Question Number 164609 by SANOGO last updated on 19/Jan/22 $${en}\:{posant}\:{x}={t}−\frac{\mathrm{1}}{{t}} \\ $$$$\underset{\mathrm{0}} {\int}^{+{oo}} \frac{\mathrm{1}+{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{4}} }{dt} \\ $$ Answered by Mathspace last updated on 19/Jan/22…
Question Number 164591 by SANOGO last updated on 19/Jan/22 $${pour}\:{quelle}\:{valeur}\:\alpha\:{la}\:{serie}\:{converge} \\ $$$$\underset{{n}=\mathrm{2}} {\sum}\left({ln}\left({n}\right)+\alpha{ln}\left({n}−\frac{\mathrm{1}}{{n}}\right)\right. \\ $$ Answered by mindispower last updated on 19/Jan/22 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{ln}\left({n}\right)+{aln}\left({n}−\frac{\mathrm{1}}{\left.{n}\right)}\right. \\…
Question Number 99055 by Ar Brandon last updated on 18/Jun/20 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{arcosh}\left(\frac{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\right)\:? \\ $$ Commented by mathmax by abdo last updated on…
Question Number 33511 by mondodotto@gmail.com last updated on 18/Apr/18 $$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:'\boldsymbol{\mathrm{k}}'\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}} \\ $$$$\boldsymbol{\mathrm{k}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} \right)+\left(\boldsymbol{{y}}−\mathrm{2}\boldsymbol{{x}}+\mathrm{1}\right)\left(\boldsymbol{{y}}+\mathrm{2}\boldsymbol{{x}}+\mathrm{3}\right)=\mathrm{0} \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{circle}}.\boldsymbol{\mathrm{Hence}}\:\boldsymbol{\mathrm{obtain}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{centre}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{resulting}}\:\boldsymbol{\mathrm{circle}}. \\ $$ Answered by MJS last updated…
Question Number 33513 by mondodotto@gmail.com last updated on 18/Apr/18 $$\boldsymbol{\mathrm{In}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{recent}}\:\boldsymbol{\mathrm{pool}}\:\boldsymbol{\mathrm{of}}\:\mathrm{500}\:\boldsymbol{\mathrm{men}}\:\boldsymbol{\mathrm{and}}\:\mathrm{500}\:\boldsymbol{\mathrm{women}} \\ $$$$\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{was}}\:\boldsymbol{\mathrm{observed}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{total}}\:\boldsymbol{\mathrm{of}}\:\mathrm{650}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{married}}. \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{those}}\:\boldsymbol{\mathrm{married}}\:\mathrm{275}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{men}}\:\boldsymbol{\mathrm{and}}\:\mathrm{500} \\ $$$$\boldsymbol{\mathrm{claimed}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{happy}}.\boldsymbol{\mathrm{out}}\:\boldsymbol{\mathrm{of}}\:\mathrm{750}\:\boldsymbol{\mathrm{who}}\:\boldsymbol{\mathrm{claimed}} \\ $$$$\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{happy}},\mathrm{400}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{men}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{which}}\:\mathrm{200} \\ $$$$\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{married}}.\boldsymbol{\mathrm{Represent}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{information}} \\ $$$$\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{venn}}−\boldsymbol{\mathrm{diagram}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{find}} \\ $$$$\left(\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{married}}\:\boldsymbol{\mathrm{who}}\: \\…
