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Question Number 218889 by Spillover last updated on 17/Apr/25 Answered by mehdee7396 last updated on 17/Apr/25 $${tanx}+{cotx}=−\mathrm{1} \\ $$$${tan}^{\mathrm{3}} +{cot}^{\mathrm{3}} {x}=\left({tanx}+{cotx}\right)^{\mathrm{3}} −\mathrm{3}\left({tanx}×{cotx}\right)\left({tanx}+{cotx}\right) \\ $$$$=−\mathrm{1}+\mathrm{3}=\mathrm{2}=\mathrm{2}{m}^{\mathrm{2}} \Rightarrow{m}=\pm\mathrm{1}…
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Question Number 218799 by depressiveshrek last updated on 15/Apr/25 $$\mathrm{For}\:\mathrm{those}\:\mathrm{who}\:\mathrm{are}\:\mathrm{interested}\:\mathrm{in}\:\mathrm{cryptography}. \\ $$$$\mathrm{The}\:\mathrm{below}\:\mathrm{text}\:\mathrm{has}\:\mathrm{been}\:\mathrm{encrypted}\:\mathrm{using} \\ $$$$\mathrm{Vigenere}\:\mathrm{cipher},\:\mathrm{such}\:\mathrm{that}\:\mathrm{numbers},\:\mathrm{punctuation} \\ $$$$\mathrm{marks}\:\mathrm{and}\:\mathrm{the}\:\mathrm{letter}\:\overset{..} {\mathrm{E}}\:\mathrm{have}\:\mathrm{remained}\:\mathrm{the}\:\mathrm{same}. \\ $$$$\mathrm{A}\:\mathrm{keyword}\:\mathrm{of}\:\mathrm{length}\:\mathrm{9}\:\mathrm{has}\:\mathrm{been}\:\mathrm{used},\:\mathrm{which} \\ $$$$\mathrm{starts}\:\mathrm{with}\:\mathrm{the}\:\mathrm{letter}\:\mathrm{K}.\:\mathrm{Decrypt}\:\mathrm{the}\:\mathrm{text}. \\ $$ Commented by…
Question Number 218675 by Spillover last updated on 14/Apr/25 Answered by Nicholas666 last updated on 14/Apr/25 $$ \\ $$$$\:\:\:\:\frac{\mathrm{2020}^{\mathrm{2}} +\mathrm{1}}{\mathrm{0}^{\mathrm{2}} +\mathrm{1}}\:=\:\frac{\mathrm{4080400}}{\mathrm{1}}\:=\mathrm{4080401}\:\checkmark \\ $$$$ \\ $$…
Question Number 218312 by Rojarani last updated on 06/Apr/25 Answered by mr W last updated on 07/Apr/25 $${say}\:{the}\:{time}\:{needed}\:{from}\:{house}\:{to}\: \\ $$$${station}\:{A}\:{is}\:{x},\:{and}\:{from}\:{house}\:{to} \\ $$$${station}\:{B}\:{is}\:{y}. \\ $$$${for}\:{up}\:{train}\:{it}\:{is}\:{given}: \\…