Question Number 220456 by Nicholas666 last updated on 12/May/25 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:{a},\:{b},\:{c},\:{d}\:\geqslant\:\mathrm{1}\:\:\:\:\:\:;\:\:\:{a}\:+\:{b}\:+\:{c}\:=\:{d} \\ $$$$\:\:\:\:\:\:\:\:{show}\:{that};\: \\ $$$$\:\:\:{ab}\:+\:{bc}\:+\:{ca}\:+\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:\geqslant\:\mathrm{2}{d}\:−\:\mathrm{3}\:+\:\frac{\mathrm{9}}{{d}}\:\:\:\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 220457 by hardmath last updated on 12/May/25 $$\mathrm{Find}:\:\:\:\boldsymbol{\Omega}\:=\:\int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} \:\frac{\left(\mathrm{x}+\mathrm{1}\right)\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)\mathrm{ln}\left(\mathrm{y}^{\mathrm{3}} +\mathrm{1}\right)}{\mathrm{xy}\left(\mathrm{y}^{\mathrm{2}} +\mathrm{1}\right)}\:\mathrm{dxdy}\:=\:? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 220393 by Hanuda354 last updated on 12/May/25 Commented by Hanuda354 last updated on 12/May/25 $$\mathrm{ABCD}\:\:\mathrm{is}\:\:\mathrm{a}\:\:\mathrm{square}.\:\mathrm{Find}\:\:\mathrm{the}\:\:\mathrm{value}\:\:\mathrm{of}\:\:{x}. \\ $$ Answered by mr W last updated…
Question Number 220459 by mr W last updated on 12/May/25 $${find}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} +{a}^{\mathrm{2}} }=?\:\:\:\:\:\:\:\:\:\:\left({a}\in{R}\right) \\ $$ Answered by MrGaster last updated on 13/May/25 Commented…
Question Number 220395 by hardmath last updated on 12/May/25 $$\mathrm{Find}:\:\:\:\Omega\:=\underset{\boldsymbol{\mathrm{x}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\underset{\boldsymbol{\mathrm{y}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:\mathrm{y}^{\mathrm{3}} \:\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\left(\mathrm{y}\:+\:\mathrm{2}\right)}\:=\:? \\ $$ Answered by MathematicalUser2357 last updated on…
Question Number 220388 by MrGaster last updated on 12/May/25 Commented by MrGaster last updated on 12/May/25 When\(n\)is an integer and\(x\)is a positive number,is the sum of\(J_n(x)\cdot J{n+2}(x)\)over\(n\)equal to 0?If so,how to prove it? Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 220454 by PaulDirac last updated on 12/May/25 $$\:\mathrm{In}\:\mathrm{the}\:{CO}_{\mathrm{2}} \:\mathrm{molecule},\:\mathrm{each}\:\mathrm{oxygen}\:\mathrm{atom}\:\mathrm{forms}\:\mathrm{a}\:\mathrm{double}\:\mathrm{bond}\:\mathrm{with}\:\mathrm{central}\:\mathrm{carbon}\:\mathrm{atom}. \\ $$$$\:\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{Bohr}\:\mathrm{radius}\:\left({a}_{{o}} \right)\:\mathrm{is}\:\mathrm{approximately}\:\mathrm{0}.\mathrm{529}\:\overset{\mathrm{o}} {\mathrm{A}}\:\mathrm{and}\:\mathrm{the}\:\mathrm{experimental}\:{C}={O}\: \\ $$$$\:\:\mathrm{bond}\:\mathrm{length}\:\mathrm{is}\:\mathrm{about}\:\mathrm{1}.\mathrm{16}\:\overset{\mathrm{o}\:} {\mathrm{A}},\:\mathrm{calculate}\:: \\ $$$$\: \\ $$$$\left.\:\mathrm{a}\right)\:\mathrm{The}\:\mathrm{approximate}\:\mathrm{region}\:\left(\mathrm{in}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{Bohr}\:\mathrm{radii}\right)\:\mathrm{where}\:\mathrm{the}\:\mathrm{shared}\:\mathrm{electrons}\:\mathrm{are} \\ $$$$\:\mathrm{most}\:\mathrm{likely}\:\mathrm{to}\:\mathrm{be}\:\mathrm{found}\:\mathrm{between}\:{C}\:\mathrm{and}\:{O}. \\…
Question Number 220390 by MATHEMATICSAM last updated on 12/May/25 $$\mathrm{sin}\theta\:+\:\mathrm{sin}\left(\pi\:+\:\theta\right)\:+\:\mathrm{sin}\left(\mathrm{2}\pi\:+\:\theta\right)\:+\:…\: \\ $$$$+\:\mathrm{sin}\left({n}\pi\:+\:\theta\right)\:=\:?\:\mathrm{when}\:{n}\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd} \\ $$$$\mathrm{integer}. \\ $$ Answered by mr W last updated on 12/May/25 $$\mathrm{sin}\:\left({k}\pi+\theta\right)=\mathrm{sin}\:{k}\pi\:\mathrm{cos}\:\theta+\mathrm{cos}\:{k}\pi\:\mathrm{sin}\:\theta…
Question Number 220391 by Lekhraj last updated on 12/May/25 Answered by MathematicalUser2357 last updated on 13/May/25 $${yes} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 220380 by MrGaster last updated on 12/May/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}tan}\left[\frac{\pi}{\mathrm{4}}+\frac{\mathrm{1}}{{n}}\right]^{{n}} =? \\ $$ Answered by SdC355 last updated on 12/May/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:\mathrm{tan}\left(\left(\frac{\pi}{\mathrm{4}}+\frac{\mathrm{1}}{{n}}\right)^{{n}} \right)=\mathrm{tan}\left(\mathrm{0}\right)=\mathrm{0} \\…