Question Number 203270 by MrGHK last updated on 13/Jan/24 $$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{last}}\:\mathrm{4}\:\boldsymbol{\mathrm{digits}}\:\boldsymbol{\mathrm{of}}\:\mathrm{2024}^{\mathrm{2023}} \\ $$ Answered by Frix last updated on 14/Jan/24 $$\mathrm{Last}\:\mathrm{4}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{2024}^{{n}} \\ $$$${n}=\mathrm{1}\:\mathrm{2024} \\ $$$$\mathrm{Then}\:\mathrm{a}\:\mathrm{loop}\:\mathrm{of}\:\mathrm{length}\:\mathrm{50} \\…
Question Number 203264 by hardmath last updated on 13/Jan/24 $$\mathrm{If}\:\:\:\:\:\mathrm{x}\:=\:\frac{\mathrm{1}\:+\:\sqrt{\mathrm{5}}}{\mathrm{2}}\:\:\:\:\:\mathrm{find}:\:\mathrm{x}^{\mathrm{12}} \:=\:? \\ $$ Answered by MM42 last updated on 13/Jan/24 $$\begin{cases}{{x}^{\mathrm{2}} =\frac{\mathrm{3}+\sqrt{\mathrm{5}}}{\mathrm{2}}}\\{{x}^{\mathrm{4}} =\frac{\mathrm{7}+\mathrm{3}\sqrt{\mathrm{5}}}{\mathrm{2}}}\end{cases}\:\:\Rightarrow{x}^{\mathrm{6}} =\mathrm{9}+\mathrm{4}\sqrt{\mathrm{5}} \\…
Question Number 203232 by Mathstar last updated on 13/Jan/24 Answered by mr W last updated on 13/Jan/24 Commented by mr W last updated on 13/Jan/24…
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Question Number 203199 by MathedUp last updated on 12/Jan/24 $$\mathrm{Let}'{s}\:\mathrm{define}\:\mathrm{linear}\:\mathrm{Operator}\:\boldsymbol{\mathcal{L}}\:\mathrm{as}\:\boldsymbol{\mathcal{L}}=\int_{\mathrm{0}} ^{\infty} \:{e}^{−{st}} \centerdot \\ $$$$\boldsymbol{\mathcal{L}}\left\{{W}\left({t}\right)\right\}=??? \\ $$$${W}\left({t}\right)\:\mathrm{is}\:\mathrm{inverse}\:\mathrm{function}\:\mathrm{of}\:{y}\left({t}\right)={te}^{{t}} \:,\:{t}\in\left[−\frac{\mathrm{1}}{{e}},\infty\right) \\ $$ Commented by shunmisaki007 last updated…
Question Number 203192 by MrGHK last updated on 12/Jan/24 $$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{last}}\:\boldsymbol{\mathrm{four}}\:\boldsymbol{\mathrm{digits}}\:\boldsymbol{\mathrm{of}}\:\mathrm{2022}^{\mathrm{2023}} +\mathrm{2023}^{\mathrm{2022}} \\ $$ Answered by AST last updated on 12/Jan/24 $${x}=\mathrm{2022}^{\mathrm{2023}} +\mathrm{2023}^{\mathrm{2022}} \overset{\mathrm{16}} {\equiv}\mathrm{6}^{\mathrm{2023}} +\mathrm{7}^{\mathrm{2022}}…
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Question Number 203222 by Tawa11 last updated on 12/Jan/24 XYZ Ltd wants to borrow money to finance a project. They can pay N2500 monthly in…
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