Question Number 139805 by mr W last updated on 01/May/21 $${solve}\:{for}\:{x}\in\mathbb{R} \\ $$$$\boldsymbol{{x}}^{\boldsymbol{{x}}^{\boldsymbol{{n}}} } =\boldsymbol{{a}} \\ $$$${with}\:{n},\:{a}\in\mathbb{R}^{+} \\ $$$${find}\:{also}\:{the}\:{range}\:{of}\:\boldsymbol{{a}}\:{such}\:{that}\:{a} \\ $$$${solution}\:{exists}. \\ $$ Commented by…
Question Number 139800 by bramlexs22 last updated on 01/May/21 $$\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{6}}{\mathrm{21}}+\frac{\mathrm{11}}{\mathrm{147}}+\frac{\mathrm{16}}{\mathrm{1029}}+\frac{\mathrm{21}}{\mathrm{7203}}+\frac{\mathrm{26}}{\mathrm{50421}}+\ldots=? \\ $$ Answered by EDWIN88 last updated on 01/May/21 $$\mathrm{Jakob}\:\mathrm{Bernoulli}'\mathrm{s}\:\mathrm{sumation} \\ $$$$\frac{{a}}{{b}}+\frac{{a}+{c}}{{bd}}+\frac{{a}+\mathrm{2}{c}}{{bd}^{\mathrm{2}} }+\frac{{a}+\mathrm{3}{c}}{{bd}^{\mathrm{3}} }+\frac{{a}+\mathrm{4}{c}}{{bd}^{\mathrm{4}} }\:\ddot…
Question Number 74266 by smartsmith459@gmail.com last updated on 22/Nov/19 $${please}\:{kindly}\:{help}\:{me}\:{with}\:{the}\:{solutions}\:{to}\:{these}\:{question}?{very}\:{urgent}\:{please}\:\left(\mathrm{1}\right)\:{if}\:{dy}={x}^{\mathrm{3}} {dx}.\:{find}\:{the}\:{equation}\:{of}\:{y}\:{in}\:{terms}\:{of}\:{x} \\ $$$$\:{if}\:{the}\:{curve}\:{passes}\:{through}\:\left(\mathrm{1},\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\:{Given}\:{that}\:{the}\:{volume}\:{v}\left({t}\right)\:{of}\:{cell}\:{at}\:{a}\:{time}\:{t}\:{changes}\:{according}\:{to} \\ $$$$\frac{{dV}\left({t}\right)}{{dt}}=\:{sin}\:{t},\:{with}\:{v}\left({t}\right)=\mathrm{4}.\:{find}\:{v}\left({t}\right) \\ $$$$\left.\mathrm{3}\right)\:{Given}\:\frac{{dP}}{{dt}}\:+\:\mathrm{3}{P}\:=\:\mathrm{0}.\:{determine}\:{P}\:\left({t}\right)\: \\ $$$${if}\:{p}\left(\mathrm{0}\right)=\:\mathrm{4} \\ $$$$\left.\mathrm{4}\right)\:{Radium}\:{decomposes}\:{at}\:{a}\:{rate}\:{proportion}\:{to}\:{the}\:{amount}\: \\ $$$${present}.\:{if}\:{the}\:{half}−{life}\:{of}\:{the}\:{radium}\:{is}…
Question Number 8718 by www.matikzone.tk last updated on 24/Oct/16 $$\frac{\left({x}−\mathrm{5}\right)^{{x}^{\mathrm{2}} −\mathrm{11}×−\mathrm{26}} +\left({x}−\mathrm{5}\right)^{{x}^{\mathrm{2}} −\mathrm{171}×+\mathrm{26}} }{{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{203}}={x}\:.\: \\ $$$${fine}\:{x}. \\ $$$$ \\ $$ Commented by www.matikzone.tk last…
Question Number 8707 by Sopheak last updated on 22/Oct/16 $${Find}\:{an}\:{integer}\:{x}\:{that}\:{satisfies}\:{the}\:{equation}\: \\ $$$${x}^{\mathrm{5}} −\mathrm{101}{x}^{\mathrm{3}} −\mathrm{999}{x}^{\mathrm{2}} +\mathrm{100900}=\mathrm{0} \\ $$ Answered by Rasheed Soomro last updated on 23/Oct/16…
Question Number 139765 by mathlove last updated on 01/May/21 Commented by mathlove last updated on 01/May/21 $${what}\:{answer}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 139762 by mathdanisur last updated on 01/May/21 $${x};{y};{z}>\mathrm{0},\:\gamma\geqslant\mathrm{0},\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} +{xyz}=\mathrm{4} \\ $$$${proof}:\:\left({x}+{y}+{z}\right)^{\mathrm{3}} +\gamma\left({x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} \right)\geqslant\mathrm{27}+\mathrm{3}\gamma \\ $$ Answered by mindispower last…
Question Number 74213 by FCB last updated on 20/Nov/19 Commented by MJS last updated on 20/Nov/19 $$\mathrm{information}\:\mathrm{missing} \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{the}\:\mathrm{question}\:\mathrm{is}\:\mathrm{find}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{expression} \\ $$$$\mathrm{this}\:\mathrm{should}\:\mathrm{be}\:\mathrm{at}\:{a}={b}={c}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is}\:\frac{\mathrm{69}}{\mathrm{4}}=\mathrm{17}.\mathrm{25}…
Question Number 74209 by FCB last updated on 20/Nov/19 Answered by mind is power last updated on 20/Nov/19 $${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{48} \\ $$$${a}\geqslant{b}\geqslant{c} \\…
Question Number 139737 by mathsuji last updated on 30/Apr/21 $${Find}\:{the}\:{value}\:{of}\:{X}\:{such}\:{that}: \\ $$$$\mathrm{1}\centerdot\mathrm{5}\centerdot\mathrm{9}\centerdot\mathrm{13}\centerdot\mathrm{17}\centerdot…\centerdot\mathrm{2021}\equiv{X}\left({mod}\mathrm{1000}\right) \\ $$ Answered by mindispower last updated on 01/May/21 $${A}=\underset{{k}=\mathrm{0}} {\overset{\mathrm{505}} {\prod}}\left(\mathrm{1}+\mathrm{4}{k}\right)\equiv{X}\left[\mathrm{1000}\right] \\…