of}\:{simple}\:{beam}\: \\ $$$${under}\:{uniform}\:{load}\:{is} \\ $$$$\delta=\frac{\mathrm{5}{wl}^{\mathrm{4}} }{\mathrm{384}{EI}} \\ $$$$\Rightarrow{EI}=\frac{\mathrm{5}{wl}^{\mathrm{4}}…