Question Number 219465 by SdC355 last updated on 26/Apr/25 $${prove} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\:\sqrt{{r}^{\mathrm{2}} −{t}^{\mathrm{2}} }{e}^{−{pt}} \mathrm{d}{t}=\frac{−{r}\pi\boldsymbol{\mathrm{L}}_{\mathrm{1}} \left({rp}\right)+\pi{rI}_{\mathrm{1}} \left({up}\right)+\mathrm{2}\boldsymbol{{i}}{rK}_{\mathrm{1}} \left({rp}\right)}{\mathrm{2}{p}} \\ $$$$\boldsymbol{\mathrm{L}}_{\nu} \left({x}\right)\:\mathrm{is}\:\mathrm{Modified}\:\mathrm{Struve}\:\mathrm{function} \\ $$$${I}_{\nu}…
Question Number 219492 by hardmath last updated on 26/Apr/25 $$\mathrm{a}\:+\:\mathrm{b}\:=\:\mathrm{1} \\ $$$$\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{2} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{a}^{\mathrm{11}} \:+\:\mathrm{b}^{\mathrm{11}} \:=\:? \\ $$ Answered by mr W last…
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 $$\frac{\mathrm{d}{y}}{\mathrm{d}{t}}+\mathrm{2}{ty}\left({t}\right)=\mathrm{2}{e}^{−{t}^{\mathrm{2}} }…
Question Number 219491 by OmoloyeMichael last updated on 26/Apr/25 $$\boldsymbol{{if}}\:\boldsymbol{{x}}''−\mathrm{2}\boldsymbol{{x}}'+\mathrm{10}\boldsymbol{{x}}=\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{{t}}} ,\:\boldsymbol{{at}}\:\boldsymbol{{t}}=\mathrm{0},\boldsymbol{{x}}=\mathrm{0}\:\boldsymbol{{and}}\:\boldsymbol{{x}}'=\mathrm{1} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{x}}\left(\boldsymbol{{t}}\right)\:\boldsymbol{{using}}\:\boldsymbol{{laplace}}\:\boldsymbol{{transform}} \\ $$ Answered by mahdipoor last updated on 26/Apr/25 $${Laplace}\:\Rightarrow \\ $$$$\left({Xs}^{\mathrm{2}}…
Question Number 219453 by Nicholas666 last updated on 25/Apr/25 $$ \\ $$$$\:\:\int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \int_{\mathrm{1}} ^{\:\mathrm{2}} \:\frac{{x}_{\mathrm{1}} +{x}_{\mathrm{2}\:} +{x}_{\mathrm{3}} −{x}_{\mathrm{4}} }{{x}_{\mathrm{1}} +{x}_{\mathrm{2}}…
Question Number 219454 by mr W last updated on 25/Apr/25 $${a},\:{b},\:{c}\:{are}\:{the}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{1}=\mathrm{0}. \\ $$$${find}\:\sqrt[{\mathrm{3}}]{{a}}+\sqrt[{\mathrm{3}}]{{b}}+\sqrt[{\mathrm{3}}]{{c}}=?\:\&\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{a}}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{b}}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{c}}}=? \\ $$ Commented by mr W last updated on…
Question Number 219448 by hardmath last updated on 25/Apr/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219449 by Lukos last updated on 25/Apr/25 $${L}\left\{{sinx}\right\}=\int_{\mathrm{0}} ^{\infty} {e}^{−{sx}} {sinx}\:{dx}=\int_{\mathrm{0}} ^{\infty} {e}^{−{sx}} \frac{{e}^{{ix}} −{e}^{−{ix}} }{\mathrm{2}{i}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}{i}}\left[\int_{\mathrm{0}} ^{\infty} {e}^{−\left({s}−{i}\right){x}} {dx}\:\:−\int_{\mathrm{0}} ^{\infty} {e}^{−\left({s}+{i}\right){x}}…
Question Number 219450 by hardmath last updated on 25/Apr/25 Commented by mr W last updated on 25/Apr/25 $${the}\:{geometry}\:{is}\:{not}\:{uniquely}\:{defined}. \\ $$$${you}\:{can}'{t}\:{determine}\:\angle{CDO}\:{with} \\ $$$${given}\:{conditions}. \\ $$ Commented…
Question Number 219451 by Nicholas666 last updated on 25/Apr/25 Commented by Nicholas666 last updated on 25/Apr/25 $$\mathrm{This}\:\mathrm{is}\:\mathrm{problem}\:\mathrm{is}\:\mathrm{beyond}\:\mathrm{My}\:\mathrm{control},\:\:\: \\ $$$$\:\mathrm{can}\:\mathrm{You}\:\mathrm{solve}\:\mathrm{friends}? \\ $$$$ \\ $$ Terms of…