Question Number 99025 by joki last updated on 18/Jun/20 Commented by bobhans last updated on 18/Jun/20 $$\mathrm{set}\:\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−…}}}\:=\:{q} \\ $$$$\mathrm{2207}−\frac{\mathrm{1}}{{q}}\:=\:{q}\:\Rightarrow{q}^{\mathrm{2}} −\mathrm{2207}{q}+\mathrm{1}=\mathrm{0} \\ $$$${q}=\:\frac{\mathrm{2207}\:\pm\:\sqrt{\mathrm{4870845}}}{\mathrm{2}}\:=\:\frac{\mathrm{2207}\:\pm\:\mathrm{2207}}{\mathrm{2}} \\ $$$$\mathrm{case}\left(\mathrm{1}\right)\:{q}\:=\:\mathrm{2207}\:\Rightarrow\sqrt[{\mathrm{8}\:\:}]{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−…}}}=\:\sqrt[{\mathrm{8}\:\:\:}]{\mathrm{2207}}\:\approx\:\mathrm{2}.\mathrm{618034056} \\…
Question Number 164560 by PRITHWISH SEN 2 last updated on 18/Jan/22 $$\mathrm{6}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{6}\:\mathrm{girls}\:\mathrm{go}\:\mathrm{to}\:\mathrm{an}\:\mathrm{exhibition}\:\mathrm{and}\:\mathrm{the}\:\mathrm{cost} \\ $$$$\mathrm{of}\:\mathrm{ticket}\:\mathrm{is}\:\mathrm{Rs}\:\mathrm{10}.\mathrm{Each}\:\mathrm{girl}\:\mathrm{has}\:\mathrm{a}\:\mathrm{10}\:\mathrm{rupees}\:\mathrm{note} \\ $$$$\mathrm{while}\:\mathrm{each}\:\mathrm{boy}\:\mathrm{has}\:\mathrm{a}\:\mathrm{20}\:\mathrm{rupees}\:\mathrm{note}.\:\mathrm{They}\:\mathrm{stand}\: \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{queue}\:\mathrm{at}\:\mathrm{the}\:\mathrm{counter}\:\mathrm{and}\:\mathrm{the}\:\mathrm{cashier}\:\mathrm{does} \\ $$$$\mathrm{not}\:\mathrm{have}\:\mathrm{any}\:\mathrm{money}\:\mathrm{at}\:\mathrm{the}\:\mathrm{begining}\:,\:\mathrm{then}\:\mathrm{the}\: \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{of}\:\mathrm{arranging}\:\mathrm{the}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{girls} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{no}\:\mathrm{one}\:\mathrm{waits}\:\mathrm{for}\:\mathrm{a}\:\mathrm{change}\:\mathrm{is} \\…
Question Number 33494 by mondodotto@gmail.com last updated on 17/Apr/18 $$\:\int\frac{\boldsymbol{\mathrm{e}}^{\boldsymbol{{x}}} }{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{{x}}\:\:\:\:}\boldsymbol{{dx}} \\ $$ Commented by math khazana by abdo last updated on 18/Apr/18 $$\int\:\:\:\:\frac{{e}^{{x}}…
Question Number 164553 by mkam last updated on 18/Jan/22 Commented by tabata last updated on 18/Jan/22 $$???? \\ $$ Answered by mathmax by abdo last…
Question Number 99023 by joki last updated on 18/Jun/20 Commented by bobhans last updated on 18/Jun/20 $$\mathrm{x}−\mathrm{y}\:=\:\frac{\left(\mathrm{2012}+\mathrm{2014}\right)^{\mathrm{2}} −\mathrm{2}.\mathrm{2012}.\mathrm{2014}}{\mathrm{4027}}−\:\frac{\left(\mathrm{2013}+\mathrm{2017}\right)^{\mathrm{2}} −\mathrm{2}.\mathrm{2013}.\mathrm{2017}}{\mathrm{4041}} \\ $$$$=\:\frac{\mathrm{4026}^{\mathrm{2}} −\mathrm{8104336}}{\mathrm{4027}}−\:\frac{\mathrm{4030}^{\mathrm{2}} −\mathrm{8120442}}{\mathrm{4041}} \\ $$$$=\frac{\mathrm{8104340}}{\mathrm{4027}}−\:\frac{\mathrm{8120458}}{\mathrm{4041}}\:=\:\mathrm{2}.\mathrm{987628976}…