Question Number 185529 by Rupesh123 last updated on 23/Jan/23 Answered by Frix last updated on 23/Jan/23 $${x}=\frac{\mathrm{1}}{{a}}\wedge{y}=\frac{\mathrm{1}}{{b}}\wedge{z}=\frac{\mathrm{1}}{{c}}\:\Rightarrow \\ $$$$\left({x}+{y}+{z}\right)^{\mathrm{2}} ={x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \\ $$$$\mathrm{2}\left({xy}+{yz}+{zx}\right)=\mathrm{0}\:\Rightarrow \\…
Question Number 185522 by Mingma last updated on 23/Jan/23 Commented by Frix last updated on 23/Jan/23 $$\mathrm{This}\:\mathrm{only}\:\mathrm{requires} \\ $$$${r}=\frac{{D}}{\mathrm{2}\left({a}+{b}+{c}\right)} \\ $$$${R}=\frac{{abc}}{{D}} \\ $$$${D}=\sqrt{\left({a}+{b}+{c}\right)\left({b}+{c}−{a}\right)\left({a}+{c}−{b}\right)\left({a}+{b}−{c}\right)} \\ $$…
Question Number 185515 by HeferH last updated on 23/Jan/23 $$\:{At}\:{a}\:{party}\:{with}\:“{m}''\:{people},\:{a}\:{lady}\:{dances} \\ $$$$\:{with}\:{p}\:{gentlemen},\:{the}\:{second}\:{with}\:{p}\:+\:\mathrm{1},\: \\ $$$$\:{the}\:{third}\:{one}\:{with}\:{p}\:+\:\mathrm{2},\:{and}\:{so}\:{on}\:{until}\:{the} \\ $$$$\:{last}\:{one}\:{dances}\:{with}\:{all}\:{the}\:{gentlemen},\: \\ $$$$\:{find}\:{the}\:{number}\:{of}\:{ladies}\:{who}\:{attended}\:{the} \\ $$$$\:{party}\:{in}\:{terms}\:{of}\:“{m}''{and}\:“{p}''. \\ $$ Answered by manxsol…
Question Number 119979 by huotpat last updated on 28/Oct/20 Commented by huotpat last updated on 28/Oct/20 $${N}\:{when}\:{n}\rightarrow+\infty\:{is}\:{not}\:{x}\rightarrow+\infty \\ $$ Answered by mathmax by abdo last…
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Question Number 119939 by huotpat last updated on 28/Oct/20 Answered by bramlexs22 last updated on 28/Oct/20 $$\:\int\:\frac{\left(\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}\right)\:\mathrm{cos}\:{x}\:{dx}\:}{\mathrm{1}−\mathrm{2sin}\:{x}} \\ $$$$\:\left[\:{let}\:\mathrm{sin}\:{x}\:=\:{s}\:\right] \\ $$$$\int\:\frac{\left(\mathrm{1}−{s}^{\mathrm{2}} \right){ds}}{\mathrm{1}−\mathrm{2}{s}}\:=\:\int\:\frac{{s}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}{s}−\mathrm{1}}\:{ds} \\…
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Question Number 119921 by bramlexs22 last updated on 28/Oct/20 $${solving}\:{the}\:{following}\:{system}\:{of}\:{equations} \\ $$$$\begin{cases}{\frac{\mathrm{3}{x}−{y}}{{x}−\mathrm{3}{y}}={x}^{\mathrm{2}} }\\{\frac{\mathrm{3}{y}−{z}}{{y}−\mathrm{3}{z}}={y}^{\mathrm{2}} }\\{\frac{\mathrm{3}{z}−{x}}{{z}−\mathrm{3}{x}}={z}^{\mathrm{2}} }\end{cases} \\ $$ Answered by mindispower last updated on 28/Oct/20 $$\Rightarrow{x}=\frac{{z}^{\mathrm{3}}…
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Question Number 119894 by danielasebhofoh last updated on 27/Oct/20 Answered by mathmax by abdo last updated on 28/Oct/20 $$\:\:\mathrm{let}\:\mathrm{I}_{\mathrm{n}} =\int\:\frac{\mathrm{dx}}{\mathrm{x}\left(\mathrm{x}^{\mathrm{n}} −\mathrm{a}^{\mathrm{n}} \right)}\:\:\mathrm{if}\:\mathrm{a}\neq\mathrm{0}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{x}=\mathrm{at}\:\Rightarrow \\ $$$$\mathrm{I}_{\mathrm{n}} =\int\:\frac{\mathrm{adt}}{\mathrm{at}\left(\mathrm{a}^{\mathrm{n}}…