Question Number 220019 by fantastic last updated on 04/May/25 $${please}\:{help}\:{me}\:.{The}\:{photos}\:{I}\:{upload} \\ $$$${becomes}\:{blurred} \\ $$$${HELP}\:{please} \\ $$ Commented by Tinku Tara last updated on 05/May/25 $$\mathrm{Please}\:\mathrm{upload}\:\mathrm{smaller}\:\mathrm{pictures}…
Question Number 220007 by Noorzai last updated on 04/May/25 Commented by MrGaster last updated on 04/May/25 conditions are not enough and the meaning is unclear, please add or upload again if there is anything that has not been added. Answered by efronzo1 last updated on 04/May/25 $$\:{a}^{\mathrm{3}}…
Question Number 219988 by Nicholas666 last updated on 04/May/25 $$ \\ $$$$\:\:\:\:\mathrm{let}\:{s}>\mathrm{1}\:\mathrm{be}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number}.\:\mathrm{for}\:\mathrm{all}\:\mathrm{continues}\:\mathrm{function}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$$\:\:\:\mathrm{such}\:\mathrm{that}\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} {f}\left({x}\right)=\mathrm{0},\:\mathrm{determind}\:\mathrm{of}\:\mathrm{the}\:\mathrm{exist}\:\mathrm{a} \\ $$$$\:\:\:\:\:\mathrm{positive}\:\mathrm{constant}\:{K}\left({s}\right)\:\mathrm{statisfying}: \\ $$$$\:\:\:\left(\int_{\mathrm{0}} ^{\:\mathrm{1}} {f}\left({x}\right)\centerdot\mathrm{Li}_{{s}} \left({x}\right){dx}\right)^{\mathrm{2}} \geqslant{K}\left({s}\right)\int_{\:\mathrm{0}} ^{\:\mathrm{1}}…
Question Number 220034 by Tawa11 last updated on 04/May/25 Answered by efronzo1 last updated on 04/May/25 $$\:\left(\mathrm{1}\right)\:\mathrm{x}^{\mathrm{2}} \:=\:\mathrm{96}{a} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{96}{b} \\ $$$$\:\left(\mathrm{3}\right)\:{a}+{b}\:=\:\mathrm{96}\Rightarrow{b}=\:\mathrm{96}−{a} \\ $$$$\:\Rightarrow\:\mathrm{36}^{\mathrm{2}}…
Question Number 219724 by Nicholas666 last updated on 01/May/25 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{prove}; \\ $$$$\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{3}} −\mathrm{3}\left(\mathrm{2}{n}+\mathrm{1}\right)+\mathrm{2}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{3}} }\:=\:\frac{\pi}{\mathrm{6}} \\ $$$$ \\ $$ Answered by nothing48 last updated…
Question Number 219676 by mathkun last updated on 30/Apr/25 $$\mathrm{The}\:\mathrm{latex}\:\mathrm{converter}\:\mathrm{is}\:\mathrm{not}\:\mathrm{converting}\:\mathrm{some}\:\mathrm{symbols}.\:\mathrm{Any}\:\mathrm{reason}\:\mathrm{why}?\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219624 by Nicholas666 last updated on 29/Apr/25 Answered by A5T last updated on 29/Apr/25 $$\Sigma\mathrm{a}\sqrt{\mathrm{a}^{\mathrm{3}} +\mathrm{15}}\leqslant\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} +\mathrm{d}^{\mathrm{2}} }\sqrt{\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} +\mathrm{c}^{\mathrm{3}} +\mathrm{d}^{\mathrm{3}}…
Question Number 219606 by Nicholas666 last updated on 29/Apr/25 $$ \\ $$$$\:\mathrm{prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers}\:{a},{b},{c},\:\:\: \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{inequality}\:\mathrm{holds}; \\ $$$$\:\:\frac{{a}^{\mathrm{2}} }{{b}\:+\:{c}}\:+\:\frac{{b}^{\mathrm{2}} }{{c}\:+\:{a}}\:+\:\frac{{c}^{\mathrm{2}} }{{a}\:+\:{b}}\:\:\geqslant\:\frac{{a}\:+\:{b}\:+\:{c}}{\mathrm{2}} \\ $$$$ \\ $$ Answered by…
Question Number 219589 by Nicholas666 last updated on 29/Apr/25 $${Evaluate};\:\mathscr{L}\left({tan}^{−\mathrm{1}} \left({t}−\frac{\mathrm{1}}{{t}}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{solution}; \\ $$$$\:\Rightarrow{F}\left({s}\right)=\:\mathscr{L}\left({tan}^{−\mathrm{1}} \left({t}−\frac{\mathrm{1}}{{t}}\right)\right) \\ $$$$\Leftrightarrow\:{sF}\left({s}\right)+\frac{\pi}{\mathrm{2}}=\mathscr{L}\left(\frac{{t}^{\mathrm{2}} +\mathrm{1}}{{t}^{\mathrm{4}} −{t}^{\mathrm{2}} +\mathrm{1}}\right)\left({s}\right) \\ $$$$\Rightarrow\:{sF}\left({s}\right)+\frac{\pi}{\mathrm{2}}=\mathscr{L}\left(\frac{\frac{\mathrm{1}}{\mathrm{2}}}{{t}^{\mathrm{2}} −\sqrt{\mathrm{3}}\:{t}\:+\mathrm{1}}+\frac{\frac{\mathrm{1}}{\mathrm{2}}}{{t}^{\mathrm{2}} −\sqrt{\mathrm{3}}\:{t}+\mathrm{1}}\right)\left({s}\right)…
Question Number 219587 by Nicholas666 last updated on 29/Apr/25 Commented by Nicholas666 last updated on 29/Apr/25 https://www.quora.com/profile/Bekicot-5/math-math-If-math-a-b-0-math-and-math-a-b-frac-2-3-math-Then-math-frac-b-3-3a-2-frac-a?ch=10&oid=221057452&share=32d38051&srid=5Xg5SU&target_type=post Answered by Ghisom last updated on 29/Apr/25 $${a},\:{b}>\mathrm{0}\wedge{a}+{b}=\frac{\mathrm{2}}{\mathrm{3}}\:\Rightarrow\:\mathrm{0}<{a},\:{b}<\frac{\mathrm{2}}{\mathrm{3}}…