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}}…
Question Number 219519 by OmoloyeMichael last updated on 27/Apr/25 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{laplace}}\:\boldsymbol{{transform}}\:\boldsymbol{{of}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \boldsymbol{{te}}^{−\mathrm{2}\boldsymbol{{t}}} \boldsymbol{{sintdt}} \\ $$ Answered by SdC355 last updated on 27/Apr/25 $$\mathrm{First}\:\mathrm{idea}..\mathrm{Let}'\mathrm{s}\:\mathrm{define}\:{F}\left({s}\right)\:\mathrm{as}\:…
Question Number 219520 by OmoloyeMichael last updated on 27/Apr/25 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{laplace}}\:\boldsymbol{{transform}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{t}}\right)=\int_{\mathrm{0}} ^{\boldsymbol{{t}}} \frac{\boldsymbol{{sint}}}{\boldsymbol{{t}}}\boldsymbol{{dt}} \\ $$ Answered by SdC355 last updated on 27/Apr/25 $$\int_{\mathrm{0}} ^{\:{T}}…
Question Number 219521 by OmoloyeMichael last updated on 27/Apr/25 Commented by OmoloyeMichael last updated on 27/Apr/25 $$\boldsymbol{{help}}\:\boldsymbol{{me}}\:\boldsymbol{{with}}\:\boldsymbol{{question}}\:\mathrm{4} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 219486 by OmoloyeMichael last updated on 26/Apr/25 Commented by OmoloyeMichael last updated on 26/Apr/25 $$\boldsymbol{{please}}\:\boldsymbol{{help}}\:\boldsymbol{{me}}\:\boldsymbol{{with}}\:\boldsymbol{{question}}\:\mathrm{4} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 219488 by OmoloyeMichael last updated on 26/Apr/25 $$\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{initial}}\:\boldsymbol{{value}}\:\boldsymbol{{problem}}\: \\ $$$$\boldsymbol{{y}}'−\mathrm{2}\boldsymbol{{e}}^{−\boldsymbol{{t}}^{\mathrm{2}} } +\mathrm{2}\boldsymbol{{ty}}=\mathrm{0}\:\:\boldsymbol{{y}}\left(\mathrm{0}\right)=\mathrm{1} \\ $$ Answered by SdC355 last updated on 26/Apr/25 $$\frac{\mathrm{d}{y}}{\mathrm{d}{t}}+\mathrm{2}{ty}\left({t}\right)=\mathrm{2}{e}^{−{t}^{\mathrm{2}} }…