Question Number 217256 by mnjuly1970 last updated on 07/Mar/25 Answered by mr W last updated on 08/Mar/25 Commented by mr W last updated on 08/Mar/25…
Question Number 217252 by mr W last updated on 07/Mar/25 Commented by mr W last updated on 07/Mar/25 $${As}\:{Q}\mathrm{217238},\:{but}\:{the}\:{other}\:{end}\:{of} \\ $$$${the}\:{string}\:{is}\:{connected}\:{with}\:{a}\:{block} \\ $$$${with}\:{mass}\:{m}\:{which}\:{can}\:{slide}\:{on}\:{the} \\ $$$${table}\:{frictionlessly}.…
Question Number 217255 by MrGaster last updated on 07/Mar/25 $$\int_{−\infty} ^{+\infty} {e}^{−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}} {dx}=\sqrt{\mathrm{2}\pi},\int_{−\infty} ^{+\infty} {e}^{−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+{x}} {dx}. \\ $$ Answered by vnm last updated…
Question Number 217228 by Tawa11 last updated on 06/Mar/25 Answered by mr W last updated on 06/Mar/25 $${I}=\frac{{mr}^{\mathrm{2}} }{\mathrm{2}} \\ $$$${KE}=\frac{{I}\omega^{\mathrm{2}} }{\mathrm{2}}+\frac{{m}\left({r}\omega\right)^{\mathrm{2}} }{\mathrm{2}}=\frac{{I}\omega^{\mathrm{2}} }{\mathrm{2}}+{I}\omega^{\mathrm{2}} =\frac{\mathrm{3}{I}\omega^{\mathrm{2}}…
Question Number 217225 by hardmath last updated on 06/Mar/25 $$\mathrm{Find}:\:\:\:\:\:\int\:−\:\frac{{d}\mathrm{x}}{\:\sqrt{\mathrm{24x}\:−\:\mathrm{16x}^{\mathrm{2}} \:−\:\mathrm{8}}}\:=\:? \\ $$ Answered by Frix last updated on 06/Mar/25 $$−\int\frac{{dx}}{\:\sqrt{−\mathrm{16}{x}^{\mathrm{2}} +\mathrm{24}{x}−\mathrm{8}}}\:\overset{\left[{t}=\mathrm{sin}^{−\mathrm{1}} \:\left(\mathrm{4}{x}−\mathrm{3}\right)\right]} {=} \\…
Question Number 217211 by Ghisom last updated on 06/Mar/25 $$\mathrm{a}\:\mathrm{nice}\:\mathrm{one}: \\ $$$$\mathrm{prove}\:\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\sqrt{−\frac{\mathrm{ln}\:{t}}{{t}}}\:{dt}=\sqrt{\mathrm{2}\pi} \\ $$ Answered by MrGaster last updated on 06/Mar/25 $$\left(\mathrm{1}\right):\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 217238 by Tawa11 last updated on 06/Mar/25 Answered by mr W last updated on 07/Mar/25 $$\alpha=\frac{{a}}{{R}} \\ $$$${I}=\frac{{MR}^{\mathrm{2}} }{\mathrm{2}} \\ $$$${Mg}−{T}={Ma}\:\:\:…\left({i}\right) \\ $$$$\frac{{MR}^{\mathrm{2}}…
Question Number 217235 by Tawa11 last updated on 06/Mar/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{x}\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{1}\:\:+\:\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Answered by MrGaster last updated on 06/Mar/25 $$=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 217219 by mnjuly1970 last updated on 06/Mar/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{calculate} \\ $$$$\begin{array}{|c|}{\:\:\mathscr{L}\:\:\left(\:\int_{\mathrm{1}} ^{\:\infty} \frac{\:\mathrm{e}^{\:−{tx}} }{{x}}{dx}\:\right)\:\underset{\mathrm{transfom}} {\overset{\mathrm{laplace}} {=}}?\:\:;\:\:{t}>\mathrm{0}\:}\\\hline\end{array} \\ $$$$ \\ $$$$\:\:\: \\ $$…
Question Number 217197 by hardmath last updated on 05/Mar/25 $$\mathrm{Find}: \\ $$$$\sqrt[{\mathrm{5}}]{−\mathrm{32}}\:\:+\:\:\sqrt[{\mathrm{8}}]{\left(−\mathrm{3}\right)^{\mathrm{8}} }\:\:=\:\:? \\ $$ Answered by Rasheed.Sindhi last updated on 05/Mar/25 $$\sqrt[{\mathrm{5}}]{−\mathrm{32}}\:\:+\:\:\sqrt[{\mathrm{8}}]{\left(−\mathrm{3}\right)^{\mathrm{8}} }\: \\…