Question Number 205599 by mnjuly1970 last updated on 25/Mar/24 $$ \\ $$$$\:{laplace}\:{transform}… \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\mathscr{L}\:\left\{\:\:{sin}\left(\sqrt{{t}}\:\right)\right\}\:=? \\ $$$$−−−− \\ $$ Commented by SANOGO last updated…
Question Number 205625 by Lindemann last updated on 25/Mar/24 $$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$ Answered by mathzup last updated on 25/Mar/24 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{4}}…
Question Number 205626 by mr W last updated on 25/Mar/24 $${if}\:{a}+{b}+{c}=\frac{\mathrm{1}}{{a}+\mathrm{1}}+\frac{\mathrm{1}}{{b}+\mathrm{2}}+\frac{\mathrm{1}}{{c}+\mathrm{3}}=\mathrm{0}, \\ $$$${find}\:\left({a}+\mathrm{1}\right)^{\mathrm{2}} +\left({b}+\mathrm{2}\right)^{\mathrm{2}} +\left({c}+\mathrm{3}\right)^{\mathrm{2}} =? \\ $$ Answered by A5T last updated on 25/Mar/24…
Question Number 205594 by cortano12 last updated on 25/Mar/24 Answered by Red1ight last updated on 25/Mar/24 $${y}^{\mathrm{2}} =\mathrm{4}{x} \\ $$$${y}=\mathrm{2}\sqrt{{x}} \\ $$$$\frac{{dy}}{{dx}}=\frac{\mathrm{1}}{\:\sqrt{{x}}}=\frac{\mathrm{2}}{{y}} \\ $$$$\left({x}_{\mathrm{0}} ,{y}_{\mathrm{0}}…
Question Number 205627 by lmcp1203 last updated on 25/Mar/24 Answered by Rasheed.Sindhi last updated on 27/Mar/24 $$\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet\Bumpeq\bullet \\ $$$$\mathrm{2},\mathrm{6},\mathrm{12},\mathrm{20},\mathrm{30},…,{i}^{\mathrm{2}} +{i} \\ $$$${S}=\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left({i}^{\mathrm{2}} +{i}\right)=\underset{{i}=\mathrm{1}}…
Question Number 205588 by cortano12 last updated on 25/Mar/24 Answered by A5T last updated on 25/Mar/24 Commented by A5T last updated on 25/Mar/24 $${BC}={r}\sqrt{\mathrm{2}};{BD}^{\mathrm{2}} ={r}^{\mathrm{2}}…
Question Number 205590 by Lindemann last updated on 25/Mar/24 $${J}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$ Commented by lepuissantcedricjunior last updated on 25/Mar/24 $$\boldsymbol{{J}}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−\boldsymbol{{x}}^{\mathrm{4}}…
Question Number 205586 by necx122 last updated on 25/Mar/24 $${Givem}\:{that}\:{the}\:{matrix}\:{A}\:=\:\begin{pmatrix}{\mathrm{3}}&{\mathrm{1}}&{\mathrm{5}}\\{\mathrm{2}}&{\mathrm{3}}&{\mathrm{5}}\\{\mathrm{5}}&{\mathrm{1}}&{\mathrm{6}}\end{pmatrix}.\: \\ $$$${If}\:{Adj}.\:{A}\:=\:\begin{pmatrix}{\mathrm{13}}&{-\mathrm{1}}&{-\mathrm{10}}\\{\mathrm{13}}&{-\mathrm{7}}&{-\mathrm{5}}\\{-\mathrm{13}}&{\mathrm{2}}&{\mathrm{7}}\end{pmatrix} \\ $$$$\left({i}\right)\:{find}\:{A}^{−\mathrm{1}} \\ $$$$\left({ii}\right)\:{Use}\:{the}\:{result}\:{in}\:\left({i}\right)\:{to}\:{find}\:{the} \\ $$$${values}\:{of}\:{x},\:{y}\:{and}\:{z}\:{that}\:{will}\:{satisfy}\:{the} \\ $$$${equations}: \\ $$$$\mathrm{3}{x}\:+\:{y}\:+\:\mathrm{5}{z}\:=\:\mathrm{8} \\ $$$$\mathrm{2}{x}\:+\mathrm{3}{y}\:+\:\mathrm{5}{z}\:=\:\mathrm{0} \\…
Question Number 205580 by universe last updated on 25/Mar/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)…\left(\mathrm{4}{n}+\mathrm{1}\right)}{\left(\mathrm{2}{n}\right)\left(\mathrm{2}{n}+\mathrm{2}\right)…\left(\mathrm{4}{n}\right)}\:\:=\:\:? \\ $$ Commented by lepuissantcedricjunior last updated on 26/Mar/24 $$\underset{\boldsymbol{{n}}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{1}\right)×\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{3}\right)×…×\left(\mathrm{4}\boldsymbol{{n}}+\mathrm{1}\right)}{\left(\mathrm{2}\boldsymbol{{n}}\right)×\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{2}\right)×..×\left(\mathrm{4}\boldsymbol{{n}}\right)} \\ $$$$=\underset{\boldsymbol{{n}}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\mathrm{2}\boldsymbol{{n}}\right)\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{1}\right)\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{2}\right)…\left(\mathrm{4}\boldsymbol{{n}}\right)\left(\mathrm{4}\boldsymbol{{n}}+\mathrm{1}\right)}{\left[\left(\mathrm{2}\boldsymbol{{n}}\right)\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{2}\right)….\left(\mathrm{4}\boldsymbol{{n}}\right)\right]^{\mathrm{2}}…
Question Number 205614 by mr W last updated on 25/Mar/24 Answered by A5T last updated on 25/Mar/24 Commented by A5T last updated on 25/Mar/24 $$\frac{{sin}\left(\angle{CFB}\right)}{\mathrm{1}}=\frac{{sin}\mathrm{90}=\mathrm{1}}{\:\sqrt{\mathrm{0}.\mathrm{5}^{\mathrm{2}}…