Question Number 143438 by Rankut last updated on 14/Jun/21 $$\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\boldsymbol{{x}}} =\boldsymbol{{log}}_{\frac{\mathrm{1}}{\mathrm{2}}} \boldsymbol{{x}} \\ $$$$\boldsymbol{{find}}\:\:\:\boldsymbol{{x}} \\ $$ Answered by mr W last updated on 14/Jun/21 $${x}=\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{{x}}…
Question Number 143435 by nitu last updated on 14/Jun/21 Commented by mr W last updated on 14/Jun/21 $${p}=\frac{\mathrm{1}\:\mathrm{334}\:\mathrm{961}}{\mathrm{2}\:\mathrm{320}\:\mathrm{196}\:\mathrm{159}\:\mathrm{531}} \\ $$ Commented by nitu last updated…
Question Number 12361 by Joel576 last updated on 20/Apr/17 $$\left(\sqrt{\mathrm{2}}\:+\sqrt{\mathrm{3}}\:+\mathrm{2}\:+\:\sqrt{\mathrm{5}}\right)\left(−\sqrt{\mathrm{2}}\:+\:\sqrt{\mathrm{3}}\:+\:\mathrm{2}\:−\:\sqrt{\mathrm{5}}\right)\left(\sqrt{\mathrm{10}}\:+\:\mathrm{2}\sqrt{\mathrm{3}}\right) \\ $$$$ \\ $$$$\mathrm{Can}\:\mathrm{you}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{without}\:\mathrm{solving}\:\mathrm{them}\:\mathrm{manually}? \\ $$ Answered by ajfour last updated on 20/Apr/17 $$\left({a}+{b}+{c}+{d}\right)\left({b}+{c}−{a}−{d}\right)\left({ad}+{bc}\right) \\…
Question Number 77897 by mathmax by abdo last updated on 11/Jan/20 $${calculateU}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} {k}\left(−\mathrm{1}\right)^{{k}} \:\:\:{and}\:{v}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} {k}^{\mathrm{2}} \left(−\mathrm{1}\right)^{{k}} \\ $$ Commented by abdomathmax…
Question Number 143429 by mnjuly1970 last updated on 14/Jun/21 $$\:\: \\ $$$$\:\:\:\:\:\:\:…….\:{nice}\:…..{integral}……. \\ $$$$\:\:\:\:{Evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\xi\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}−{t}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt}\:=? \\ $$ Answered by Dwaipayan Shikari…
Question Number 12359 by sin (x) last updated on 20/Apr/17 Answered by ajfour last updated on 20/Apr/17 $${for}\:{given}\:{range}\:{of}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}, \\ $$$$\left(\boldsymbol{{a}}^{\mathrm{4}} +\boldsymbol{{b}}^{\mathrm{3}} \right)_{\boldsymbol{{max}}} \:=\:\mathrm{1}−\frac{\mathrm{1}}{\mathrm{8}}=\:\frac{\mathrm{7}}{\mathrm{8}} \\ $$$$\left(\boldsymbol{{a}}^{\mathrm{4}}…
Question Number 143428 by mnjuly1970 last updated on 14/Jun/21 $$\:\:\:\:\: \\ $$$$…{Advanced}\:……{Mathematics}… \\ $$$$\:\:\:\:\:{Evaluate}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}\::=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{coth}\left(\pi{n}\right)}{{n}^{\mathrm{3}} }\:=? \\ $$ Answered by mindispower last…
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