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Question Number 216726 by BaliramKumar last updated on 17/Feb/25 Commented by BaliramKumar last updated on 17/Feb/25 $${Q}.\:{not}\:{in}\:{real}\:{world} \\ $$$${Let}\:\:\:\:\:\:{second}\rightarrow{minutes} \\ $$ Commented by mr W…
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Question Number 215999 by lmcp1203 last updated on 25/Jan/25 $${if}\:{the}\:{fraction}\:\frac{{m}^{\mathrm{2}} +\mathrm{25}{m}}{{m}+\mathrm{1}}\:\:{is}\:{reductible}.\:{how}\:{many}\:{values}\:{does}\:{m}\:\:{take}\:{if}\:{is}\:{a}\:\mathrm{2}\:{digit}\:\:{number}?\:{thanks} \\ $$ Answered by Rasheed.Sindhi last updated on 25/Jan/25 $$\frac{{m}^{\mathrm{2}} +\mathrm{25}{m}}{{m}+\mathrm{1}}={m}\left(\frac{{m}+\mathrm{25}}{{m}+\mathrm{1}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:={m}\left(\frac{{m}+\mathrm{1}+\mathrm{24}}{{m}+\mathrm{1}}\right)={m}\left(\mathrm{1}+\frac{\mathrm{24}}{{m}+\mathrm{1}}\right) \\…
Question Number 215845 by Tawa11 last updated on 19/Jan/25 $$\mathrm{1},\:\mathrm{3},\:−\:\mathrm{1},\:−\:\mathrm{3},\:−\:\mathrm{7},\:\:−\:\mathrm{21},\:\:−\:\mathrm{25},\:\:\:\:\:\_\_\_,\:\:\:\:\:\_\_\_,\:\:\:\:\:\_\_\_ \\ $$$$ \\ $$$$\mathrm{Next}\:\mathrm{three}\:\mathrm{terms}?? \\ $$ Commented by mr W last updated on 20/Jan/25 $${this}\:{is}\:{a}\:{game},\:{not}\:{mathematics}!!!…
Question Number 215492 by BaliramKumar last updated on 08/Jan/25 Commented by BaliramKumar last updated on 08/Jan/25 $${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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