Question Number 74329 by Learner-123 last updated on 22/Nov/19 $${Solve}\:: \\ $$$${ax}+{by}={r} \\ $$$${bx}−{ay}={s} \\ $$ Commented by Learner-123 last updated on 22/Nov/19 $${any}\:{short}\:{method}\:{when}\:{a},{b},{r},{s}\:{are}\: \\…
Question Number 8785 by FilupSmith last updated on 27/Oct/16 Commented by FilupSmith last updated on 27/Oct/16 $${f}\left({x}\right)=\sqrt{{x}^{\mathrm{2}} −\lfloor{x}\rfloor} \\ $$$$\: \\ $$$${x}={N}+{c},\:\:\:\lfloor{x}\rfloor={N}\in\mathbb{Z} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{c}<\mathrm{1} \\…
Question Number 8781 by tawakalitu last updated on 27/Oct/16 $$\mathrm{Father}\:\mathrm{reduced}\:\mathrm{the}\:\mathrm{quantity}\:\mathrm{of}\:\mathrm{food}\:\mathrm{bought}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{family}\:\mathrm{by}\:\frac{\mathrm{25}}{\mathrm{2}}\%\:.\:\mathrm{When}\:\mathrm{he}\:\mathrm{found}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{cost}\:\mathrm{of}\:\mathrm{living}\:\mathrm{has}\:\mathrm{increased}\:\mathrm{by}\:\mathrm{15\%}.\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{increase}\:\mathrm{in}\:\mathrm{the}\:\mathrm{family}'\mathrm{s}\:\mathrm{food} \\ $$$$\mathrm{bill}\:\mathrm{now}\:? \\ $$ Terms of Service Privacy Policy…
Question Number 139842 by I want to learn more last updated on 01/May/21 Commented by MJS_new last updated on 01/May/21 $$\mathrm{no}\:\mathrm{real}\:\mathrm{solution} \\ $$ Answered by…
Question Number 139838 by EnterUsername last updated on 01/May/21 $$\mathrm{If}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} \:\mathrm{and}\:{z}_{\mathrm{3}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}-\mathrm{angled}\:\mathrm{isos}- \\ $$$$\mathrm{celes}\:\mathrm{triangle}\:\mathrm{described}\:\mathrm{in}\:\mathrm{counter}\:\mathrm{clock}\:\mathrm{sense}\:\mathrm{and} \\ $$$$\mathrm{right}\:\mathrm{angled}\:\mathrm{at}\:{z}_{\mathrm{3}} ,\:\mathrm{then}\:\left({z}_{\mathrm{1}} −{z}_{\mathrm{2}} \right)^{\mathrm{2}} \:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\: \\ $$$$\left(\mathrm{A}\right)\:\left({z}_{\mathrm{1}} −{z}_{\mathrm{3}} \right)\left({z}_{\mathrm{3}}…
Question Number 8750 by tawakalitu last updated on 25/Oct/16 $$\mathrm{wx}\:+\:\mathrm{2z}\:=\:\mathrm{3}\:\:\:…………\:\left(\mathrm{i}\right) \\ $$$$\mathrm{3x}\:−\:\mathrm{y}\:+\:\mathrm{4z}\:=\:\mathrm{4}\:\:\:………..\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{6x}\:+\:\mathrm{2wy}\:=\:−\:\mathrm{4}\:\:\:………..\:\left(\mathrm{iii}\right) \\ $$$$ \\ $$$$\mathrm{find}\:\:\mathrm{w},\:\mathrm{x},\:\mathrm{y},\:\mathrm{z} \\ $$ Commented by Rasheed Soomro last…
Question Number 139824 by mathsuji last updated on 01/May/21 $${Solve}\:{in}\:\mathbb{R}\:{the}\:{following}\:{equation}: \\ $$$$\mathrm{2}\centerdot\mathrm{3}^{{x}} +\mathrm{5}\centerdot\mathrm{4}^{{x}} =\mathrm{4}\centerdot\mathrm{5}^{{x}} +\mathrm{3}\centerdot\mathrm{2}^{{x}} \\ $$ Answered by MJS_new last updated on 02/May/21 $$\mathrm{obviously}\:{x}=\mathrm{0}\vee{x}=\mathrm{1}…
Question Number 139805 by mr W last updated on 01/May/21 $${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}…