Question Number 218309 by 200392jjlv last updated on 05/Apr/25 $$\underset{−\infty} {\overset{\infty} {\int}}\frac{\mathrm{4}}{\mathrm{16}+{x}^{\mathrm{2}} }{dx} \\ $$$$=\:\underset{−\infty} {\overset{\mathrm{0}} {\int}}\frac{\mathrm{4}}{\mathrm{16}+{x}^{\mathrm{2}} }{dx}+\underset{\infty} {\int}^{\mathrm{0}} \frac{\mathrm{4}}{\mathrm{16}+{x}^{\mathrm{2}} }{dx} \\ $$$$=\: \\ $$$$…
Question Number 218280 by vahid last updated on 04/Apr/25 Answered by Frix last updated on 05/Apr/25 $$\mathrm{i}^{\mathrm{4}{n}} =\mathrm{1} \\ $$$$\mathrm{i}^{\mathrm{4}{n}+\mathrm{1}} =\mathrm{i} \\ $$$$\mathrm{i}^{\mathrm{4}{n}+\mathrm{2}} =−\mathrm{1} \\…
Question Number 218265 by SdC355 last updated on 04/Apr/25 $$\mathrm{can}\:\mathrm{interpret}\:\mathrm{the}\:\mathrm{metric}\:\mathrm{Tensor}\:\boldsymbol{\mathrm{g}}_{\mu\nu} \:\mathrm{is}\: \\ $$$$\mathrm{kinda}\:\mathrm{distance}\:\mathrm{function}\:\mathrm{at}\:\mathrm{curved}\:\mathrm{Surface}\:?? \\ $$$$\mathrm{ex}.\:\mathrm{Euclidean}\:\mathrm{space}\:\boldsymbol{\mathrm{g}}_{\mu\nu} =\begin{pmatrix}{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\end{pmatrix} \\ $$$$\mathrm{Sphere}\:\boldsymbol{\mathrm{g}}_{\mu\nu} =\begin{pmatrix}{\:\mathrm{1}}&{\:\:\:\:\mathrm{0}}&{\:\:\:\:\:\:\:\mathrm{0}}\\{\:\mathrm{0}}&{\:\:\:\:{r}^{\mathrm{2}} }&{\:\:\:\:\:\:\:\mathrm{0}}\\{\:\mathrm{0}}&{\:\:\:\:\:\mathrm{0}}&{{r}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \left(\theta\right)}\end{pmatrix} \\ $$ Answered…
Question Number 218267 by lmcp1203 last updated on 04/Apr/25 Commented by lmcp1203 last updated on 04/Apr/25 $${thanks} \\ $$ Answered by vnm last updated on…
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Question Number 218279 by Tawa11 last updated on 04/Apr/25 $$\mathrm{Evaluate}: \\ $$$$\:\:\:\:\:\frac{\mathrm{4}^{\mathrm{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}} }{\mathrm{5}^{\mathrm{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{5}} } \\ $$$$\mathrm{Show}\:\mathrm{workings}\:\mathrm{please}. \\ $$ Answered by Frix last updated…
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Question Number 218262 by hardmath last updated on 03/Apr/25 Commented by hardmath last updated on 03/Apr/25 $$\mathrm{ABCD}\:-\:\mathrm{Rectangular} \\ $$$$\mathrm{AK}\:\bot\:\mathrm{BM} \\ $$$$\mathrm{S}_{\bigtriangleup\boldsymbol{\mathrm{AKB}}} \:=\:\mathrm{S}_{\bigtriangleup\boldsymbol{\mathrm{BMC}}} \:=\:\mathrm{S}_{\boldsymbol{\mathrm{AKMD}}} \\ $$$$\mathrm{DM}\:=\:\boldsymbol{\mathrm{a}}…
Question Number 218256 by mr W last updated on 03/Apr/25 Answered by efronzo1 last updated on 03/Apr/25 $$\:\:\mathrm{f}\left(\mathrm{3}\right)+\mathrm{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)=\:\mathrm{72} \\ $$$$\:\mathrm{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)+\:\mathrm{f}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)=−\mathrm{12} \\ $$$$\:\mathrm{f}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)+\:\mathrm{f}\left(\mathrm{3}\right)\:=\:\mathrm{16} \\ $$$$\:\:\mathrm{2}\left\{\mathrm{f}\left(\mathrm{3}\right)+\:\mathrm{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)+\:\mathrm{f}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)\right\}\:=\:\mathrm{76} \\…
Question Number 218257 by cherokeesay last updated on 03/Apr/25 Commented by cherokeesay last updated on 03/Apr/25 $$\mathrm{the}\:\mathrm{4}\:\mathrm{points}\:\mathrm{are}\:\mathrm{tangent} \\ $$ Commented by Nicholas666 last updated on…