Question Number 182216 by Acem last updated on 05/Dec/22 $$\:{Find}\:{a},\:{b},\:{c}\:\in\:\mathbb{N}\:;\:\mathrm{2}^{\:{a}} +\:\mathrm{4}^{\:{b}} +\:\mathrm{8}^{\:{c}} =\:\mathrm{328} \\ $$ Commented by SANOGO last updated on 06/Dec/22 $${thank}\:{you} \\ $$…
Question Number 116683 by mathocean1 last updated on 05/Oct/20 $$\mathrm{Given}\:\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}=\mathrm{16}\:\:\:\mathrm{we}\:\mathrm{know}\:\mathrm{that} \\ $$$$\mathrm{16}=\mathrm{4}^{\mathrm{2}} \:\:\mathrm{and}\:\mathrm{4}\:\mathrm{is}\:\mathrm{the}\:\mathrm{half}\:\mathrm{of}\:\mathrm{8}\:\mathrm{which}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{successor}\:\mathrm{of}\:\mathrm{7}. \\ $$$$ \\ $$$$\mathrm{conjecture}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{this}\:\mathrm{sum}: \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}+…+\mathrm{25} \\ $$ Answered by…
Question Number 182200 by Shrinava last updated on 05/Dec/22 $$\mathrm{1}.\:\:\:\underset{\boldsymbol{\mathrm{a}}\rightarrow−\boldsymbol{\mathrm{x}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{a}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{a}^{\mathrm{3}} }\:=\:? \\ $$$$ \\ $$$$\mathrm{2}.\:\:\:\mathrm{cot}\:\mathrm{80}°\:\left(\mathrm{tan}\:\mathrm{10}°\:+\:\mathrm{2}\:\mathrm{tg}\:\mathrm{70}°\right)\:=\:? \\ $$ Answered by cortano1 last…
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Question Number 182188 by mathlove last updated on 05/Dec/22 $$\left(\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}+\mathrm{2}}+\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}−\mathrm{2}}\right)^{\mathrm{2014}} =? \\ $$ Answered by Frix last updated on 05/Dec/22 $$\sqrt[{\mathrm{3}}]{\mathrm{2}+\sqrt{\mathrm{5}}}=\varphi\wedge\sqrt[{\mathrm{3}}]{−\mathrm{2}+\sqrt{\mathrm{5}}}=\frac{\mathrm{1}}{\varphi} \\ $$$$\varphi+\frac{\mathrm{1}}{\varphi}=\sqrt{\mathrm{5}} \\ $$$$\left(\sqrt{\mathrm{5}}\right)^{\mathrm{2014}}…
Question Number 51109 by peter frank last updated on 24/Dec/18 Commented by peter frank last updated on 24/Dec/18 $${wish}\:{upcoming}\:{christmas}\:{in} \\ $$$${by}\:{sharing}\:{in}\:{mathematics}\: \\ $$ Terms of…
Question Number 182176 by peter frank last updated on 05/Dec/22 Answered by MikeH last updated on 05/Dec/22 $$\mathrm{let}\:\overset{\rightarrow} {\mathrm{w}}\:=\:{x}\mathrm{i}\:+\:\mathrm{6j}\:+\:{y}\:\mathrm{k} \\ $$$$\mathrm{orthogonal}\:\mathrm{to}\:\overset{\rightarrow} {\mathrm{u}}\:\mathrm{and}\:\overset{\rightarrow} {\mathrm{v}}\:\Rightarrow\:\overset{\rightarrow} {\mathrm{w}}\:=\:\overset{\rightarrow} {\mathrm{u}}×\:\overset{\rightarrow}…
Question Number 116633 by zakirullah last updated on 05/Oct/20 Answered by Olaf last updated on 05/Oct/20 $$\mathrm{If}\:\mathrm{B}\:\mathrm{is}\:\mathrm{a}\:\mathrm{inverse}\:\mathrm{matrix}\:\mathrm{of}\:\mathrm{A} \\ $$$$\mathrm{then}\:\mathrm{B}.\mathrm{A}\:=\:\mathrm{A}.\mathrm{B}\:=\:\mathrm{I}\:\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{C}\:\mathrm{is}\:\mathrm{another}\:\mathrm{inverse}\:\mathrm{matrix}\:\mathrm{of}\:\mathrm{A} \\ $$$$\mathrm{then}\:\mathrm{C}.\mathrm{A}\:=\:\mathrm{A}.\mathrm{C}\:=\:\mathrm{I}\:\left(\mathrm{2}\right)…
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