Question Number 223241 by Tawa11 last updated on 19/Jul/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}\:−\:\mathrm{x}\right)\:\mathrm{ln}\left(\mathrm{1}\:+\:\mathrm{x}\right)}{\mathrm{x}}\:\mathrm{dx} \\ $$ Answered by altarboy123 last updated on 19/Jul/25 $$=−\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{4}} \\ $$ Commented…
Question Number 223242 by mnjuly1970 last updated on 19/Jul/25 Answered by Tawa11 last updated on 19/Jul/25 $$\mathrm{Sir},\:\mathrm{did}\:\mathrm{you}\:\mathrm{hear}\:\mathrm{from}\:\:\:\:\:\mathrm{Mathdave}??? \\ $$$$\mathrm{Or}\:\mathrm{you}\:\mathrm{know}\:\mathrm{where}\:\mathrm{he}\:\mathrm{is}? \\ $$ Commented by mnjuly1970 last…
Question Number 223254 by Tawa11 last updated on 19/Jul/25 $$\underset{\mathrm{n}\:\:=\:\:\mathrm{1}} {\overset{\infty} {\sum}}\left(−\:\:\mathrm{1}\right)^{\mathrm{n}\:\:+\:\:\mathrm{1}} \:\frac{\mathrm{H}_{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 223255 by profrey last updated on 19/Jul/25 $${Which}\:{of}\:{the}\:{following}\:{complex} \\ $$$${numbers}\:{is}\:{equivalent}\:{to}\:\frac{\mathrm{3}−\mathrm{5}{i}}{\mathrm{8}+\mathrm{2}{i}}?\left({Note}:\:{i}=\sqrt{\left.−\mathrm{1}\right)}\right. \\ $$$$\left.{A}\right)\frac{\mathrm{3}}{\mathrm{8}}−\frac{\mathrm{5}{i}}{\mathrm{2}} \\ $$$$ \\ $$$$\left.{B}\right)\frac{\mathrm{3}}{\mathrm{8}}+\frac{\mathrm{5}{i}}{\mathrm{2}} \\ $$$$\: \\ $$$$\left.{C}\right)\frac{\mathrm{7}}{\mathrm{34}}−\frac{\mathrm{23}{i}}{\mathrm{34}} \\ $$$$ \\…
Question Number 223267 by behi834171 last updated on 19/Jul/25 $$\boldsymbol{{r}},\boldsymbol{{s}},\boldsymbol{{t}}\:;\:\boldsymbol{{are}}\:\boldsymbol{{the}}\:\boldsymbol{{roots}}\:\boldsymbol{{of}}: \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{{x}}^{\mathrm{3}} +\mathrm{5}\boldsymbol{{x}}+\mathrm{1}=\mathrm{0} \\ $$$$\boldsymbol{{find}}: \\ $$$$\:\:\:\:\:\:\left(\boldsymbol{{r}}^{\mathrm{3}} −\mathrm{1}\right)\left(\boldsymbol{{s}}^{\mathrm{3}} −\mathrm{1}\right)\left(\boldsymbol{{t}}^{\mathrm{3}} −\mathrm{1}\right) \\ $$ Answered by gregori…
Question Number 223228 by fantastic last updated on 18/Jul/25 Commented by fantastic last updated on 18/Jul/25 $${Right}! \\ $$ Commented by mr W last updated…
Question Number 223213 by mr W last updated on 18/Jul/25 Commented by mr W last updated on 18/Jul/25 $${find}\:{the}\:{area}\:{of}\:{rectangle}\:{ABCD}. \\ $$ Answered by gregori last…
Question Number 223230 by hardmath last updated on 18/Jul/25 $$\mathrm{Maksimum}\:\left(\frac{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}}\right)\:=\:? \\ $$ Answered by fantastic last updated on 18/Jul/25 $${Let}\:{f}\left({x}\right)=\left(\frac{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\right) \\…
Question Number 223224 by wewji12 last updated on 18/Jul/25 $$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{k}}=\infty \\ $$$$\underset{\mathrm{p}\:\mathrm{prime}} {\sum}\:\frac{\mathrm{1}}{{p}}=\infty \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}….\right)−\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}+…\right)=?? \\ $$ Commented by Ghisom last updated on…
Question Number 223216 by Ari last updated on 18/Jul/25 Answered by som(math1967) last updated on 18/Jul/25 $${let}\:{alcohol}=\mathrm{4}{xl},\:{water}=\mathrm{3}{xl} \\ $$$$\:\therefore\:\frac{\mathrm{4}{x}}{\mathrm{3}{x}+\mathrm{7}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\Rightarrow\mathrm{16}{x}=\mathrm{9}{x}+\mathrm{21} \\ $$$$\Rightarrow\mathrm{7}{x}=\mathrm{21}\Rightarrow{x}=\mathrm{3} \\ $$$$\:{amount}\:{of}\:{alcohol}=\mathrm{4}×\mathrm{3}=\mathrm{12}{l}…