Question Number 197475 by mnjuly1970 last updated on 19/Sep/23 $$ \\ $$$$\:\:\:\:\:\:{x}\:,\:{y}\:\in\:\mathbb{R}\:\:\:, \\ $$$$\:\:\:\:{x}^{\:\mathrm{2}} \:+\:{xy}\:=\:\mathrm{12} \\ $$$$\:\:\:\:\:{y}^{\:\mathrm{2}} \:+\:\mathrm{2}{xy}\:=\:\mathrm{7}\: \\ $$$$\:\:\:\:−−−−−\:\:\:{x}\:,\:{y}\:=? \\ $$ Answered by Sutrisno…
Question Number 197323 by Erico last updated on 13/Sep/23 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{x}}\:\:\:\mathrm{and}\:\mathrm{S}_{\mathrm{n}} \left(\alpha\right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left[\mathrm{f}\left(\mathrm{k}\pi+\frac{\pi}{\alpha}\right)+\mathrm{f}\left(\mathrm{k}\pi−\frac{\pi}{\alpha}\right)\right]\:\:\:\:\left(\alpha>\mathrm{1}\right) \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\underset{\mathrm{n}\rightarrow+\infty} {\:\mathrm{lim}}\:\mathrm{S}_{\mathrm{n}} \left(\alpha\right)=\mathrm{1}−\mathrm{f}\left(\frac{\pi}{\alpha}\right) \\ $$ Answered by witcher3 last updated on…
Question Number 197247 by Erico last updated on 11/Sep/23 $$\mathrm{calcul}\:\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{{ln}\left({cht}\right)}{{sh}\left({t}\right)}{dt} \\ $$ Answered by witcher3 last updated on 11/Sep/23 $$=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{ch}\left(\mathrm{t}\right)\right)\mathrm{sh}\left(\mathrm{t}\right)}{\mathrm{1}−\mathrm{ch}^{\mathrm{2}} \left(\mathrm{x}\right)}…
Question Number 196971 by dimentri last updated on 05/Sep/23 $$\:\:{solve}\:\begin{cases}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{9}{y}=\mathrm{1}}\\{\mathrm{3}{y}^{\mathrm{2}} −\mathrm{9}{x}=\mathrm{0}}\end{cases} \\ $$ Answered by Frix last updated on 05/Sep/23 $${y}=\frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{9}} \\ $$$${x}^{\mathrm{4}}…
Question Number 196880 by subheenoy last updated on 02/Sep/23 $$\mathrm{1}.\:{A}\:{container}\:{of}\:{milk}\:{is}\:\frac{\mathrm{4}}{\mathrm{5}}\:{full}.\:{When}\:\mathrm{10}{L}\:{of}\:{milk}\:{is}\:{poured}\:{into}\:{it}\:{the}\:{container}\:{becomes}\:\:\frac{\mathrm{9}}{\mathrm{10}}\:{full}.\:{What}\:{is}\:{the}\:{capacity}\:{of}\:{the}\:{container}? \\ $$ Answered by Frix last updated on 02/Sep/23 $$\frac{\mathrm{4}}{\mathrm{5}}{x}+\mathrm{10}=\frac{\mathrm{9}}{\mathrm{10}}{x} \\ $$$$\mathrm{10}=\left(\frac{\mathrm{9}}{\mathrm{10}}−\frac{\mathrm{4}}{\mathrm{5}}\right){x}=\left(\frac{\mathrm{9}−\mathrm{8}}{\mathrm{10}}\right){x}=\frac{\mathrm{1}}{\mathrm{10}}{x} \\ $$$${x}=\mathrm{100} \\…
Question Number 196638 by mr W last updated on 28/Aug/23 $${find}\:{the}\:{sum}\:{of}\:{the}\:{all}\:\mathrm{168}\:{prime} \\ $$$${numbers}\:{from}\:\mathrm{1}\:{to}\:\mathrm{1000}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{13245} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{52788} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{76127} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{86344} \\ $$ Commented by…
Question Number 196258 by York12 last updated on 21/Aug/23 $${If}\left({x}_{{m}} +{iy}_{{m}} \right)^{\mathrm{2}{n}+\mathrm{1}} =\mathrm{1}\:,\:{such}\:{that} \\ $$$${m}\in\left\{\mathrm{1},\mathrm{2},\mathrm{3},….,\mathrm{2}{n}\right\}\:\wedge\:{x}_{{m}} ,{y}_{{m}} \in\mathbb{R} \\ $$$${p}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{2020}} {\sum}}\left[\frac{\mathrm{1}−{x}_{{k}} +{iy}_{{k}} }{\mathrm{1}+{x}_{{k}} +{iy}_{{k}} }\right]\:,\:{Find}\:\left(\frac{{p}}{\mathrm{43}}\right)…
Question Number 196107 by maths_plus last updated on 18/Aug/23 $$ \\ $$$$\mathrm{help},\:\mathrm{please}\:! \\ $$$$\underset{{x}\:\rightarrow\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} {{lim}}\:\frac{{cos}\left(\frac{\boldsymbol{\pi}}{\mathrm{4}}\:−{x}\right)−{tan}\:{x}}{\mathrm{1}−{sin}\left(\frac{\boldsymbol{\pi}}{\mathrm{4}}+{x}\right)}\:=\:???\: \\ $$ Answered by MM42 last updated on 21/Aug/23 $${hop}\rightarrow{lim}_{{x}\rightarrow\frac{\pi}{\mathrm{4}}}…
Question Number 195560 by York12 last updated on 05/Aug/23 $$ \\ $$ Commented by mr W last updated on 05/Aug/23 $${why}\:{did}\:{you}\:{delete}\:{the}\:{question}\:{sir}? \\ $$ Answered by…
Question Number 195390 by mathlove last updated on 01/Aug/23 $${which}\:{prime}\:{number}\:{between} \\ $$$${the}\:\:\mathrm{20}\:\:{and}\:\:\:\:\mathrm{1000}\:\:\: \\ $$ Answered by BaliramKumar last updated on 01/Aug/23 $$\mathrm{1}\:\mathrm{to}\:\mathrm{1000}\:=\:\mathrm{168}\:\mathrm{prime}\:\mathrm{numbers} \\ $$$$\mathrm{1}\:\mathrm{to}\:\mathrm{20}\:=\:\mathrm{8}\:\mathrm{prime}\:\mathrm{numbers} \\…