Question Number 218150 by Shrodinger last updated on 31/Mar/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{1}−{x}^{\mathrm{2}} }{ln}\left(\frac{\mathrm{1}+{x}}{\mathrm{2}{x}}\right){dx} \\ $$ Answered by MrGaster last updated on 31/Mar/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 218183 by hardmath last updated on 31/Mar/25 $$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{33}^{\mathrm{2}} \:\:+\:\:\mathrm{544}^{\mathrm{2}} }\:\:+\:\:\sqrt{\mathrm{333}^{\mathrm{2}} \:\:+\:\:\mathrm{55444}^{\mathrm{2}} }\:\:=\:\:? \\ $$ Answered by Hanuda354 last updated on 01/Apr/25…
Question Number 218138 by hardmath last updated on 30/Mar/25 $$\sqrt[{\mathrm{4}}]{\mathrm{629}\:−\:\mathrm{x}}\:\:+\:\:\sqrt[{\mathrm{4}}]{\mathrm{77}\:\:+\:\:\mathrm{x}}\:\:=\:\:\mathrm{8} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by Ghisom last updated on 30/Mar/25 $$\mathrm{easy}\:\mathrm{to}\:\mathrm{see}: \\ $$$$\mathrm{629}\:\mathrm{is}\:\mathrm{almost}\:\mathrm{5}^{\mathrm{4}} ,\:\mathrm{77}\:\mathrm{is}\:\mathrm{almost}\:\mathrm{3}^{\mathrm{4}}…
Question Number 218148 by mnjuly1970 last updated on 30/Mar/25 $$ \\ $$$$\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{sin}\left(\sqrt{\:{x}\:}\right)}{\:\sqrt[{\mathrm{4}}]{\:{e}^{{x}} }}{dx}=? \\ $$$$ \\ $$ Answered by MrGaster last updated on…
Question Number 218119 by MrGaster last updated on 30/Mar/25 $$\begin{vmatrix}{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}\end{vmatrix}=? \\ $$$$ \\ $$ Answered by SdC355 last updated on 30/Mar/25 $$\mathrm{Holy}\:\mathrm{shit}….\mathrm{what}\:\mathrm{is}\:\mathrm{that}\:\mathrm{Lol} \\ $$$$\mathrm{But}\:\mathrm{that}\:\mathrm{det}\left\{\mathrm{A}\right\}\:\mathrm{is}\:\varepsilon^{\mathrm{6}} −\mathrm{6}\varepsilon^{\mathrm{4}}…
Question Number 218128 by mr W last updated on 30/Mar/25 $$\begin{array}{|c|}{?}&\hline{?}&\hline{?}&\hline{?}\\\hline\end{array}×\begin{array}{|c|}{?}\\\hline\end{array}=\mathrm{8044}\begin{array}{|c|}{?}\\\hline\end{array} \\ $$ Answered by A5T last updated on 30/Mar/25 $$\frac{\mathrm{8044}?}{\mathrm{8}}>\frac{\mathrm{80000}}{\mathrm{8}}=\mathrm{10000}\: \\ $$$$\Rightarrow\:\mathrm{8044}?\:\mathrm{should}\:\mathrm{be}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{9} \\ $$$$\Rightarrow\mathrm{9}\:\mid\:\mathrm{8}+\mathrm{0}+\mathrm{4}+\mathrm{4}+?\Rightarrow\:?=\mathrm{2}…
Question Number 218129 by mr W last updated on 30/Mar/25 $${how}\:{many}\:{different}\:{words}\:{can}\:{be} \\ $$$${formed}\:{from}\:{the}\:{word}\: \\ $$$$\boldsymbol{\mathrm{MATHEMATICS}}? \\ $$$${note}:\:\:{here}\:{a}\:{word}\:{should}\:{have}\:{at}\: \\ $$$${least}\:{two}\:{letters},\:{but}\:{mustn}'{t}\:{have}\:{a} \\ $$$${meaning}. \\ $$ Answered by…
Question Number 218103 by ArshadS last updated on 29/Mar/25 $${x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}\:,\:{x}^{\mathrm{5}} +\frac{\mathrm{1}}{{x}^{\mathrm{5}} }=? \\ $$ Answered by Rasheed.Sindhi last updated on 29/Mar/25 $${x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}\:,\:{x}^{\mathrm{5}} +\frac{\mathrm{1}}{{x}^{\mathrm{5}} }=? \\…
Question Number 218099 by Rasheed.Sindhi last updated on 29/Mar/25 $${x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0}\:,\:{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}=? \\ $$ Answered by Rasheed.Sindhi last updated on 29/Mar/25 $$\mathrm{Another}\:\mathrm{way} \\ $$$$\left({x}^{\mathrm{2}}…
Question Number 218093 by ArshadS last updated on 29/Mar/25 $${Solve}\:{for}\:{x} \\ $$$$\sqrt{\mathrm{2}{x}+\mathrm{3}}\:−\sqrt{{x}−\mathrm{2}}\:=\sqrt{{x}+\mathrm{2}}\: \\ $$ Answered by vnm last updated on 29/Mar/25 $$\mathrm{2}{x}+\mathrm{3}=\left(\sqrt{{x}+\mathrm{2}}+\sqrt{{x}−\mathrm{2}}\right)^{\mathrm{2}} = \\ $$$${x}+\mathrm{2}+{x}−\mathrm{2}+\mathrm{2}\sqrt{\left({x}+\mathrm{2}\right)\left({x}−\mathrm{2}\right)}…