Question Number 227370 by Math1 last updated on 18/Jan/26 $$\frac{\mathrm{16}\centerdot\mathrm{3}^{\boldsymbol{\mathrm{x}}−\mathrm{1}} \:+\:\mathrm{16}\centerdot\mathrm{3}^{\boldsymbol{\mathrm{x}}} }{\mathrm{4}\centerdot\mathrm{3}^{\boldsymbol{\mathrm{x}}+\mathrm{1}} \:−\:\mathrm{2}\centerdot\mathrm{3}^{\boldsymbol{\mathrm{x}}−\mathrm{1}} }\:=\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}^{\boldsymbol{\mathrm{x}}−\mathrm{1}} }}{\mathrm{17}}\:\:\:\:\:\mathrm{find}:\:\:\mathrm{x}=? \\ $$ Answered by Kassista last updated on 18/Jan/26 $$…
Question Number 227371 by Math1 last updated on 18/Jan/26 $$\mathrm{3}^{\mathrm{444}} \:\:+\:\:\mathrm{4}^{\mathrm{333}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\mathrm{dividing}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{by}\:\mathrm{7} \\ $$ Answered by A5T last updated on 19/Jan/26 $$\phi\left(\mathrm{7}\right)=\mathrm{6}…
Question Number 227346 by Spillover last updated on 17/Jan/26 Answered by Kassista last updated on 18/Jan/26 $$ \\ $$$${Note}\:{that}: \\ $$$$\lfloor{x}\rfloor=\:{n},\:{if}\:{n}\leqslant{x}<{n}+\mathrm{1}\:\left({n}\in\mathbb{Z}\right) \\ $$$${similarly}: \\ $$$$\lceil{x}\rceil={n}+\mathrm{1},\:{n}\leqslant{x}<{n}+\mathrm{1}\:\left({n}\in\mathbb{Z}\right)…
Question Number 227325 by hardmath last updated on 16/Jan/26 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\mathrm{acute}\:\bigtriangleup\mathrm{ABC}\: \\ $$$$\mathrm{if}\:\mathrm{I}\:\mathrm{is}\:\mathrm{the}\:\mathrm{in}-\mathrm{center}\:\mathrm{and}\:\mathrm{H}\:\mathrm{is}\:\mathrm{the}\:\mathrm{ortho}-\mathrm{center} \\ $$$$\mathrm{then}: \\ $$$$\frac{\mathrm{1}}{\mathrm{IA}}\:+\:\frac{\mathrm{1}}{\mathrm{IB}}\:+\:\frac{\mathrm{1}}{\mathrm{IC}}\:\:\leqslant\:\:\frac{\mathrm{1}}{\mathrm{HA}}\:+\:\frac{\mathrm{1}}{\mathrm{HB}}\:+\:\frac{\mathrm{1}}{\mathrm{HC}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 227312 by hardmath last updated on 13/Jan/26 $$\mathrm{tg}\left(\mathrm{15}\right)\:+\:\mathrm{ctg}\left(\mathrm{5}\right)\:=\:? \\ $$ Answered by Kassista last updated on 13/Jan/26 $$ \\ $$$${tg}\left(\mathrm{3}\theta\right)\:=\:\frac{\mathrm{3}{tg}\left(\theta\right)−{tg}^{\mathrm{3}} \left(\theta\right)}{\mathrm{1}−\mathrm{3}{tg}^{\mathrm{2}} \left(\theta\right)}\:\therefore\:{tg}\left(\mathrm{15}\right)=\frac{\mathrm{3}{tg}\left(\mathrm{5}\right)−{tg}^{\mathrm{3}} \left(\mathrm{5}\right)}{\mathrm{1}−\mathrm{3}{tg}^{\mathrm{2}}…
Question Number 227306 by Spillover last updated on 12/Jan/26 Commented by Spillover last updated on 12/Jan/26 $${Find}\:{the}\:{digit}\:{in}\:{the}\:{box} \\ $$ Answered by peace2 last updated on…
Question Number 227286 by hardmath last updated on 12/Jan/26 $$\mathrm{tg}\left(\mathrm{4}\right)\:+\:\mathrm{ctg}\left(\mathrm{4}\right)\:=\:? \\ $$ Answered by Frix last updated on 12/Jan/26 $$=\frac{\mathrm{2}}{\mathrm{sin}\:\mathrm{8}} \\ $$ Answered by Kassista…
Question Number 227245 by Spillover last updated on 10/Jan/26 Answered by Spillover last updated on 10/Jan/26 Answered by Spillover last updated on 11/Jan/26 Terms of…
Question Number 227246 by Spillover last updated on 10/Jan/26 Answered by Spillover last updated on 11/Jan/26 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 227247 by Spillover last updated on 10/Jan/26 Answered by Spillover last updated on 11/Jan/26 Answered by mr W last updated on 12/Jan/26 $$\frac{{r}}{{R}}=\frac{{h}−{y}}{{h}}\:\Rightarrow{y}={h}\left(\mathrm{1}−\frac{{r}}{{h}}\right)…