Question Number 181707 by amin96 last updated on 28/Nov/22 $$\boldsymbol{{if}}\:\:\:\:\:\mathrm{2}\boldsymbol{{x}}+\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\:\:\mathrm{8}\boldsymbol{{x}}+\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}}}=? \\ $$ Answered by mr W last updated on 29/Nov/22 $${t}=\sqrt{{x}}>\mathrm{0} \\ $$$${f}\left({t}\right)=\mathrm{2}{t}^{\mathrm{2}}…
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Question Number 181025 by KINMATICS last updated on 20/Nov/22 $$\mathrm{Send}\:\mathrm{you}\:\mathrm{solutions}\:\mathrm{to}\:\boldsymbol{\mathrm{kinmatics}}@\boldsymbol{\mathrm{gmail}}.\boldsymbol{\mathrm{com}} \\ $$ Commented by mr W last updated on 20/Nov/22 $${at}\:{first}\:{send}\:{your}\:{questions}\:{to}\: \\ $$$${tinku}@{tara}!\:{that}'{s}\:{here}. \\ $$…
Question Number 115258 by bobhans last updated on 24/Sep/20 $${A}\:{vector}\:{of}\:{magnitude}\:\mathrm{2}\:{along}\:{a}\:{bisector} \\ $$$${of}\:{the}\:{angle}\:{between}\:{the}\:{two}\:{vectors} \\ $$$$\mathrm{2}\hat {{i}}−\mathrm{2}\hat {{j}}+\hat {{k}}\:{and}\:\hat {{i}}+\mathrm{2}\hat {{j}}−\mathrm{2}\hat {{k}}\:{is}\:\_\_ \\ $$ Answered by bemath…
Question Number 114975 by mnjuly1970 last updated on 22/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\:\:{nice}\:\:{mathematics}….\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:{show}\:\:{that}\:::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Phi\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {li}_{\mathrm{2}} \left({x}\right){dx}\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}}\:−\mathrm{1}\:\:\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.{july}.\mathrm{1970} \\ $$$$ \\…
Question Number 114808 by mnjuly1970 last updated on 21/Sep/20 $$\:\:\:\:\:\:…{nice}\:{math}… \\ $$$$ \\ $$$$\:\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{{ln}\left(\mathrm{1}+{sin}\left({x}\right)\right)}{{cos}\left({x}\right)}{dx}=???\: \\ $$$$ \\ $$$$…{m}.{n}.{july}.\mathrm{1970}… \\ $$$$\: \\…
Question Number 180254 by Noorzai last updated on 09/Nov/22 Answered by mr W last updated on 09/Nov/22 $$\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{cos}\:{x}} =\left(\frac{\mathrm{1}}{\mathrm{2}−\sqrt{\mathrm{3}}}\right)^{\mathrm{sin}\:{x}} =\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{−\mathrm{sin}\:{x}} \\ $$$$\Rightarrow\mathrm{cos}\:{x}=−\mathrm{sin}\:{x} \\ $$$$\Rightarrow\mathrm{cot}\:{x}=−\mathrm{1} \\…
Question Number 48993 by Raj Singh last updated on 01/Dec/18 Answered by $@ty@m last updated on 01/Dec/18 $${In}\:{order}\:{to}\:{save}\:{time}, \\ $$$${I}'{ll}\:{write}\:\mathrm{a}\:{instead}\:{of}\:\overset{\rightarrow} {\mathrm{a}} \\ $$$${LHS}=\left[{a}×{b}\:{b}×{c}\:{c}×{a}\right] \\ $$$$=\left({a}×{b}\right).\left\{\left({b}×{c}\right)×\left({c}×{a}\right)\right\}…