Question Number 184093 by Ib last updated on 02/Jan/23 Answered by manxsol last updated on 03/Jan/23 $$\left(\mathrm{1}+\frac{{t}}{\mathrm{100}}\right)^{\mathrm{10}} =\mathrm{3} \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{\left(\frac{\mathrm{100}}{{t}}\right)}\right)^{\mathrm{10}} =\mathrm{3} \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{\left(\frac{\mathrm{100}}{{t}}\right)}\right)^{\mathrm{10}×\frac{\mathrm{10}}{{t}}} =\mathrm{3}^{\frac{\mathrm{10}}{{t}}} \\…
Question Number 184098 by paul2222 last updated on 02/Jan/23 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)}{\mathrm{1}−\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}} \\ $$ Commented by paul2222 last updated on 02/Jan/23 $$\boldsymbol{\mathrm{let}}\:\mathrm{1}−\boldsymbol{\mathrm{x}}=\boldsymbol{\mathrm{u}} \\ $$$$\int_{\mathrm{0}}…
Question Number 184091 by Ib last updated on 02/Jan/23 Commented by Ib last updated on 02/Jan/23 $${j}\:{ai}\:{besoin}\:{d}\:{aide} \\ $$$$ \\ $$$$ \\ $$ Answered by…
Question Number 184076 by liuxinnan last updated on 02/Jan/23 $$\mathrm{6647}^{\mathrm{3}} {mod}\mathrm{10000}=\mathrm{2023} \\ $$ Commented by liuxinnan last updated on 02/Jan/23 $${maybe}\:{there}\:{are}\:{other}\:{number} \\ $$$${a}^{{n}} {mod}\mathrm{10000}=\mathrm{2023} \\…
Question Number 184066 by Matica last updated on 02/Jan/23 $$\frac{{dy}}{{dx}}={y}\left({y}+\mathrm{2}\right).\:{find}\:\:{y}=? \\ $$ Answered by mr W last updated on 02/Jan/23 $$\int\frac{{dy}}{{y}\left({y}+\mathrm{2}\right)}=\int{dx} \\ $$$$\int\left(\frac{\mathrm{1}}{{y}}−\frac{\mathrm{1}}{{y}+\mathrm{2}}\right){dy}=\mathrm{2}\int{dx} \\ $$$$\mathrm{ln}\:{y}−\mathrm{ln}\:\left({y}+\mathrm{2}\right)=\mathrm{2}{x}+{C}_{\mathrm{1}}…
Question Number 184062 by CrispyXYZ last updated on 02/Jan/23 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\:\sqrt{{i}^{\mathrm{2}} +{i}}}\:>\:\mathrm{ln}\left({n}+\mathrm{1}\right) \\ $$ Answered by mr W last updated on 02/Jan/23…
Question Number 118511 by ZiYangLee last updated on 18/Oct/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{positive}\:\mathrm{integers}\:{x}\:\mathrm{satisfy} \\ $$$$\mathrm{log}_{\frac{{x}}{\mathrm{8}}} \frac{{x}^{\mathrm{2}} }{\mathrm{4}}<\mathrm{7}+\mathrm{log}_{\mathrm{2}} \frac{\mathrm{8}}{{x}} \\ $$ Answered by mr W last updated on 18/Oct/20…
Question Number 118506 by meireza last updated on 18/Oct/20 Answered by Lordose last updated on 18/Oct/20 $$\sqrt{\mathrm{2}}\mathrm{sin}\left(\mathrm{x}°+\mathrm{15}°\right)=\mathrm{1} \\ $$$$\mathrm{Divide}\:\mathrm{by}\:\sqrt{\mathrm{2}} \\ $$$$\mathrm{sin}\left(\mathrm{x}°+\mathrm{15}°\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$$$\mathrm{take}\:\mathrm{sin}^{−\mathrm{1}} \:\mathrm{of}\:\mathrm{both}\:\mathrm{sides} \\…
Question Number 184037 by liuxinnan last updated on 02/Jan/23 $${i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\underset{{j}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}{ji}^{{j}} =? \\ $$ Answered by SEKRET last updated on 02/Jan/23…
Question Number 184029 by SEKRET last updated on 02/Jan/23 $$\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\boldsymbol{\mathrm{x}}−\mathrm{1}}{\boldsymbol{\mathrm{x}}+\mathrm{1}}\centerdot\frac{\mathrm{1}}{\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}\right)}\:\boldsymbol{\mathrm{dx}}\:=? \\ $$ Answered by ARUNG_Brandon_MBU last updated on 02/Jan/23 $$\Omega\left(\alpha\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\alpha} −\mathrm{1}}{{x}+\mathrm{1}}\centerdot\frac{\mathrm{1}}{\mathrm{ln}{x}}{dx}…