Question Number 215492 by BaliramKumar last updated on 08/Jan/25 Commented by BaliramKumar last updated on 08/Jan/25 $${Decimal}\:\:{to}\:{binary} \\ $$ Answered by khorshidi17 last updated on…
Question Number 215229 by Mingma last updated on 01/Jan/25 Answered by devdutt last updated on 01/Jan/25 $$\mathrm{1}.\:{f}\left(\frac{{k}}{{n}}\right)\:=\:\frac{{n}^{\mathrm{2025}} }{{n}^{\mathrm{2025}} +{k}^{\mathrm{2025}} } \\ $$$$ \\ $$$$\mathrm{2}.\:{f}\left(\frac{{k}}{{n}}\right)+{f}\left(\frac{{n}}{{k}}\right)\:=\:\mathrm{1},\: \\…
Question Number 215231 by Mingma last updated on 01/Jan/25 Answered by A5T last updated on 01/Jan/25 $$\mathrm{2024}=\mathrm{8}×\mathrm{253}=\mathrm{8}×\mathrm{11}×\mathrm{23} \\ $$$$\mathrm{2025}=\mathrm{45}^{\mathrm{2}} =\mathrm{3}^{\mathrm{4}} ×\mathrm{5}^{\mathrm{2}} ;\:\:\:\:\mathrm{2026}=\mathrm{2}×\mathrm{1013} \\ $$$$\Rightarrow\mathrm{smallest}\:\mathrm{perfect}\:\mathrm{square} \\…
Question Number 215232 by Mingma last updated on 01/Jan/25 Answered by devdutt last updated on 01/Jan/25 $$\mathrm{ln}\:\mathrm{3}\sqrt{\mathrm{5}}\:+\:\mathrm{ln}\:{x}\:\mathrm{log}\:_{\mathrm{45}} {x}\:=\:\mathrm{2ln}\:{x}\: \\ $$$$\Rightarrow\:\mathrm{ln}\:\mathrm{3}\sqrt{\mathrm{5}}\:+\:\frac{\mathrm{ln}\:^{\mathrm{2}} {x}}{\mathrm{ln}\:\mathrm{45}}\:=\:\mathrm{2ln}\:{x}\: \\ $$$$\Rightarrow\:\mathrm{ln}\:^{\mathrm{2}} {x}\:−\:\mathrm{2ln}\:\mathrm{45}\:\mathrm{ln}\:{x}\:+\:\mathrm{ln}\:\mathrm{3}\sqrt{\mathrm{5}}\:\mathrm{ln}\:\mathrm{45}\:=\:\mathrm{0} \\…
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Question Number 214622 by Frangg last updated on 13/Dec/24 Answered by Rasheed.Sindhi last updated on 14/Dec/24 $$\underline{{If}\:{to}\:{determine}\:{x}:} \\ $$$$\bigtriangleup\mathrm{ABE}\:\sim\bigtriangleup\mathrm{DCE} \\ $$$$\frac{\mathrm{AB}}{\mathrm{DC}}=\frac{\mathrm{AE}}{\mathrm{DE}} \\ $$$$\frac{\mathrm{19}}{\mathrm{6}}=\frac{\mathrm{2x}+\mathrm{8}}{\mathrm{x}−\mathrm{2}} \\ $$$$\mathrm{19x}−\mathrm{38}=\mathrm{12x}+\mathrm{48}…
Question Number 214097 by MathematicalUser2357 last updated on 28/Nov/24 Answered by issac last updated on 28/Nov/24 $$\mathrm{16}/\mathrm{3}\approx\mathrm{5}.\mathrm{333333333}……=\mathrm{5}.\overset{\centerdot} {\mathrm{3}} \\ $$ Terms of Service Privacy Policy…
Question Number 213802 by efronzo1 last updated on 17/Nov/24 Answered by A5T last updated on 17/Nov/24 $${t}_{\mathrm{1}} ={k}−\mathrm{1};{t}_{\mathrm{2}} ={k} \\ $$$${t}_{\mathrm{3}} =\frac{\mathrm{5}{k}+\mathrm{1}}{\mathrm{25}{k}−\mathrm{25}};\:\:\:\:{t}_{\mathrm{4}} =\frac{\frac{\mathrm{10}{k}−\mathrm{4}}{\mathrm{5}{k}−\mathrm{5}}}{\mathrm{25}{k}}=\frac{\mathrm{10}{k}−\mathrm{4}}{\mathrm{125}{k}\left({k}−\mathrm{1}\right)} \\ $$$${t}_{\mathrm{5}}…
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Question Number 213522 by efronzo1 last updated on 07/Nov/24 $$\:\:\mathrm{The}\:\mathrm{two}\:\mathrm{corner}\:\mathrm{points}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\: \\ $$$$\:\:\mathrm{lie}\:\mathrm{on}\:\mathrm{curve}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{3}\:\mathrm{and}\: \\ $$$$\:\mathrm{the}\:\mathrm{other}\:\mathrm{two}\:\mathrm{corner}\:\mathrm{points}\:\mathrm{lie}\:\mathrm{on}\: \\ $$$$\:\mathrm{curve}\:\mathrm{g}\left(\mathrm{x}\right)=\:−\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{3}\:.\:\mathrm{It}\:\mathrm{is}\:\mathrm{known} \\ $$$$\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{can}\:\mathrm{be}\: \\ $$$$\:\:\mathrm{expressed}\:\mathrm{by}\:\mathrm{p}+\mathrm{q}\sqrt{\mathrm{r}}\:,\:\mathrm{for}\:\mathrm{a}\:\mathrm{natural}\: \\ $$$$\:\mathrm{number}\:\mathrm{p},\mathrm{q}\:,\mathrm{r}\:\mathrm{where}\:\mathrm{r}\:\mathrm{is}\:\mathrm{not}\:\mathrm{divisible}\: \\…