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Author: Tinku Tara

Find-the-type-of-triangle-such-that-the-following-relationship-holds-between-its-angles-tan-B-tan-C-tan-2-B-C-2-

Question Number 215349 by mnjuly1970 last updated on 03/Jan/25 $$ \\ $$$$\:\:\:\:{Find}\:{the}\:{type}\:{of}\:{triangle} \\ $$$$\:\:\:\:{such}\:{that}\:{the}\:{following} \\ $$$$\:\:\:\:\:{relationship}\:{holds}\:{between}\: \\ $$$${its}\:{angles}. \\ $$$$\:\:\:\:\:\: \\ $$$$\:{tan}\:\left({B}\right){tan}\left({C}\right)=\:{tan}^{\mathrm{2}} \left(\frac{{B}+{C}}{\mathrm{2}}\:\right)\:\:\:\:\blacksquare \\ $$$$…

Find-x-x-2-200-x-

Question Number 215350 by hardmath last updated on 03/Jan/25 $$\mathrm{Find}:\:\:\:\mathrm{x}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{2}^{\sqrt{\mathrm{200}}} \:\:\Rightarrow\:\:\mathrm{x}\:=\:? \\ $$ Answered by zetamaths last updated on 03/Jan/25 $$.{is}\:{just}\:{the}\:{lambert}\:{function} \\ $$$${x}^{{x}} =\mathrm{2}^{\sqrt{\mathrm{200}}}…

Question-215344

Question Number 215344 by universe last updated on 03/Jan/25 Answered by MrGaster last updated on 04/Jan/25 $$\:\mathrm{Let}\:\Sigma\:\mathrm{be}\:\mathrm{the}\:\mathrm{boundary}\:\mathrm{of}\:{D}. \\ $$$$\Sigma=\sum_{\mathrm{1}} \cup\sum_{\mathrm{2}} \cup\sum_{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{where} \\ $$$$\sum_{\mathrm{1}}…

Question-215313

Question Number 215313 by AlagaIbile last updated on 02/Jan/25 Answered by mr W last updated on 02/Jan/25 $$\angle{ABD}=\mathrm{135}° \\ $$$$\Rightarrow\angle{CBD}=\mathrm{45}° \\ $$$$\Rightarrow{CD}={CB}=\mathrm{2} \\ $$$$\Rightarrow{AD}=\sqrt{\left(\mathrm{12}+\mathrm{2}\right)^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}}…

Show-that-x-64-and-y-729-x-1-3-y-1-3-13-x-y-35-

Question Number 215282 by arkanmathematics63 last updated on 02/Jan/25 $${Show}\:{that}\:{x}=\mathrm{64}\:{and}\:{y}=\mathrm{729}\: \\ $$$$\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{3}}]{{y}}=\mathrm{13} \\ $$$$\sqrt{{x}}+\sqrt{{y}}=\mathrm{35} \\ $$ Commented by Ghisom last updated on 02/Jan/25 $$\mathrm{to}\:“\mathrm{show}\:\mathrm{that}\:{x}=\mathrm{64}\:\mathrm{and}\:{y}=\mathrm{729}''\:\mathrm{it}'\mathrm{s}\:\mathrm{enough} \\…

Evaluate-lim-n-1-2n-1-1-2n-2-1-4n-

Question Number 215315 by depressiveshrek last updated on 02/Jan/25 $$\mathrm{Evaluate}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{2}}+…+\frac{\mathrm{1}}{\mathrm{4}{n}}\right) \\ $$ Answered by mr W last updated on 02/Jan/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}{n}+{k}}…