Question Number 69457 by mhmd last updated on 23/Sep/19 $${find}\:{value}\:{log}\mathrm{40}/\mathrm{9}\:\:+\mathrm{4}{log}\mathrm{5}\:\:+\mathrm{2}{log}\mathrm{6}\:\:? \\ $$ Answered by MJS last updated on 23/Sep/19 $$\mathrm{log}\:\frac{\mathrm{40}}{\mathrm{9}}\:+\mathrm{4log}\:\mathrm{5}\:+\mathrm{2log}\:\mathrm{6}\:= \\ $$$$=\mathrm{log}\:\mathrm{40}\:−\mathrm{log}\:\mathrm{9}\:+\mathrm{4log}\:\mathrm{5}\:+\mathrm{2log}\:\mathrm{2}\:+\mathrm{2log}\:\mathrm{3}= \\ $$$$=\mathrm{3log}\:\mathrm{2}\:+\mathrm{log}\:\mathrm{5}\:−\mathrm{2log}\:\mathrm{3}\:+\mathrm{4log}\:\mathrm{5}\:+\mathrm{2log}\:\mathrm{2}\:+\mathrm{2log}\:\mathrm{3}= \\…
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Question Number 134984 by Dwaipayan Shikari last updated on 09/Mar/21 $$\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{2}}+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} }+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{2}} }{\mathrm{2}^{\mathrm{3}} }+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}} }{\mathrm{2}^{\mathrm{4}} }+… \\ $$$$ \\ $$Find in a closed…
Question Number 134987 by 0731619177 last updated on 09/Mar/21 Answered by Olaf last updated on 09/Mar/21 $$\mathrm{I}_{\mathrm{2}} \left({k}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}\mathrm{sin}{x}\mathrm{cos}{x}}{\:\sqrt{\mathrm{1}−{k}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} {x}}}\:{dx} \\ $$$$\mathrm{I}_{\mathrm{2}} \left({k}\right)\:=\:−\frac{\mathrm{1}}{{k}^{\mathrm{2}}…
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Question Number 134981 by oooooooo last updated on 09/Mar/21 $$\left(\mathrm{a}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{b}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{c}}+\mathrm{1}\right)=\mathrm{2}\boldsymbol{\mathrm{abc}}\: \\ $$$$\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}}\:\varepsilon\:\mathrm{N} \\ $$ Answered by MJS_new last updated on 10/Mar/21 $$\mathrm{let}\:{a}\leqslant{b}\leqslant{c} \\ $$$$\left(\mathrm{1}\right)\:{c}=\left({a}+\mathrm{1}\right)\left({b}+\mathrm{1}\right) \\…
Question Number 134977 by 0731619177 last updated on 09/Mar/21 Answered by Ñï= last updated on 09/Mar/21 $${tanhx}=\frac{{x}}{\mathrm{1}+\frac{{x}^{\mathrm{2}} }{\mathrm{3}+\frac{{x}^{\mathrm{2}} }{\mathrm{5}+\frac{{x}^{\mathrm{2}} }{\mathrm{7}+…}}}} \\ $$$$\int_{{a}} ^{{b}} {tanhxdx}={ln}\left(\mathrm{cosh}\:{x}\right)\mid_{{a}} ^{{b}}…
Question Number 69436 by azizullah last updated on 23/Sep/19 Answered by $@ty@m123 last updated on 23/Sep/19 $$\left({x}+\mathrm{4}\right)=\mathrm{2}\left({x}−\mathrm{6}\right) \\ $$$${x}=\mathrm{16} \\ $$ Commented by azizullah last…
Question Number 3900 by Filup last updated on 24/Dec/15 $$\mathrm{I}\:\mathrm{asked}\:\mathrm{this}\:\mathrm{question}\:\mathrm{a}\:\mathrm{while}\:\mathrm{ago}, \\ $$$$\mathrm{but}\:\mathrm{I}\:\mathrm{forgot}\:\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{it}: \\ $$$$ \\ $$$${S}=\int_{\mathrm{0}} ^{\:{n}} \lfloor{x}\rfloor{dx} \\ $$ Answered by Yozzii last updated…